speed regulation/tracking of BLDC motor, regardless the presence of external disturbances and/or parameters variation. The first technique is. GAbased PID ...
Speed Control of High Performance Brushless DC Motor A Thesis Submitted to Faculty of Engineering at Helwan University In partial Fulfilment of the requirements for the Degree of Master of Science in System Automation and Engineering Management
By
Eng. Mohamed Abdelbar Shamseldin Ali Under Supervision of Prof. Abdel Ghany Mohamed Abdel Ghany Prof. Adel A. ELSamahy
Faculty of Engineering, Helwan University, Helwan Cairo, Egypt
2016
Speed Control of High Performance Brushless DC Motor A Thesis Submitted to Faculty of Engineering at Helwan University In partial Fulfilment of the requirements for the Degree of Master of Science in System Automation and Engineering Management
By
Eng. Mohamed Abdelbar Shamseldin Ali Exam Committee Prof. Mohamed Ahmed Moustafa Hassan
Professor, Faculty of Eng., Cairo University (External Examiner)
Prof. Abdel Ghany .M. Abdel Ghany
Professor, Faculty of Eng., Helwan University (Supervisor)
Prof. A. Halim Bassiuny
Professor Faculty of Eng., Helwan University (Internal Examiner)
Prof. Adel A. AlSamahy
Professor Faculty of Eng., Helwan University (Supervisor)
ACKNOWLEDGEMENT The author wishes to express his sincere gratitude and appreciation to the research supervisors, 1Prof. Dr. Abdel Ghany Mohamed Abdel Ghany – Helwan University for his continuous help during preparing this work.
2 Prof. Dr. Adel A. ELSamahy –Helwan University for his constructive guidance, and warm encouragement during preparing this work, without which the present study would not have been carried out.
Finally, I would like to thank my family and all my friends, for the support and encouragement they provided me.
Mohamed Abdelbar Shamseldin 2016
i
ABSTRACT This thesis proposes the design and implementation of four different advanced control techniques. The controller objective to achieve a good speed regulation/tracking of BLDC motor, regardless the presence of external disturbances and/or parameters variation. The first technique is GAbased PID controller, in which the genetic algorithm (GA) optimization technique is used to determine the proper PID controller parameters. In this thesis three different cost functions are tested during optimization process. Although, GA optimization technique improves the overall performance of the PID controller, but it has poor performance in case of sudden change in operating point and parameters variation. So, the second technique is a selftuning fuzzy PID control in which the PID controller parameters are continuously changing to satisfy the required performance. The main role of the fuzzy logic control adjusts the PID controller parameters online, according to the error and the change of error. The third technique is a model reference adaptive control (MRAC), where the desired performance is expressed in terms of a reference model. The MRAC is known with its fast response. On other hand, it suffers from high overshoot. This disadvantage can be alleviated using the fourth control technique. The fourth technique is a new hybrid control technique (MRAC with PID compensator), in which the controller action depends on both the MRAC and the PID compensator. In this technique, the fast response will be achieved without high overshoot. A complete simulation for the advanced control techniques has been studied. A hardware has been implemented to verify the theoretical study. The simulation as well as the experimental results are agreed well. Both simulation and experimental results clarify that the MRAC with PID compensator has the best performance compared to the different studied techniques.
 ii 
Contents ACKNOWLEDGEMENT ................................................................................... i ABSTRACT ......................................................................................................... ii 1. INTRODUCTION ......................................................................................  2 1.1 Background ............................................................................................  2 Typical BLDC Motor Applications..................................................  3 
1.1
1.1.1
Applications with Constant Loads ........................................  3 
1.1.2
Applications with Varying Loads .........................................  3 
1.2
Literature Review .............................................................................  4 
1.3
Thesis Objectives .............................................................................  6 
1.4
Thesis Outlines .................................................................................  6 
2. MATHEMATICAL MODEL OF BRUSHLESS DC MOTOR .............  9 2.1
Introduction ......................................................................................  9 
2.2
Construction of Brushless DC Motor ...............................................  9 
2.3
Brushless DC Motor Operation Method ........................................  11 
2.4
Mathematical Model ......................................................................  14 
2.4.1
Transfer Function Model.....................................................  15 
2.4.2
State Space Model ................................................................  20 
3. CONTROL TECHNIQUES ....................................................................  23 3.1
Introduction ....................................................................................  23 
3.2
GABased PID Controller ..............................................................  23 
3.2.1
First Cost Function...............................................................  26 
3.2.2
Second Cost Function...........................................................  27 
3.2.3
Third Cost Function .............................................................  28 
SelfTuning Fuzzy PID Controller .................................................  28 
3.3
3.3.1
Fuzzification..........................................................................  30 
3.3.2
Rule Base ...............................................................................  31 
3.3.3
Defuzzification ......................................................................  32 
3.4
Model Reference Adaptive Control ...............................................  32 
 iii 
Contents 3.5
MRAC with PID Compensator ......................................................  38 
4. SIMULATION RESULTS ......................................................................  41 4.1
Introduction ....................................................................................  41 
4.2
Open Loop Response Results .........................................................  41 
4.3
Closed Loop Response Results ......................................................  44 
4.3.1
GABased PID Control ........................................................  44 
4.3.2
SelfTuning Fuzzy PID Control ..........................................  48 
4.3.3
Model Reference Adaptive Control ....................................  50 
4.3.4
MRAC with PID Compensator ...........................................  52 
4.4
Control Techniques Performance Investigation .............................  54 
4.4.1
Speed Regulation at Sudden Load ......................................  54 
4.4.2
Speed Response at Parameters Variation ..........................  57 
4.4.2.1
Sudden Change in Rotor Inertia (J) ...............................  57 
4.4.2.2
Sudden Change in Phase Resistance (R) ........................  58 
4.4.2.3
Effect Changes of Both (R) and (J) .................................  60 
4.4.3
Speed Regulation at Sinusoidal Load .................................  63 
4.4.4
Speed Tracking .....................................................................  66 
4.4.4.1
Different Commands of Reference Speed ......................  66 
4.4.4.2
Trapezoidal Speed Tracking ...........................................  68 
5. LABORATORY SETUP AND EXPERIMENTAL RESULTS ...........  71 5.1
Introduction ....................................................................................  71 
5.2
Laboratory Setup ............................................................................  71 
5.3
Data Acquisition in MATLAB .......................................................  73 
5.4
System Identification......................................................................  74 
5.5
Open Loop Response Results .........................................................  75 
5.6
Closed Loop Response Results ......................................................  76 
5.6.1
GABased PID Control ........................................................  76 
5.6.2
SelfTuning Fuzzy PID Control ..........................................  79 
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Contents 5.6.3
Model Reference Adaptive Control ....................................  81 
5.6.4
MRAC with PID Compensator ...........................................  82 
5.7.
Control Techniques Performance Investigation .............................  83 
5.7.1.
Speed Regulation Test ..........................................................  83 
5.7.2.
Speed Tracking Test.............................................................  84 
6. CONCLUSIONS AND RECOMMENDATIONS .................................  87 6.1
Conclusions ....................................................................................  87 
6.2
Contributions ..................................................................................  88 
6.3
Future Work ...................................................................................  89 
References ..........................................................................................................91 Appendix A ........................................................................................................96 Appendix B ......................................................................................................103
v
List of Figures Figure 2.1: Brushless DC motor transverse section [1]..................................  11 Figure 2.2: Backemf's, phase currents and position sensor signals [1]. ........  12 Figure 2.3: BLDC motor cross section and phase energizing sequence [1]. ..  12 Figure 2.4: Simplified BLDC drive scheme [32]. ..........................................  13 Figure 2.5: Equivalent circuit of the BLDC motor [1]. ..................................  16 Figure 2.6: Brushless DC Motor Schematic Diagram [39]. ...........................  17 Figure 2.7: Simplified equivalent circuit of the BLDC motor [1]. .................  17 Figure 3.1: Finding plant parameters K, TD and T1 [44]..................................  24 Figure 3.2: The structure of GA tuning system for (CF1)..............................  26 Figure 3.3: The structure of GA tuning system for (CF2) and (CF3). ...........  27 Figure 3.4: Structure of selftuning PID fuzzy controller [51].......................  29 Figure 3.5: Fuzzy logic control structure [23]................................................  30 Figure 3.6: Memberships function of inputs (e, ∆e).......................................  30 Figure 3.7: Memberships functions of outputs (Kp1, Ki1 and Kd1). .............  31 Figure 3.8: A schematic diagram of a general MRAC controller [53]. ..........  33 Figure 3.9: A general linear controller with two degrees of freedom. ...........  34 Figure 3.10: Block diagram of MRAC with PID compensator. .....................  39 Figure 4.1: Simulink diagram of the BLDC motor drive system. ..................  42 Figure 4.2: Open loop response of BLDC motor at sudden load. ..................  43 Figure 4.3: The open loop response of phase current.....................................  43 Figure 4.4: The open loop response of electromagnetic torque. ....................  44 Figure 4.5: Simulink diagram of whole drive system with PID controller. ...  45 Figure 4.6: Speed response of each PID controller. .......................................  46 Figure 4.7: The controller output of each PID controller. ..............................  47 Figure 4.8: The DC supply current of each PID controller. ...........................  48 Figure 4.9: Simulink diagram of selftuning fuzzy PID control. ...................  49 Figure 4.10: The speed response of selftuning fuzzy PID controller. ...........  49 Figure 4.11: The selftuning fuzzy PID controller output. .............................  50 Figure 4.12: Simulink diagram of BLDC motor with MRAC. ......................  51 Figure 4.13: Response of MRAC at different adaptation gains. ....................  51 Figure 4.14: MRAC output at different adaptation gains. ..............................  52 Figure 4.15: Simulink diagram of MRAC with PID compensator.................  53 Figure 4.16: Response of MRAC with PID compensator at different adaptation gains. ..............................................................................................................  53 Figure 4.17: Output of MRAC with PID compensator at different adaptation gains. ..............................................................................................................  54 
 vi 
List of Figures Figure 4.18: Speed response of control techniques at sudden load. ...............  55 Figure 4.19: Controller output of control techniques at sudden load. ............  56 Figure 4.20: DC supply current of control techniques at sudden load. ..........  56 Figure 4.21: Response of control techniques at sudden change in (J)............  57 Figure 4.22: Output of control techniques at sudden change in (J). ...............  58 Figure 4.23: Response of control techniques at sudden change in (R). .........  59 Figure 4.24: Output of control techniques at sudden change in (R). ..............  60 Figure 4.25: Response of control techniques at change (R) and (J) simultaneously................................................................................................  61 Figure 4.26: Control techniques output at change (R) and (J) simultaneously…………………………………………………………………………………………… 62 Figure 4.27: DC supply current of control techniques at change (R) and (J) simultaneously................................................................................................  62 Figure 4.28: Sinusoidal load torque varies between 0% and 50% of rated torque.. ........................................................................................................................  63 Figure 4.29: Speed response of control techniques at sinusoidal load. ..........  64 Figure 4.30: Output of control techniques at sinusoidal load.........................  65 Figure 4.31: DC supply current of control technique at sinusoidal load. .......  65 Figure 4.32: Response of control techniques at different commands of speed…... ................................................................................................................. …….. 66 Figure 4.33: Output of control techniques at different commands of speed... 67 Figure 4.34: DC supply current of control techniques at different commands of speed...............................................................................................................  67 Figure 4.35: Response of control techniques at trapezoidal speed tracking...  68 Figure 4.36: Output of control techniques at trapezoidal speed tracking. ......  69 Figure 4.37: DC supply current of control techniques at trapezoidal speed tracking. ..........................................................................................................  69 Figure 5.1: Brushless DC motor drive system [27]. .......................................  71 Figure 5.2: Brushless DC motor experimental setup. ....................................  72 Figure 5.3: Data Acquisition Toolbox............................................................  73 Figure 5.4: System Identification Toolbox.....................................................  74 Figure 5.5: Open loop response of identified model and real system. ...........  75 Figure 5.6: The BLDC motor drive system with GA tuning system..............  76 Figure 5.7: Response the sets of PID controller parameters applied on identified model. .............................................................................................................  77 Figure 5.8: Response the sets of PID controller parameters applied on the real system. ............................................................................................................  78 
 vii 
List of Figures Figure 5.9: Simulink diagram of practical selftuning fuzzy PID controller.  80 Figure 5.10: Response of selftuning fuzzy PID controller practically. .........  80 Figure 5.11: Response of MRAC at different adaptation gains practically. ..  81 Figure 5.12: Response of modified MRAC at different adaptation gains practically. ......................................................................................................  82 Figure 5.13: Response of control techniques at speed regulation practically…… ........................................................................................................................  83 Figure 5.14: MRAC with other techniques at different commands of speed.  85 Figure 5.15: Modified MRAC with other techniques at different commands of speed...............................................................................................................  85 .
 viii 
List of Tables Table 2.1: Switching sequence [1]. ................................................................  13 Table 3.1: Openloop Ziegler–Nichols settings [44]. .....................................  24 Table 3.2: The Rule base of 𝐾𝑝1. .................................................................  31 Table 3.3: The Rule base of 𝐾𝑖1. ..................................................................  31 Table 3.4: The Rule base of 𝐾𝑑1. .................................................................  32 Table 4.1: BLDC Motor Parameters. .............................................................  41 Table 4.2: Values of PID controller gains. .....................................................  45 Table 4.3: The performance of four sets of PID controller parameters..........  46 Table 4.4: The performance of each control technique. .................................  55 Table 4.5: The performance of each control technique at change R, J. .........  61 Table 4.6: The speed deviation of each control technique. ............................  64 Table 5.1: Values of PID controller gains. .....................................................  77 Table 5.2: Performance of each set using identified model. ..........................  78 Table 5.3: Performance of each set using real system. ..................................  79 Table 5.4: Comparison between control techniques. .....................................  84 
 ix 
Nomenclature 𝐴0 :
Calibration gain.
𝐴𝑚 and 𝐵𝑚 :
Polynomials depend on the reference model.
𝐵𝑣 :
The friction constant.
𝐾𝑃0 :
Initial proportional gain (constant value).
𝐾𝑑0 :
Initial derivative gain (constant value).
𝐾𝑑1 :
Derivative modification coefficient.
𝐾𝑒 :
The line backemf constant.
𝐾𝑖0 :
Initial integral gain (constant value).
𝐾𝑖1 :
Integral modification coefficient.
𝐾𝑝 , 𝐾𝑖 and 𝑘𝑑 :
Proportional, Integral and Differential gains.
𝐾𝑝1 :
Proportional modification coefficient.
𝐾𝑝2 , 𝐾𝑖2 and 𝐾𝑑2 :
The new gains of PID controller.
𝐾𝑡 :
The line torque constant.
𝐿𝑎 :
Equivalent line inductance of winding.
𝑀𝑝 :
Maximum overshoot.
𝑀𝑝𝑑 :
The desired maximum.
𝑇𝐿 :
The load torque.
𝑇𝑒 :
The electrical torque.
𝑈𝑑 :
DC bus voltage.
𝑎1 , 𝑎2 , 𝑎3 , 𝑏:
BLDC motor transfer function coefficient.
𝑎𝑚1 , 𝑎𝑚2 , 𝑎𝑚3 , 𝑏𝑚 :
The model reference transfer function coefficient.
𝑐1 , 𝑐2 , 𝑐3 , 𝑐4 :
Weighting factors.
𝑒𝑎 , 𝑒𝑏 , 𝑒𝑐 :
The phase backemf’s.
𝑒𝑎𝑏 , 𝑒𝑏𝑐 , 𝑒𝑐𝑎 :
The line backemf’s.
𝑒𝑠𝑠 :
Steady state error.
𝑒𝑠𝑠𝑑 :
The desired steady state error.
x
Nomenclature 𝑖𝑎 , 𝑖𝑏 , 𝑖𝑐 :
The phase current.
𝑟𝑎 :
Line resistance of winding.
𝑡𝑒 :
The electromagnetic time constant.
𝑡𝑚 :
The mechanical time constant.
𝑡𝑟 :
Rise time.
𝑡𝑟𝑑 :
The desired rise time.
𝑡𝑠 :
Settling time.
𝑢𝑐 (𝑡):
The desired speed of BLDC motor.
𝑣𝑎𝑏 , 𝑣𝑏𝑐 , 𝑣𝑐𝑎 :
The linetoline voltages.
𝑦𝑚 (𝑡):
The output of model reference.
𝜃𝑒 :
The electrical angle.
𝜃𝑚 :
The rotor angle.
𝜔𝑚 :
Rotor speed.
𝜔𝑛 :
Natural frequency.
𝜉:
Damping ratio
∆𝑒:
The change of error.
A and B:
Polynomials depend on the BLDC motor.
ACO:
Ant colony optimization.
CF1:
First cost function.
CF2:
Second cost function.
CF3:
Third cost function.
E:
The error between the output speed of the BLDC motor and the reference model output.
e:
The error between the reference input and the actual output.
F:
Fitness values.
GA:
Genetic Algorithm.
j:
Loss function.
K, TD and T1:
ZieglerNichols parameters.
L:
Large.
 xi 
Nomenclature M:
Medium.
NB:
Negative Big.
NM:
Negative Medium.
NS:
Negative Small.
PB:
Positive Big.
PID:
ProportionalIntegralDerivative.
PM:
Positive Medium.
PS:
Positive Small.
PSO:
Particle swarm optimization.
Q:
The population matrix.
S:
Laplace transform coefficient.
S:
Small.
SM:
Small Medium.
Z, T and X :
Controller polynomials.
Z.N:
Ziegler. Nichols.
ZE:
Zero.
𝐽:
The rotor inertia.
𝐿:
The phase inductance.
𝑃:
The number of pole pairs.
𝑅:
The phase resistance.
𝑖∶
Line current.
𝑢(𝑡):
The output of controller.
𝑣(𝑡) :
The process disturbance.
𝑦(𝑡):
The output speed of BLDC motor.
𝛾 (𝐺𝑎𝑚𝑚𝑎):
Adaptation gain.
𝜃:
The controller parameters.
.
 xii 
Chapter (1)
Introduction
vcx
Chapter One INTRODUCTION
1
Chapter (1)
Introduction
Chapter (1) INTRODUCTION 1.1 Background Many industrial, commercial, and domestic applications require variable speed motor drives [1]. Traditionally, DC motors have dominated this application area. Although the DC motors are more expensive than the rival induction motors, the control principles and the power inverter required are somewhat simpler in dc brushed drives because, generally, armature current is approximately proportional to torque and armature voltage is approximately proportional to speed [2],[3]. However, the main disadvantages are routine maintenance of commutators, frequent periodic replacement of brushes and high initial cost. Also, DC motors cannot be used in clean or explosive environment [4]. Squirrel cage induction motor is alternative to the conventional DC motors. It offers the robustness with low cost. However, its disadvantages have poor starting torque and low power factor [5]. In addition, neither conventional DC motors nor induction motors can be used for highspeed application. The alternative to both conventional DC motor and induction motor is the brushless DC motor, which can be considered the most dominant electric motor for these applications [6]. Brushless DC (BLDC) motors are a type of permanent magnet synchronous motors. They are driven by DC voltage, but current commutation is achieved by solidstate switches. The commutation instant is determined by the rotor position which is detected either by position sensors or by sensorless techniques [7]. BLDC motors have many advantages compared to other electric motors such as [1]:
2
Chapter (1)
Introduction
Long operating life.
Reduced Maintenance (no brushes).
High dynamic response.
High efficiency.
High speed range.
High Torque –weight ratio.
Better speed / torque characteristics.
Much smaller rotor inertia (No rotor windings or iron core).
1.1 Typical BLDC Motor Applications It is possible to use the BLDC motor in many applications such as steel rolling mills, electric trains, electric automotive, aviation and robotics [8]. We can categorize the BLDC motor applications according to the type of load such as [9]: Constant loads. Varying loads.
1.1.1 Applications with Constant Loads These are the types of applications where a variable speed is more important than keeping the accuracy of the speed at a set speed. In these types of applications, the load is directly coupled to the motor shaft. For example, fans, pumps and blowers come under these types of applications. These applications demand lowcost controllers, mostly operating in open loop [10], [11], [12].
1.1.2 Applications with Varying Loads These are the types of applications where the load on the motor varies over a wide speed range. These applications may demand highspeed control accuracy and good dynamic responses. In home appliances, washers, dryers and compressors are good examples. Also, In Automotive,
3
Chapter (1)
Introduction
fuel pump control, electronic steering control, engine control and electric vehicle control. Moreover, in aerospace, there are a number of applications, like centrifuges, pumps, robotic arm controls, gyroscope controls and so on. These applications may use speed feedback devices and may run in closed loop. These applications use advanced control algorithms, thus complicating the controller. Also, this increases the price of the complete system [13].
1.2 Literature Review The need for high performance variable speed motor drive system is very important in many of industrial applications such as steel rolling mills, robotics, electric automotive, electric trains and aviation. In such applications the motor is exposed to different types of external disturbances and parameters variation. So, resorting to advanced control techniques is essential to achieve high performance drive system. The PID controller is applied in various fields in engineering owing to its simplicity, robustness, reliability and easy tuning parameters [14]. The limitations of conventional PID control divide into two problems. The first problem is parameters selection where some of methods cannot reach the proper PID controller parameters such as trial and error and ZieglerNichols rule. It can be realized that using different types of optimization techniques. Genetic tuned PID controller based speed control of DC motor drive has been introduced in [15]. Optimal PID control of a brushless DC motor using PSO and BF techniques has been presented in [16]. Optimal tuning of PID controller for a linear brushless DC motor using particle swarm optimization technique has been discussed in [17]. Practical implementation of GAbased PID controller for brushless DC motor has been explained in [18]. Comparative analysis of tuning a PID
4
Chapter (1)
Introduction
controller using intelligent methods has been demonstrated in [19]. Optimization of PID controller for brushless DC motor by using bioinspired algorithms has been presented in [20]. The second problem of conventional PID control is the fixed parameters where it not suitable for all operating conditions and it cannot deal with high external disturbances and parameters variation. So, this problem can be alleviated by implementing advanced control techniques such as adaptive control, variable structure control, fuzzy control and neural network. Comparison of fuzzy PID controller with conventional PID controller in controlling the Speed of a brushless DC motor has been investigated in [21]. Design of fuzzy PID controller for brushless DC Motor has been discussed in [22]. Fuzzy logic based sensorless control of threephase brushless DC motor using virtual instrumentation has been implemented in [23]. Performance analysis of fuzzy logic based speed control of DC motor has been introduced in [24] . Design of hybrid fuzzyPI controller for speed control of brushless DC motor has been explained in [25]. Design Fuzzy Self Tuning of PID Controller for ChopperFed DC Motor Drive has been illustrated in [26]. Robust model reference adaptive control for a second order system has been designed in [27] where the controller parameters are adjusted automatically to give the desired results. Study the effect of adaptation gain in model reference adaptive controlled second order system has been demonstrated in [28]. A Modified model reference adaptive controller for brushless DC motor has been implemented in [29]. In [30], designing of a model reference adaptive control for a second order system using the MIT rule. The implementation of MRAC improved by fuzzy system to choosing adaptation gain for servo system has been introduced in [31]. Direct and indirect model reference adaptive control has been demonstrated in [32].
5
Chapter (1)
Introduction
1.3 Thesis Objectives According to the previous literature review this thesis seeks to design and implementation advanced control techniques, for high performance BLDC motor drive system. The controller objective to achieve a good speed regulation/tracking of BLDC motor, regardless the presence of external disturbances and/or parameters variation. In this thesis four different advanced control techniques are implemented for this purpose. The first technique is the GAbased PID controller where the GA optimization technique is used to find the proper PID controller parameters based on three different cost functions. The second technique is the selftuning fuzzy PID controller, where the PID controller parameters are tuned online according to the error and the change of error. The adaptive control is one of the widely used control strategies to design advanced control systems for better performance and accuracy. So, the third control technique is a model reference adaptive control (MRAC), where the desired performance is expressed in terms of a reference model. The fourth technique is MRAC with PID compensator, which is considered a new hybrid control technique, where the control action depends on both the output of MRAC and the PID compensator.
1.4 Thesis Outlines This thesis is composed of Six Chapters arranged as follows:
● ●
●
Chapter one presents an introduction. Chapter Two demonstrates the principal and operation of brushless dc motor. Also, it discusses the mathematical model of BLDC motor in transfer function and state space form. Chapter Three discusses the design of different control techniques such as the GAbased PID controller, selftuning fuzzy PID
6
Chapter (1)
Introduction
controller, model reference adaptive control and MRAC with PID compensator.
●
●
● ●
Chapter Four shows the simulation results of BLDC motor drive system using different control schemes. The effectiveness of each control technique is investigated by carrying out several tests such as sudden load, sinusoidal load and parameters variation. Chapter Five presents the laboratory setup of BLDC motor drive system. The validity and effectiveness of each control technique is tested experimentally. The experimental results will be shown and discussed in this chapter. Chapter Six draws the conclusions of the research work presented in this thesis in addition to some recommendations for future work. Finally, a list of references and some appendices in addition to an Arabic summary of the thesis are included.
7
Chapter (2)
Mathematical Model of Brushless DC Motor
Chapter Two MATHEMATICAL MODEL OF BRUSHLESS DC MOTOR
8
Chapter (2)
Mathematical Model of Brushless DC Motor
Chapter (2) MATHEMATICAL MODEL OF BRUSHLESS DC MOTOR 2.1 Introduction The mathematical model of the brushless DC (BLDC) motor is essential for analysis and study the behavior of the motor. The structure characteristics and working modes of the BLDC motor should be considered when we are building its model [2]. The BLDC motor generally consists of three parts: the motor structure, the power driving circuit and the position sensor [33]. This chapter discusses the construction and driving mode of BLDC motors. Moreover, the common mathematical models, which mainly include differential equation model, transfer function model, and statespace model are presented.
2.2 Construction of Brushless DC Motor The main design principle of a BLDC motor is to remove the mechanical commutator which needs to periodic maintenance and replacing it with an electrical switch circuit [34]. In traditional DC motors, the brushes are used for commutation, making the directions of the main magnetic field and the armature magnetic field perpendicular to each other when the motor is running [35]. The BLDC motors have several similarities to AC induction motors and brushed DC motors in terms of construction and working principles respectively. Like all other motors, BLDC motors have a rotor and a stator. The stator is similar to an induction AC motor, the BLDC motor stator is made out of laminated steel stacked up to carry the windings. Windings in a stator can be arranged in two patterns a star pattern (Y) or delta pattern (∆). The major difference between the two patterns is that the Y pattern
9
Chapter (2)
Mathematical Model of Brushless DC Motor
gives high torque at low RPM and the ∆ pattern gives low torque at low RPM [36]. This is because in the ∆ configuration, half of the voltage is applied across the winding that is not driven. The rotor of a typical BLDC motor is made out of permanent magnets. Depending upon the application requirements, the number of poles in the rotor may change. Increasing the number of poles will give better torque [17]. There are two main types of BLDC motors: trapezoidal type and sinusoidal type. In trapezoidal motor the backemf induced in the stator windings has a trapezoidal shape and its phases must be supplied with quasisquare currents for ripplefree torque operation [37]. The sinusoidal motor on the other hand has a sinusoidally shape backemf and require sinusoidal phase currents for ripplefree torque operation. The shape of backemf is determined by the shape of the rotor magnets and the stator winding distribution. The sinusoidal motor need high resolution position sensor because the rotor position must be known at every time instant for optimal operation. It also requires more complex software and hardware [38]. The trapezoidal motor is a more attractive alternative for most industrial applications due to its simplicity, lower price and higher efficiency [1]. This type of motor also offers good compromise between precise control and the number of power electronic devices needed to control the stator currents [39]. The remaining part of this chapter discusses trapezoidal BLDC motor only. Figure 2.1 shows a transverse section of BLDC motor. Position detection is usually implemented using three Halleffect sensors that detects the presence of small magnets that are attached to the BLDC motor shaft [23].
 10 
Chapter (2)
Mathematical Model of Brushless DC Motor
Figure 2.1: Brushless DC motor transverse section [1].
2.3 Brushless DC Motor Operation Method The three phase BLDC motor is operated in a twophaseson fashion. The two phases that produce the highest torque are energized while the third phase is off. Which two phases are energized depend on the rotor position. The signals from the position sensors produce a three digit number (H1, H2, H3) that changes every 60⁰(electrical degrees) as shown in Figure 2.2 [39], [40]. Figure 2.3 shows a cross section of threephase starconnected motor along with its phase energizing sequence [25]. Each interval starts with the rotor and the stator field lines 120⁰ apart and ends when they are 60⁰ apart. Maximum torque is reached when the field lines are perpendicular [41]. Current commutation is done by a sixstep inverter as shown in a simplified form in Figure 2.4. The switches are shown as bipolar junction transistor but MOSFET switches are more common. Table 2.1 shows switching sequence, the current direction and the position sensor signals.  11 
Chapter (2)
Mathematical Model of Brushless DC Motor
Figure 2.2: Backemf's, phase currents and position sensor signals [1].
Figure 2.3: BLDC motor cross section and phase energizing sequence [1].
 12 
Chapter (2)
Mathematical Model of Brushless DC Motor
Figure 2.4: Simplified BLDC drive scheme [39].
Table 2.1: Switching sequence [1].
Switching Interval
Position Sensor
Sequence number
Phase Current
Switch Closed
H1 H2 H3
A
B
C
0o – 60o
0
1
0
0
Q1  Q6
+

off
60o – 120o
1
1
1
0
Q1 – Q2
+
off

120o – 180o
2
0
1
0
Q3 – Q2
off
+

180o – 240o
3
0
1
1
Q3 – Q4

+
off
240o – 300o
4
0
0
1
Q5 – Q4

off
+
300o – 360o
5
1
0
1
Q5 – Q6
off

+
 13 
Chapter (2)
Mathematical Model of Brushless DC Motor
2.4 Mathematical Model The model equations of a BLDC motor are composed of a voltage equation, a torque equation and a motion equation. The stator of a general BLDC motor has three windings like an induction motor [1]. Equations (2.1) through (2.9) represents the dynamical model of BLDC motor. These equations are based on the following [42]:
The stator has a Yconnected concentrated fullpitch winding.
The inner rotor has a nonsalient pole structure.
Three hall sensors are placed symmetrically at 120o interval.
𝑑 (𝑖 − 𝑖𝑏 ) + 𝑒𝑎 − 𝑒𝑏 𝑑𝑡 𝑎 𝑑 𝑣𝑏𝑐 = 𝑅(𝑖𝑏 − 𝑖𝑐 ) + (𝐿 − 𝑀) (𝑖𝑏 − 𝑖𝑐 ) + 𝑒𝑏 − 𝑒𝑐 𝑑𝑡 𝑑 𝑣𝑐𝑎 = 𝑅(𝑖𝑐 − 𝑖𝑎 ) + (𝐿 − 𝑀) (𝑖𝑐 − 𝑖𝑎 ) + 𝑒𝑐 − 𝑒𝑎 𝑑𝑡 𝑑𝑤𝑚 𝑇𝑒 = 𝐽 + 𝐵𝑣 𝑤𝑚 + 𝑇𝐿 𝑑𝑡 𝐾𝑒 𝑒𝑎 = 𝑤 𝐹(𝜃𝑒 ) 2 𝑚 𝐾𝑒 2𝜋 𝑒𝑏 = 𝑤𝑚 𝐹(𝜃𝑒 − ) 2 3 Ke 4π ec = wm F(θe − ) 2 3 𝐾𝑡 2𝜋 4𝜋 𝑇𝑒 = [𝐹(𝜃𝑒 )𝑖𝑎 + 𝐹 (𝜃𝑒 − ) 𝑖𝑏 + 𝐹 (𝜃𝑒 − ) 𝑖𝑐 ] 2 3 3 𝑣𝑎𝑏 = 𝑅(𝑖𝑎 − 𝑖𝑏 ) + (𝐿 − 𝑀)
1
𝐹(𝜃𝑒 ) =
0 ≤ 𝜃𝑒 ≤
6 2𝜋 1 − (𝜃𝑒 − ) 𝜋 3 6 5𝜋 −1 + (𝜃𝑒 − ) 𝜋 3 {
 14 
(2.2) (2.3) (2.4) (2.5) (2.6) (2.7) (2.8)
2𝜋 3
2𝜋 ≤ 𝜃𝑒 ≤ 𝜋 3 5𝜋 𝜋 ≤ 𝜃𝑒 ≤ 3 5𝜋 ≤ 𝜃𝑒 ≤ 2𝜋 3 }
−1
(2.1)
(2.9)
Chapter (2)
Mathematical Model of Brushless DC Motor
where: 𝐵𝑣 :
the friction constant.
𝐾𝑒 :
the line backemf constant.
𝐾𝑡 :
the line torque constant.
𝑇𝐿 :
the load torque.
𝑇𝑒 :
the electrical torque.
𝑒𝑎 , 𝑒𝑏 , 𝑒𝑐 :
the phase backemf’s.
𝑖𝑎 , 𝑖𝑏 , 𝑖𝑐 :
the phase current.
𝑣𝑎𝑏 , 𝑣𝑏𝑐 , 𝑣𝑐𝑎 : the linetoline voltages. 𝑃
𝜃𝑒 :
the electrical angle (𝜃𝑒 = 2 𝜃𝑚 ).
𝜃𝑚 :
the rotor angle.
𝜔𝑚 :
rotor speed.
𝐽:
the rotor inertia.
𝐿:
the phase inductance.
𝑃:
the number of pole pairs.
𝑅:
the phase resistance. Two mathematical models will be presented in this section based on
these differential equations. The first is transfer function model and the second is state space model.
2.4.1 Transfer Function Model Transfer functions are usually used to study the systems such as singleinput singleoutput filters, typically within the fields of signal processing, communication theory, and control theory [43]. The term is often used exclusively to refer to linear, timeinvariant systems (LTI). Most real systems have nonlinear input/output characteristics, but many systems, when operated within nominal parameters its behavior will near enough to linear that LTI system theory is an acceptable representation of the input/output behavior [44].  15 
Chapter (2)
Mathematical Model of Brushless DC Motor
To simplify the proposed transfer function model of BLDC motor the following assumptions are made [1]:
Neglect the core saturation, as well as the eddy current losses and the hysteresis losses.
Neglect the armature reaction, and the distribution of airgap magnetic field is thought to be a trapezoidal wave with a flattop width of 120 0 electrical angle.
Neglect the cogging effect and suppose the conductors are distributed continuously and evenly on the surface of the armature.
Power switches and flywheel diodes of the inverter circuit have ideal switch features. Implementing such assumption leads to the following linearized
model. Figure 2.5 illustrates the threephase BLDC motor is controlled by the fullbridge driving in the two phase conduction mode [1].
Figure 2.5: Equivalent circuit of the BLDC motor [1].
 16 
Chapter (2)
Mathematical Model of Brushless DC Motor
The mechanisms of backEMF and electromagnetic torque are all the same with those of the traditional brushed DC motor, thus similar analysis methods can be adopted as displayed in Figure 2.6 [].
Figure 2.6: Brushless DC Motor Schematic Diagram [20].
At any time the two phases are excited either AB or BC or CA. the simplified equivalent circuit will be as Figure 2.7.
Figure 2.7: Simplified equivalent circuit of the BLDC motor [1].
𝑖𝑎 = −𝑖𝑏 = 𝑖
(2.10)
𝑑𝑖𝑎 𝑑𝑖𝑏 𝑑𝑖 =− = 𝑑𝑡 𝑑𝑡 𝑑𝑡
(2.11)
𝑣𝑎𝑏 = 2𝑅𝑖 + 2(𝐿 − 𝑀)
𝑑𝑖 + (𝑒𝑎 − 𝑒𝑏 ) 𝑑𝑡
 17 
(2.12)
Chapter (2)
Mathematical Model of Brushless DC Motor ∵ 𝑒𝑏 = −𝑒𝑎
𝑣𝑎𝑏 = 𝑈𝑑 = 2𝑅𝑖 + 2(𝐿 − 𝑀)
𝑑𝑖 + 2𝑒𝑎 𝑑𝑡
𝑑𝑖 + 𝐾𝑒 𝜔𝑚 𝑑𝑡
(2.14)
𝑑𝜔𝑚 + 𝐵𝑣 𝜔𝑚 𝑑𝑡
(2.15)
𝑈𝑑 = 𝑟𝑎 𝑖 + 𝐿𝑎 𝐾𝑡 𝑖 − 𝑇𝐿 = 𝐽
(2.13)
Assume 𝑇𝐿 = 0 . 𝑖=
𝐽 𝑑𝜔𝑚 𝐵𝑣 + 𝜔𝑚 𝐾𝑡 𝑑𝑡 𝐾𝑡
(2.16)
Substituting (2.16) into (2.14) 𝐽 𝑑𝜔𝑚 𝐵𝑣 𝑑 𝐽 𝑑𝜔𝑚 𝐵𝑣 𝑈𝑑 = 𝑟𝑎 ( + 𝜔𝑚 ) + 𝐿𝑎 ( + 𝜔𝑚 ) + 𝐾𝑒 𝜔𝑚 𝐾𝑡 𝑑𝑡 𝐾𝑡 𝑑𝑡 𝐾𝑡 𝑑𝑡 𝐾𝑡
𝑈𝑑 =
𝐿𝑎 𝐽 𝑑 2 𝜔𝑚 𝑟𝑎 𝐽 + 𝐿𝑎 𝐵𝑣 𝑑𝜔𝑚 𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 + + 𝜔𝑚 𝐾𝑡 𝑑𝑡 2 𝐾𝑡 𝑑𝑡 𝐾𝑡
(2.17)
Using Laplace transform 𝐺𝑢 (𝑆) =
𝜔𝑚 (𝑆) 𝐾𝑡 = 2 𝑈𝑑 (𝑆) 𝐿𝑎 𝐽𝑆 + (𝑟𝑎 𝐽 + 𝐿𝑎 𝐵𝑣 )𝑆 + (𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 )
(2.18)
By the same method 𝐺𝐿 (𝑆) =
𝜔𝑚 (𝑆) −(𝑟𝑎 + 𝐿𝑎 𝑆) = 𝑇𝐿 (𝑆) 𝐿𝑎 𝐽𝑆 2 + (𝑟𝑎 𝐽 + 𝐿𝑎 𝐵𝑣 )𝑆 + (𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 )
(2.19)
The speed response of BLDC motor affected together by applied voltage and load torque. 𝜔𝑚 (𝑆) = 𝐺𝑢 (𝑆)𝑈𝑑 (𝑆) + 𝐺𝐿 (𝑆)𝑇𝐿 (𝑆) 𝜔𝑚 (𝑆) =
𝐿𝑎
𝐽𝑆 2
𝐾𝑡 𝑈𝑑 (𝑆) + (𝑟𝑎 𝐽 + 𝐿𝑎 𝐵𝑣 )𝑆 + (𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 )
𝑟𝑎 + 𝐿𝑎 𝑆 − 𝐿𝑎 𝐽𝑆 2 + (𝑟𝑎 𝐽 + 𝐿𝑎 𝐵𝑣 )𝑆 + (𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 )
(2.20)
The structure of BLDC motor transfer function with load can be built as shown in Figure 2.8.  18 
Chapter (2)
Mathematical Model of Brushless DC Motor
Figure 2.8: Block diagram of the linearized BLDC motor model [1].
where: 𝑈𝑑 : DC bus voltage. 𝑟𝑎 : line resistance of winding, 𝑟𝑎 = 2𝑅. 𝐿𝑎 : equivalent line inductance of winding, 𝐿𝑎 = 2(L – M). 𝑖 ∶ line current. M : mutual linkage, assume M = 0. 𝑟 𝐽+𝐿𝑎 𝐵𝑣
Let the mechanical time constant be 𝑡𝑚 = 𝑟 𝑎𝐵
𝑎 𝑣 +𝐾𝑒 𝐾𝑡
electromagnetic time constant can be 𝑡𝑒 = 𝑟
𝐿𝑎 𝐽
𝑎 𝐽+𝐿𝑎 𝐵𝑣
and the
, then equation (2.18)
can be rewritten as 𝐺𝑢 (𝑆) =
𝜔𝑚 (𝑆) 𝐾𝑡 1 = 2 𝑈𝑑 (𝑆) 𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 (𝑡𝑚 . 𝑡𝑒 . 𝑆 + 𝑡𝑚 . 𝑆 + 1)
(2.21)
In general, the mechanical time constant is much larger than the electromagnetic time constant (𝑡𝑚 ≫ 𝑡𝑒 ), so the transfer function expressed in Equation (2.21) can be further simpliﬁed as 𝐺𝑢 (𝑆) =
𝜔𝑚 (𝑆) 𝐾𝑡 1 ≈ 2 𝑈𝑑 (𝑆) 𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 (𝑡𝑚 . 𝑡𝑒 . 𝑆 + 𝑡𝑚 . 𝑆 + 𝑡𝑒 . 𝑆 + 1) =
𝐾𝑡 1 𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 (𝑡𝑚 . 𝑆 + 1)(𝑡𝑒 . 𝑆 + 1)
 19 
(2.22)
Chapter (2)
Mathematical Model of Brushless DC Motor
If the effect of electromagnetic time constant is ignored, i.e. the armature inductance is negligible, then 𝑡𝑒 can be deemed to be zero, so Equation (2.22) can be simpliﬁed into a ﬁrstorder model as 𝐺𝑢 (𝑆) =
𝐾𝑡 1 𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡 𝑡𝑚 . 𝑆 + 1
(2.23)
Further, the step response of Equation (2.23) is given by 𝜔𝑚 (𝑡) =
𝑡 𝐾𝑡 . 𝑈𝑑 − (1 − 𝑒 𝑡𝑚 ) 𝑟𝑎 𝐵𝑣 + 𝐾𝑒 𝐾𝑡
(2.24)
2.4.2 State Space Model State space equation method is one of the most important analysis method in modern control theory [45]. The statespace method is becoming more and more popular in designing control systems with the fast development of computer techniques. Especially in recent years, computer online control systems such as optimal control, Kalman ﬁlters, dynamic system identiﬁcation, selfadaptive ﬁlters and self adaptive control have been applied to motor control. All these control techniques are based on the state space equation [22]. Using the current relationship 𝑖𝑎 + 𝑖𝑏 + 𝑖𝑐 = 0
(2.25)
The voltage equations will become as follows. 𝑣𝑎𝑏 = 𝑅(𝑖𝑎 − 𝑖𝑏 ) + 𝐿
𝑑 (𝑖 − 𝑖𝑏 ) + 𝑒𝑎𝑏 𝑑𝑡 𝑎
(2.26)
𝑣𝑏𝑐 = 𝑅(𝑖𝑎 + 2𝑖𝑏 ) + 𝐿
𝑑 (𝑖 + 2𝑖𝑏 ) + 𝑒𝑏𝑐 𝑑𝑡 𝑎
(2.27)
Subtract Equation (2.26) from Equation (2.27) 𝑑 𝑣𝑎𝑏 − 𝑣𝑏𝑐 = −3𝑅𝑖𝑏 − 3𝐿 𝑖𝑏 + 𝑒𝑎𝑏 − 𝑒𝑏𝑐 𝑑𝑡
 20 
(2.28)
Chapter (2)
Mathematical Model of Brushless DC Motor
𝑖𝑏∙ = −
𝑅 1 1 𝑖𝑏 − (𝑣𝑎𝑏 − 𝑒𝑎𝑏 ) + (𝑣𝑏𝑐 − 𝑒𝑏𝑐 ) 𝐿 3𝐿 3𝐿
𝑣𝑎𝑏 = 𝑅(2𝑖𝑎 + 𝑖𝑏 ) + 𝐿 𝑣𝑐𝑎 = 𝑅(𝑖𝑐 − 𝑖𝑎 ) + 𝐿
(2.29)
𝑑 (2𝑖 + 𝑖𝑏 ) + 𝑒𝑎𝑏 𝑑𝑡 𝑎
(2.30)
𝑑 (𝑖 − 𝑖𝑎 ) + 𝑒𝑐𝑎 𝑑𝑡 𝑐
(2.31)
Subtract Equation (2.30) from Equation (2.31). (𝑣𝑎𝑏 − 𝑒𝑎𝑏 ) − (𝑣𝑐𝑎 − 𝑒𝑐𝑎 ) = 3𝑅𝑖𝑎 + 3𝐿 𝑖𝑎∙ = −
𝑑 𝑖 𝑑𝑡 𝑎
𝑅 1 1 𝑖𝑎 + (𝑣𝑎𝑏 − 𝑒𝑎𝑏 ) − (𝑣𝑐𝑎 − 𝑒𝑐𝑎 ) 𝐿 3𝐿 3𝐿
(2.32) (2.33)
𝑣𝑎𝑏 = 𝑣𝑏𝑐
(2.34)
𝑒𝑎𝑏 = 𝑒𝑏𝑐
(2.35)
𝑣𝑐𝑎 = −(𝑣𝑎𝑏 + 𝑣𝑏𝑐 ) = −2𝑣𝑎𝑏
(2.36)
𝑒𝑐𝑎 = −(𝑒𝑎𝑏 + 𝑒𝑏𝑐 ) = −2𝑒𝑎𝑏
(2.37)
Substituting (2.34), (2.35), (2.36), (2.37) into (2.33) will become. 𝑖𝑎∙ = −
𝑅 1 2 𝑖𝑎 + (𝑣𝑏𝑐 − 𝑒𝑏𝑐 ) + (𝑣𝑎𝑏 − 𝑒𝑎𝑏 ) 𝐿 3𝐿 3𝐿
(2.38)
From Equation (2.15). 𝜔𝑚 ∙ =
−𝐵𝑣 1 𝜔𝑚 + (𝑇𝑒 − 𝑇𝐿 ) 𝐽 𝐽 𝑇𝑒 = 𝐾𝑡 𝑖
where 𝑖𝑎∙ 𝑖∙ [ 𝑏 ∙] = 𝜔𝑚 𝜃𝑚 ∙
(2.39)
−
𝑅 𝐿
0 𝑅
0
0
−𝐿
0
0
0
[ 0
−𝐵𝑣 𝐽
0
1
(2.40) 2
0
3𝐿 𝑖𝑎 −1 0 𝑖𝑏 [ ] + 3𝐿 𝜔𝑚 0 𝜃 0 𝑚 [0 0]
𝑖𝑎 1 0 0 𝑖𝑏 0 1 0 𝑖𝑐 = −1 −1 0 𝜔𝑚 0 0 1 [ 𝜃𝑚 ] [ 0 0 0
1 3𝐿 1 3𝐿
0
𝑣𝑎𝑏 − 𝑒𝑎𝑏 0 𝑣 −𝑒 [ 𝑏𝑐 𝑏𝑐 ] 1 𝑇𝑒 − 𝑇𝐿
0
0]
0 𝑖 𝑎 0 𝑖 0 [𝜔𝑏 ] 0 𝜃𝑚 1] 𝑚
 21 
0
(2.41)
𝐽
(2.42)
Chapter (3)
Control Techniques
Chapter Three CONTROL TECHNIQUES
 22 
Chapter (3)
Control Techniques
Chapter (3) CONTROL TECHNIQUES 3.1 Introduction This chapter presents the theoretical analysis of four different advanced control techniques that are used to achieve high performance BLDC motor drive system. The first technique is the GAbased PID controller, where the proper PID controller parameters are obtained using GA optimization technique based on three different cost functions [46]. The second technique is the selftuning fuzzy PID control, in which the fuzzy control is used to tune the PID controller parameters online according to the error and the change of error, in order to achieve the required speed tracking [47]. The third technique is Model Reference Adaptive Control (MRAC), where the reference model presents the desired performance of the BLDC motor drive system. The fourth technique is a new hybrid technique, which combines the model reference adaptive control with PID compensator (modified MRAC).
3.2 GABased PID Controller The PID controller is applied in various fields in engineering owing to its simplicity, reliability and easy tuning its parameters. The transfer function of the PID controller is 𝐾(𝑠) = 𝐾𝑃 +
𝐾𝑖 𝑠
+ 𝐾𝑑 𝑠. Where 𝐾𝑝 , 𝐾𝑖
and 𝑘𝑑 are proportional, integral and differential gains respectively. The function of each part of a PID controller can be described as follows, the proportional part reduces the error responses of the system to disturbances, the integral part eliminates the steadystate error, and finally the derivative part dampens the dynamic response and improves the system stability [21]. The famous method in conventional PID control to find the proper PID
 23 
Chapter (3)
Control Techniques
controller parameters is ZieglerNichols rule [48]. For open loop tuning, we first find the plant parameters by applying a step input to the open loop system. The plant parameters K, TD and T1 are then found from the result of the step test as shown in Figure 3.1. Ziegler and Nichols then suggest using the PID controller settings given in Table 3.1 when the loop is closed. These parameters are based on the concept of minimizing the integral of the absolute error after applying a step change to the set point.
Figure 3.1: Finding plant parameters K, TD and T1 [15]. Table 3.1: Openloop Ziegler–Nichols settings [15].
Controller
𝐾𝑝
𝑇𝑖
𝑇𝑑
Proportional
𝑇1 𝐾𝑇𝐷


PI
0.9𝑇1 𝐾𝑇𝐷
3.3TD

PID
1.2𝑇1 𝐾𝑇𝐷
2TD
0.5TD
 24 
Chapter (3)
Control Techniques
The parameters of the conventional PID controller based on ZieglerNichols rule, sometimes are not the best. So, it can be realized that using optimization techniques such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO) may lead to better PID controller parameters to achieve better performance [16]. Genetic Algorithm (GA) is a very useful tool to search and optimize many engineering and scientific problems. In this thesis GA is used to tune the PID controller parameters to find the optimal solutions using three different cost functions. Here we use MATLAB Genetic Algorithm Toolbox to simulate it. The first and the most critical step is to encoding the problem into suitable GA chromosomes and then construct the population. Some works recommend 20 to 100 chromosomes in one population. The more chromosomes number will give the better chance to get the optimal results. However, because we have to consider the execution time, we use 80 chromosomes in each generation [49], [50]. Each chromosome comprises of three parameters 𝐾𝑝 , 𝐾𝑖 and 𝐾𝑑 with value bounds varied depend on the cost functions used. The initial values of 𝐾𝑝 , 𝐾𝑖 and 𝐾𝑑 are obtained from ZieglerNichols rule, in order to get the better result. The population in each generation is represented by 80 x 4 matrix as obvious in Equation (3.1), depends on the chromosomes number in population. 𝐾𝑝1 𝐾𝑝2 Q = .. .. [𝐾𝑝𝑛
𝐾𝑖1 𝐾𝑖2 .. .. 𝐾𝑖𝑛
𝐾𝑑1 𝐾𝑑2 .. .. 𝐾𝑑𝑛
where n: number of chromosomes.
 25 
𝐹1 𝐹2 .. .. 𝐹𝑛]
(3.1)
Chapter (3)
Control Techniques
Each row is one chromosome that comprise 𝐾𝑝 , 𝐾𝑖 and 𝐾𝑑 values and the last column added to accommodate fitness values (F) of corresponding chromosomes [15], [51]. The final values of 𝐾𝑝 , 𝐾𝑖 and 𝐾𝑑 is determined by minimizing a certain cost function. Several cost functions may be used for this purpose. In this thesis, three different cost function are considered [52].
3.2.1 First Cost Function The First Cost Function (CF1) as shown in Equation (3.2) minimizes the integrated square error e(t) and improve the overall performance, but not guarantee a good rise time and acceptable overshoot for the system [52]. Figure 3.2 shows the structure of GA tuning system for first cost function. It can be noted that the input for GA tuning system is the error signal only, which sometimes not enough to obtain good results. ∞
𝐶𝐹1 = ∫ (𝑒(𝑡))2 𝑑𝑡 0
Figure 3.2: The structure of GA tuning system for (CF1).
 26 
(3.2)
Chapter (3)
Control Techniques
3.2.2 Second Cost Function The Second Cost Function (CF2) obvious in Equation (3.3). It is used to improve the performance of system according to the priority of designer, but the inverse relationship between the rise time and overshoot of the closed loop system will be obstacle to obtain on a good response [52]. The actual closedloop specification of the system with controller, rise time (𝑡𝑟 ), maximum overshoot (𝑀𝑝 ), settling time (𝑡𝑠 ), and steady state error (𝑒𝑠𝑠 ) are used to evaluate the cost function. This is done by summing the absolute errors between actual and specified specification [18]. 𝐶𝐹2 =
1 [𝑐1 (𝑡𝑟 − 𝑡𝑟𝑑 ) + 𝑐2 (𝑀𝑝 − 𝑀𝑃𝑑 ) + 𝑐3 (𝑡𝑠 − 𝑡𝑠𝑑 ) + 𝑐4 (𝑒𝑠𝑠 − 𝑒𝑠𝑠𝑑 )]
(3.3)
where 𝑐1: 𝑐4 are positive constants (weighting factors), their values are chosen according to prioritizing their importance, (𝑡𝑟𝑑 ) is the desired rise time, (𝑀𝑝𝑑 ) is the desired maximum overshoot, (𝑡𝑠𝑑 ) is the desired settling time, and (𝑒𝑠𝑠𝑑 ) is the desired steady state error. Figure 3.3 illustrates the structure of GA tuning system for second and third cost functions.
Figure 3.3: The structure of GA tuning system for (CF2) and (CF3).
 27 
Chapter (3)
Control Techniques
3.2.3 Third Cost Function The Third Cost Function (CF3) can treat the drawbacks in the previous two cost functions and is given by Equation (3.4) [52]. 𝐶𝐹3 =
1 (1 −
𝑒 −𝛽 )(𝑀𝑝
+ 𝑒𝑠𝑠 ) + 𝑒 −𝛽 (𝑡𝑠 − 𝑡𝑟 )
(3.4)
This cost function can satisfy the designer requirement using the weighting factor value (β). The factor is set larger than 0.7 to reduce over shoot and steadystate error. If this factor is set smaller than 0.7 the rise time and settling time will be reduced [15]. All of these cost functions have been minimized subjected to: 𝐾𝑃 min ≤ 𝐾𝑃 ≤ 𝐾𝑃 𝑚𝑎𝑥 𝐾𝑖 min ≤ 𝐾𝑖 ≤ 𝐾𝑖 𝑚𝑎𝑥 𝐾𝑑 min ≤ 𝐾𝑑 ≤ 𝐾𝑑 𝑚𝑎𝑥
3.3 SelfTuning Fuzzy PID Controller It has been reported in many researches that online tuning of the controller parameters enhances its performance and increases the robustness of the system. [53], [47]. For this reason, this thesis seeks to design selftuning fuzzy PID controller, where the PID controller parameters are updated online according to error and change of error. This type of controllers are suitable for systems which exposed to external disturbances and parameters variation [5]. The proposed controller consists of two parts: the first part is PID controller and the second part is fuzzy logic control (FLC) as shown in Figure 3.4. In this case the parameters of the PID controller are changed adaptively using fuzzy logic algorithm. The PID controller parameters are updated according to the following equations [54].
 28 
Chapter (3)
Control Techniques
Figure 3.4: Structure of selftuning PID fuzzy controller [26].
𝐾𝑃2 = 𝐾𝑝1 ∗ 𝐾𝑃0 ,
𝐾𝑖2 = 𝐾𝑖1 ∗ 𝐾𝑖0 𝑎𝑛𝑑 𝐾𝑑2 = 𝐾𝑑1 ∗ 𝐾𝑑0
(3.5)
where: 𝐾𝑝1 : proportional modification coefficient. 𝐾𝑖1 : integral modification coefficient. 𝐾𝑑1 : derivative modification coefficient. 𝐾𝑃0 : initial proportional gain (constant value). 𝐾𝑖0 : initial integral gain (constant value). 𝐾𝑑0 : initial derivative gain (constant value). Hence, the control signal of selftuning fuzzy PID controller can be described as follows. 𝑈 𝑃𝐼𝐷 = 𝐾𝑝2 𝑒(𝑡) + 𝐾𝑖2 ∫ 𝑒(𝑡) + 𝐾𝑑2
𝑑𝑒(𝑡) 𝑑𝑡
(3.6)
Where 𝐾𝑝2 , 𝐾𝑖2 and 𝐾𝑑2 are the new gains of PID controller. The general structure of fuzzy logic control is represented in Figure 3.5 and comprises three principal components [31].
 29 
Chapter (3)
Control Techniques
Figure 3.5: Fuzzy logic control structure [48].
3.3.1 Fuzzification This converts input data into suitable linguistic values. As shown in Figure 3.5 there are two inputs to the controller: error and rate change of the error signals. For the system under study the universe of discourse for both e(t) and ∆e(t) may be normalized from [1,1], and the linguistic labels are {Negative Big, Negative medium, Negative small, Zero, Positive small, Positive medium, Positive Big}. These are referred to in the rules bases as {NB,NM,NS,ZE,PS,PM,PB}. The linguistic labels of the outputs are {Zero, Medium small, Small, Medium, Big, Medium big, very big} and referred to in the rules bases as {Z,.MS, S, M, B, MB, VB} [54]. Figures 3.6 and 3.7 display the memberships of inputs and output of fuzzy logic control respectively.
Figure 3.6: Memberships function of inputs (e, ∆e).
 30 
Chapter (3)
Control Techniques
Figure 3.7: Memberships functions of outputs (𝑲𝒑𝟏 , 𝑲𝒊𝟏 and 𝑲𝒅𝟏 ).
3.3.2 Rule Base A decision making logic simulates a human decision process. The rule base is simplified in Tables [3.2  3.4]. The input e has 7 linguistic labels and ∆e has 7 linguistic labels. Then we have 7×7 = 49 rule base. Which are simplified into 25 rulebase by ignoring the medium label [26] (proved in Appendix (A)). Table 3.2: The Rule base of 𝑲 𝒑𝟏 .
∆e/e NB NS ZE PS PB
NB VB B ZE B VB
NS VB B ZE B VB
ZE VB B MS B VB
PS VB MB S MB VB
PB VB VB S VB VB
PS M S MS S M
PB M S MS S M
Table 3.3: The Rule base of 𝑲𝒊𝟏 .
∆e/e NB NS ZE PS PB
NB M S MS S M
NS M S MS S M
ZE M S ZE S M
 31 
Chapter (3)
Control Techniques Table 3.4: The Rule base of 𝑲𝒅𝟏 .
∆e/e NB NS ZE PS PB
NB ZE S M B VB
NS S B MB VB VB
ZE M MB MB VB VB
PS MB VB VB VB VB
PB VB VB VB VB VB
3.3.3 Defuzzification The purpose of defuzzification process convert the fuzzy output to crisp value to use as a nonfuzzy control action. There are many different methods of defuzzification. The defuzzification technique that has been used in this thesis is the center of gravity as shown in Equation (3.7) [47]. ∑𝑛𝑗=1 𝑢(𝑢𝑗 )𝑢𝑗 𝑢(𝑛𝑇) = 𝑛 ∑𝑗=1 𝑢(𝑢𝑗 )
(3.7)
Where u(uj) member ship grad of the element uj, u(nT) is the fuzzy control output, n is the number of discrete values on the universe of discourse. The drawback of selftuning fuzzy PID control that the PID controller parameters are changed in limited ranges. So, in this thesis, we will resort to use the adaptive control to guarantee high performance for BLDC motor.
3.4 Model Reference Adaptive Control The Model Reference Adaptive Control (MRAC) is highranking adaptive controller. It may be regarded as an adaptive servo system in which the desired performance is expressed in terms of a reference model, Which gives the desired response to a command signal. This is a convenient way to give specification for a servo problem [29], [27].
 32 
Chapter (3)
Control Techniques
A typical MRAC controller consists of a reference model, a control law, and an adaptive mechanism that updates the controller parameters by using the feedback error between the reference model and actual plant, as shown in Figure 3.8. The basic principle of this adaptive controller is to build a reference model that specifies the desired output of the controller, and then the adaptation law adjusts the unknown parameters of the plant so that the tracking error converges to zero [28].
Figure 3.8: A schematic diagram of a general MRAC controller [28].
The Adaptive Controller has two loops. The inner loop consists of the process and an ordinary feedback controller. The outer loop adjusts the controller parameters in such a way that the error, which is the difference between the process output y and model output 𝑦𝑚 is small [29].
 33 
Chapter (3)
Control Techniques
The MIT rule is the original approach to modelreference adaptive control. The name is derived from the fact that it was developed at the Instrumentation Laboratory (now the Draper Laboratory) at MIT. To adjust parameters in such a way that the loss function is minimized [28]. 𝑗(𝜃) =
1 2 𝐸 2
(3.8)
To make j small, it is reasonable to change the parameters in the direction of the negative gradient of j, that is, 𝑑𝜃 𝜕𝑗 𝜕𝐸 = −𝛾 = −𝛾𝐸 𝑑𝑡 𝜕𝜃 𝜕𝜃
(3.9)
where: 𝛾: adaptation gain. E: the error between the output speed of the BLDC motor and the model reference output (𝐸 = 𝑦 − 𝑦𝑚 ). 𝜃: the controller parameter. Figure 3.9 shows the BLDC motor is described by the singleinput, singleoutput (SISO) system [30].
Figure 3.9: A general linear controller with two degrees of freedom.
 34 
Chapter (3)
Control Techniques 𝐴. 𝑦(𝑡) = 𝐵(𝑢(𝑡) + 𝑣(𝑡))
(3.10)
where: A , B : polynomials depend on the BLDC motor. 𝑢(𝑡): the output of controller. 𝑦(𝑡): the output speed of BLDC motor. 𝑣(𝑡) : the process disturbance. the controller is described in (3.10). 𝑍. 𝑢(𝑡) = 𝑇. 𝑢𝑐 (𝑡) − 𝑋. 𝑦(𝑡)
(3.11)
where: Z, T and X : controller parameters polynomials. 𝑢𝑐 (𝑡): the desired speed of BLDC motor. Substituting (3.11) into (3.10) will result (3.12) 𝑦(𝑡) =
𝐵𝑇 𝐵𝑍 𝑢𝑐 (𝑡) + 𝑣(𝑡) 𝐴𝑍 + 𝐵𝑋 𝐴𝑍 + 𝐵𝑋
(3.12)
Assume that the model reference is described by the singleinput, singleoutput (SISO) system. 𝐴𝑚 𝑦𝑚 (𝑡) = 𝐵𝑚 𝑢𝑐 (𝑡) ⟹ 𝑦𝑚 (𝑡) =
𝐵𝑚 𝑢 (𝑡) 𝐴𝑚 𝑐
(3.13)
where: 𝐴𝑚 , 𝐵𝑚 : polynomials depend on the reference model. 𝑦𝑚 (𝑡): the output of model reference. Assuming, ( 𝑣(𝑡) = 0) the following condition must hold: 𝑦(𝑡) = 𝑦𝑚 (𝑡) ⟹
𝐵𝑇 𝐵𝑚 = 𝐴𝑍 + 𝐵𝑋 𝐴𝑚
Assume the transfer function of reference model is
 35 
(3.14)
Chapter (3)
Control Techniques 𝑦𝑚 𝑏𝑚 = 𝑢𝑐 𝑎𝑚1 𝑆 2 + 𝑎𝑚2 𝑆 + 𝑎𝑚3
(3.15)
where: 𝑆=
𝑑 𝑑𝑡
.
𝑎𝑚1 , 𝑎𝑚2 , 𝑎𝑚3 , 𝑏𝑚 : the model reference transfer function coefficient. Assume the transfer function of the BLDC motor is 𝑦 𝑏 = 𝑢 𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3
(3.16)
where 𝑎1 , 𝑎2 , 𝑎3 , 𝑏: BLDC motor transfer function coefficient. From Equation (3.14) the Diophantine equation as follows. 𝐴𝑍 + 𝐵𝑋 = 𝐴0 𝐴𝑚
(3.17)
where: A = 𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3 , 𝐴𝑚 = 𝑎𝑚1 𝑆 2 + 𝑎𝑚2 𝑆 + 𝑎𝑚3 A0: Calibration gain. deg ( 𝑋) = deg(𝐴) − 1 = 2 − 1 = 1 where deg is the polynomial degree. 𝑋 = 𝑥0 + 𝑥1 𝑆 deg(𝑍) = deg(𝑋)
⟹
(3.18) 𝑍 = 𝑧0 + 𝑧1 𝑆
(3.19)
deg(𝐴0 ) = deg(𝐴) + deg(𝑅) − deg(𝐴𝑚 ) = 2 + 1 − 2 = 1
Similarly
A0 = S
(3.20)
T=S
(3.21)
 36 
Chapter (3)
Control Techniques
Substituting Equations (3.18, 3.19, 3.20 and 3.21) into Equation (3.11) will result Equation (3.22). (𝑧0 + 𝑧1 𝑆)𝑢 = 𝑆𝑢𝑐 − (𝑥1 𝑆 + 𝑥0 )𝑦 𝑢=
𝑆 𝑋(𝑆) 𝑢𝑐 − 𝑦 𝑍(𝑆) 𝑍(𝑆)
(3.22) (3.23)
From Equation (3.10) and assume 𝑣(𝑡) = 0 (𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3 ) = 𝑏𝑢
(3.24)
Substituting (3.23) into (3.24) will result (3.25) (𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3 )𝑦 = 𝑏 (
⟹ ((𝑎1𝑆 2 + 𝑎2 𝑆 + 𝑎3 ) + 𝑏
𝑇(𝑆) 𝑋(𝑆) 𝑢𝑐 − 𝑦) 𝑍(𝑆) 𝑍(𝑆)
(3.25)
𝑋(𝑆) 𝑇(𝑆) )𝑦 = 𝑏 𝑢 𝑍(𝑆) 𝑍(𝑆) 𝑐
Rewritten (3.25) to become (3.26) 𝑦=
𝑏𝑇(𝑆) 𝑢 (𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3 )𝑍(𝑆) + 𝑏𝑆(𝑆) 𝑐 𝐸 = 𝑦 − 𝑦𝑚
(3.26) (3.27)
Substituting Equations (3.15, 3.26) into Equation (3.27) will result (3.29) 𝑏𝑇(𝑆) 𝐸=( (𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3 )𝑍(𝑆) + 𝑏𝑋(𝑆) 𝑏𝑚 − )𝑢 𝑎𝑚1 𝑆 2 + 𝑎𝑚2 𝑆 + 𝑎𝑚3 𝑐 𝜕𝐸 𝑏 = 𝑢 2 𝜕𝑇 (𝑎1 𝑆 + 𝑎2 𝑆 + 𝑎3 )𝑍(𝑆) + 𝑏𝑋(𝑆) 𝑐
 37 
(3.28)
(3.29)
Chapter (3)
Control Techniques
𝜕𝐸 −𝑏 2 𝑇(𝑆) = 𝑢 𝜕𝑆 ((𝑎 𝑆 2 + 𝑎 𝑆 + 𝑎 )𝑍(𝑆) + 𝑏𝑋(𝑆))2 𝑐 1 2 3
(3.30)
From Equation (3.5) 𝜕𝑇 𝑏 = −𝛾𝐸 𝑢 (𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3 )𝑍(𝑆) + 𝑏𝑆(𝑆) 𝑐 𝜕𝑡 𝜕𝑇 1 = −𝛾 ′ 𝐸 𝑢 (𝑎1 𝑆 2 + 𝑎2 𝑆 + 𝑎3 )𝑍(𝑃) + 𝑏𝑋(𝑆) 𝑐 𝜕𝑡
(3.31)
𝛾 ′ = 𝑏𝛾
(3.32)
where Similarly
𝜕𝑋 1 = −𝛾 ′ 𝐸 𝑦 2 𝜕𝑡 𝑎𝑚1 𝑆 + 𝑎𝑚2 𝑆 + 𝑎𝑚3
𝐵𝑚 𝜔𝑛 2 = 2 𝐴𝑚 𝑆 + 2𝜉𝜔𝑛 𝑆 + 𝜔𝑛 2
(3.33)
(3.34)
where: 𝜉 (𝑑𝑎𝑚𝑝𝑖𝑛𝑔 𝑟𝑎𝑡𝑖𝑜) = 1. 𝜔𝑛 (𝑛𝑎𝑡𝑢𝑟𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦) = 500.
(Selected by designer)
Of considerations taken during the design has to be 𝜔𝑛 of reference model is greater than 𝜔𝑛 of BLDC motor transfer function.
3.5 MRAC with PID Compensator MRAC is designed to eliminate the difference between the output of reference model and the actual speed. It does not take into account the error between reference speed and actual speed. This will cause high overshooting and high settling time. This disadvantage can be alleviated by adopting PID compensator as displayed in Figure 3.10.
 38 
Chapter (3)
Control Techniques
Figure 3.10: Block diagram of MRAC with PID compensator.
The input of PID compensator is the error between reference speed and actual speed. In this case the controller action depends on both the MRAC and the PID compensator as shown in Equation (3.34). This technique consider a new technique in this thesis. 𝑢 = 𝑢𝑀𝑅𝐴𝐶 + 𝑢𝑃𝐼𝐷 𝑐𝑜𝑚𝑝𝑒𝑛𝑠𝑎𝑡𝑜𝑟
(3.35)
There are many of methods to select the PID compensator parameters such as trial and error and ZieglerNichols rule. In this thesis the parameters of PID compensator are the same parameters of GAbased PID controller (CF3) to give us the best performance. .
 39 
Chapter (4)
Simulation Results
Chapter Four SIMULATION RESULTS
 40 
Chapter (4)
Simulation Results
Chapter (4) SIMULATION RESULTS 4.1 Introduction This chapter consists of three major parts. The first part presents the open loop simulation results of BLDC motor drive system model. The second part shows the performance of each control technique individually, which have been designed in the previous chapter. The third part investigates the robustness of each control technique through several tests applied on BLDC motor such as sudden load test, sinusoidal load test, parameters variation test and speed tracking test.
4.2 Open Loop Response Results This section investigates the steady and dynamic characteristics of BLDC motor in case of free runing. The simulation of BLDC motor drive system model is carried out using Matlab/Simulink. Table 4.1 shows the BLDC motor parameters used in the simulation. Table 4.1: BLDC Motor Parameters.
Rating
Symbol
Value
Units
Phase resistance
R
0.57
Phase Inductance
L
1.5
mH
Torque constant
𝐾𝑡
0.082
N.m/A
Number of Poles
P
4
Peak torque
𝑇𝑝
0.42
Rated Voltage
V
36
Rotor Inertia Friction coefficient Rated Speed Rated current
J 𝐵𝑣 Ω I
 41 
N.m V −6
23 × 10
0.0000735
4000 5
Kg.𝑚2 N.m.s RPM A
Chapter (4)
Simulation Results
Using the BLDC motor parameters in Table 4.1 and substitute it in Equation (2.20). The linearized transfer function model of BLDC motor at noload will become as follows. 𝜔(𝑠) 1 .232 × 106 = 2 𝑈𝑑 (𝑠) 𝑠 + 383.19 𝑠 + 105.9 ∗ 103
(4.1)
Figure 4.1 demonstrates the simulink diagram of the whole drive system of BLDC motor. It is clear that the motor is fed by a six step voltage inverter. The inverter gates signals are produced by decoding the hall effect signals of the motor. Figure 4.2 illustrates the open loop speed response of BLDC motor drive system. It can be noted that motor reaches steady speed 4000 rpm. When the load is increased by 50 % of its rated value at time equals 0.1 second, the speed drops to 3100 rpm.
Figure 4.1: Simulink diagram of the BLDC motor drive system.
 42 
Chapter (4)
Simulation Results
Figure 4.2: Open loop response of BLDC motor at sudden load.
Figure 4.3 demonstrates the corresponding phase current. When the load torque increases, the value of the phase current increases to about ± 2.5 A.
Figure 4.3: The open loop response of phase current.
 43 
Chapter (4)
Simulation Results
Figure 4.4: The open loop response of electromagnetic torque.
Figure 4.4 illustrates the corresponding electromagnetic torque. It can be noted that the electromagnetic torque equals 0.03 N.m at no load and increases to 0.2 N.m, when the motor is loaded.
4.3 Closed Loop Response Results In this section, the performance of BLDC motor drive system has been investigated using different advanced control techniques that have been discussed in chapter (3).
4.3.1 GABased PID Control This section illustrates the performance of BLDC motor drive system using four sets of PID controller parameters. The first set was obtained using Ziegler–Nichols rule, while the other three sets are obtained using GA based on three different cost functions as described in chapter (3). The range of change of PID controller parameters through optimization process will be as follows:  44 
Chapter (4)
Simulation Results 0.0001 ≤ 𝐾𝑃 ≤ 0.01 0.01 ≤ 𝐾𝑖 ≤ 2 10−12 ≤ 𝐾𝑑 ≤ 10−2
Figure 4.5 illustrates the simulink diagram of BLDC motor drive system with PID controller.
Figure 4.5: Simulink diagram of whole drive system with PID controller.
Table 4.5 demonstrates the parameters of the PID controller, which are obtained using Ziegler–Nichols rule and GA based on three different cost functions. Table 4.2: Values of PID controller gains.
𝑲𝑷
𝑲𝒊
𝑲𝒅
ZN method
0.001
0.167
3 × 10−6
GA based on (CF1)
0.01
0.9999
1.2307 × 10−4
GA based on (CF2)
0.0102
0.843
3.4 × 10−8
GA based on (CF3)
0.004
0.882
5.6 × 10−12
Optimization Method
 45 
Chapter (4)
Simulation Results
Figure 4.6: Speed response of each PID controller.
Figure 4.6 shows a comparison of the speed response of the drive system using the above PID controller parameters sets. It can be noted that GAbased PID controller with (CF3) has the better performance (less rise time, less settling time, smaller overshoot) among other techniques. Table 4.3: The performance of four sets of PID controller parameters.
Rise Time (sec)
Settling Time (sec)
Overshoot (%)
Z.N. method
0.1178
0.2030
0.0093
GA based on (CF1)
0.0210
0.0748
7.2170
GA based on (CF2)
0.0284
0.0569
0.0209
GA based on (CF3)
0.0219
0.0342
1.1063
Optimization Method
 46 
Chapter (4)
Simulation Results
Table 4.3 demonstrates the performance of each set of the PID controller parameters, which were obtained from ZN rule and the GA based on three different cost functions. It is clear that the GAbased PID controller based on (CF3) has a better performance (less settling time, less rise time and acceptable overshoot) among other techniques. Figures 4.7 and 4.8 display the corresponding controller output and DC supply currents respectively. The time scale of Figure 4.8 is magnified to increase the clarification. It is clear that the starting currents of GA based on first and second cost function have high values compared to GA based on third cost function.
Figure 4.7: The controller output of each PID controller.
 47 
Chapter (4)
Simulation Results
Figure 4.8: The DC supply current of each PID controller.
4.3.2 SelfTuning Fuzzy PID Control This section discusses the performance of BLDC motor drive system with selftuning fuzzy PID controller. It is clear from the previous section that the GAbased PID controller with (CF3) has the best performance among other techniques. So, the initial values of selftuning fuzzy PID controller gains equal to GAbased PID controller with (CF3) gains to obtain the best results. Figure 4.9 demonstrates the Simulink diagram of BLDC motor drive system with selftuning fuzzy PID controller. The controller consists of two parts, PID controller and fuzzy logic controller. The fuzzy logic controller is used to tune online the PID controller parameters according to the error and the change of error.
 48 
Chapter (4)
Simulation Results
Figure 4.9: Simulink diagram of selftuning fuzzy PID control.
Figure 4.10 illustrates the speed response of BLDC motor using selftuning fuzzy PID controller. It can be noted that the selftuning fuzzy PID controller has a good performance (small rise time and there is no overshoot), while Figure 4.11 shows the corresponding controller output.
Figure 4.10: The speed response of selftuning fuzzy PID controller.
 49 
Chapter (4)
Simulation Results
Figure04.11: The selftuning fuzzy PID controller output.
4.3.3 Model Reference Adaptive Control The adaptive controllers are very effective to handle the unknown parameters variation and external disturbances. This section shows the performance of BLDC motor drive system when using MRAC. Figure 4.11 demonstrates the Simulink diagram of MRAC with BLDC motor. The main obstacle when using MRAC is the selection of the adaptation gain [28]. Too small values cause poor performance, while large values cause system instability [29]. Suitable adaptation gain value may be selected by trial error [55]. Figure 4.13 shows the performance of MRAC at different values of adaptation gain. It can be concluded that increasing the adaptation gain will increase the system overshoot and decreases the rise time (faster response) while Figure 4.14 illustrates the corresponding MRAC output at the same values of adaptation gain. It can be noted the voltage saturation effect at Gamma = 0.15.
 50 
Chapter (4)
Simulation Results
Figure 4.12: Simulink diagram of BLDC motor with MRAC.
Figure 4.13: Response of MRAC at different adaptation gains.
 51 
Chapter (4)
Simulation Results
Figure 4.14: MRAC output at different adaptation gains.
4.3.4 MRAC with PID Compensator This section shows the performance of BLDC motor drive system using MRAC with PID compensator. Figure 4.15 demonstrates the Simulink diagram of MRAC with PID compensator. It is obvious from the simulation results of previous section that the MRAC suffer from high overshooting and high settling time. Figure 4.16 illustrates the effect of adding PID compensator to MRAC at different values of adaptation gain. It can be noted that the fast response can be achieved without overshoot. This means that increasing the adaptation gain will decrease the rise time without increasing the overshoot. Figure 4.17 demonstrates the corresponding controller output of MRAC with PID compensator at same values of adaptation gain.
 52 
Chapter (4)
Simulation Results
Figure04.15: Simulink diagram of MRAC with PID compensator.
Figure 4.16: Response of MRAC with PID compensator at different adaptation gains.
 53 
Chapter (4)
Simulation Results
Figure 4.17: Output of MRAC with PID compensator at different adaptation gains.
4.4 Control Techniques Performance Investigation To investigate the performance of each control algorithm, several tests have been carried out at different operating conditions.
4.4.1 Speed Regulation at Sudden Load In this test, the ability of each controller to achieve the required speed regulation, regardless the sudden external disturbance is investigated. Figure 4.18 shows a comparison between the behaviors of each control technique. The comparison demonstrates that the MRAC with PID compensator has better performance (less rise time, less settling time and small overshoot). Also, during sudden load disturbance, the MRAC with PID compensator can recover the desired speed faster than other control techniques.
 54 
Chapter (4)
Simulation Results
Figure04.18: Speed response of control techniques at sudden load.
Table 4.4 demonstrates the performance of each control technique. It is clear that the MRAC with PID compensator has the best performance compared to other techniques (less settling time, less rise time and small overshoot). Figures 4.19 and 4.20 display the corresponding controller output and DC supply current at sudden load respectively. The subjected load is 50% of rated torque. Table 4.4: The performance of each control technique.
Rise Time (sec)
Settling Time (sec)
Overshoot (%)
GAbased PID controller (CF3)
0.0219
0.0342
1.1063
Selftuning fuzzy PID controller
0.0101
0.0203
0.0264
Model reference adaptive control
0.009
0.0806
18.85
MRAC with PID compensator
0.0075
0.0169
0.0238
Control Technique
 55 
Chapter (4)
Simulation Results
Figure 4.19: Controller output of control techniques at sudden load.
Figure 4.20: DC supply current of control techniques at sudden load.
 56 
Chapter (4)
Simulation Results
4.4.2 Speed Response at Parameters Variation This section interested to investigate the robustness of the proposed control techniques through change the parameters of BLDC motor suddenly such as rotor inertia and phase resistance. 4.4.2.1 Sudden Change in Rotor Inertia (J) In this test the rotor inertia of BLDC motor will be increased suddenly at time 0.1 second from 23𝑒 −6 Kg.𝑚2 to 75𝑒 −6 Kg.𝑚2 . Figure 4.21 shows the ability of MRAC with PID compensator to accommodate the speed disturbance in a short time compared to other control techniques, while Figure 4.22 shows the corresponding controller output of each control technique.
Figure 4.21: Response of control techniques at sudden change in (J).
 57 
Chapter (4)
Simulation Results
Figure 4.22: Output of control techniques at sudden change in (J).
4.4.2.2 Sudden Change in Phase Resistance (R) Some industrial applications need to run the BLDC motor for long periods, which leads to change its phase resistance. So, this test investigates the robustness of proposed control techniques where the phase resistance of BLDC motor will be decreased suddenly by 50% from its original value at time 0.1 second. Figure 4.23 illustrates the performance of each control technique through this test. It can be noted that the MRAC and the MRAC with PID compensator can eliminate the speed disturbance faster than the other control techniques (GAbased PID controller (CF3) and selftuning fuzzy PID controller).
 58 
Chapter (4)
Simulation Results
Figure 4.23: Response of control techniques at sudden change in (R).
Figure 4.24 demonstrates the corresponding controller output of each control technique at sudden change in phase resistance. It can be noted that the MRAC with PID compensator has reacted faster than other control techniques. It can be concluded that the MRAC with PID compensator more robust and has more flexibility to deal with different types of disturbances such as sudden change in load and sudden change in motor parameters (phase resistance and rotor inertia).
 59 
Chapter (4)
Simulation Results
Figure 4.24: Output of control techniques at sudden change in (R).
4.4.2.3 Effect Changes of Both (R) and (J) This test investigates the robustness of proposed control techniques in case of change both the phase resistance (R) and rotor inertia (J) simultaneously from beginning of the simulation time. Where the phase resistance and rotor inertia of BLDC motor will be increased simultaneously by 20% from its original values. Figure 4.25 shows the speed response of each control technique when increasing the values of phase resistance (R) and rotor inertia (J) by 20% simultaneously. It can be noted that MRAC with PID compensator more robust and has less sensitivity with parameters variation compared to other techniques.  60 
Chapter (4)
Simulation Results
Figure04.25: Response of control techniques at change (R) and (J) simultaneously.
Table 4.5 summarizes the performance of each control technique with an increase in (R) and (J) by 20%. It is clear that MRAC with PID compensator has less rise time, less settling time and acceptable overshoot. Figures 4.26 and 4.27 display the corresponding controller output and the DC supply current respectively. Table 4.5: The performance of each control technique at change R, J.
Rise Time (sec)
Settling Time (sec)
Overshoot (%)
GABased PID controller (CF3)
0.0211
0.0597
3.0708
Selftuning fuzzy PID controller
0.0095
0.0169
1.189
Model reference adaptive control
0.0106
0.0951
20.18
MRAC with PID compensator
0.0082
0.0125
1.621
Control Technique
 61 
Chapter (4)
Simulation Results
Figure 4.26: Control techniques output at change (R) and (J) simultaneously.
Figure 4.27: DC supply current of control techniques at change (R) and (J) simultaneously.
 62 
Chapter (4)
Simulation Results
4.4.3 Speed Regulation at Sinusoidal Load The robustness of the proposed control techniques is tested by loading the BLDC motor with load torque, which is continously changed in sinsoidal form as shown in Figure 4.28.
Figure 4.28: Sinusoidal load torque varies between 0% and 50% of rated torque.
Figure 4.29 shows the speed response of each control technique when the motor is exposed to sinusoidal load torque variations between 0% and 50% of the rated torque. It can be noted that the motor speed is oscillated around the reference speed. Each control technique seek to track the reference speed, regardless the continous sinsoidal oscillations of the load. Maximum deviation percentage about reference speed varies from control technique to another. When the maximum deviation of control technique has a small value, the good performance will be achieved. It is expected that the control techniques, that allow online tuning, will give better performance.
 63 
Chapter (4)
Simulation Results
Figure 4.29: Speed response of control techniques at sinusoidal load.
Table 4.6 summarrizes the maximum deviation of each control technique. It is obvious that the MRAC with PID compensator possesses the lowest maximum deviation about reference speed compared to other control techniques. Figures 4.30 and 4.31 display the corresponding controller output and DC supply current of each control technique respectively through change the load in sinusoidal form. Table04.6: The speed deviation of each control technique.
Maximum Deviation (RPM)
Maximum Deviation (%)
GAbased PID controller (CF3)
± 48.4
±1.614
Selftuning fuzzy PID controller
± 25.2
±0.84
Model reference adaptive control
± 15.3
±0.51
MRAC with PID compensator
± 10.7
±0.35
Control Technique
 64 
Chapter (4)
Simulation Results
Figure 4.30: Output of control techniques at sinusoidal load.
Figure 4.31: DC supply current of control technique at sinusoidal load.
 65 
Chapter (4)
Simulation Results
4.4.4 Speed Tracking Many industrial processes such as assembly lines must operate at different speeds for different products. Where speeds may be selected from several different preselected ranges. In this test the ability of each control technique will be investigated to track a certain reference speed profile. 4.4.4.1 Different Commands of Reference Speed Figure 4.32 shows the speed response of each control technique at different commands of reference speed. It can be noted that the MRAC with PID compensator can track the reference speed profile faster than other control techniques. Figures 4.33 and 4.34 display the corresponding controller output and DC supply current of each control technique respectively at different commands of speed. It can be noted that the DC supply current will be increased at each new command of reference speed.
Figure 4.32: Response of control techniques at different commands of speed.
 66 
Chapter (4)
Simulation Results
Figure 4.33: Output of control techniques at different commands of speed.
Figure 4.34: DC supply current of control techniques at different commands of speed.
 67 
Chapter (4)
Simulation Results
4.4.4.2 Trapezoidal Speed Tracking The trapezoidal profile changes speed in a linear fashion until the target speed is reached. When decelerating, the speed again changes in a linear manner until it reaches zero. Graphing speed versus time results in a trapezoidal form is shown in Figure 4.35. It can be noted that model reference adaptive control has a bad performance in beginning the tracking. Also, it is clear that GAbased PID controller has a high deviation about reference speed, while both MRAC with PID compensator and selftuning fuzzy PID controller have a small deviation about reference speed. Figures 4.36 and 4.37 show the corresponding controller output and DC supply current respectively of each control technique at trapezoidal speed tracking.
Figure 4.35: Response of control techniques at trapezoidal speed tracking.
 68 
Chapter (4)
Simulation Results
Figure 4.36: Output of control techniques at trapezoidal speed tracking.
Figure 4.37: DC supply current of control techniques at trapezoidal speed tracking.
 69 
Chapter (5)
Laboratory Setup and Experimental Results
Chapter Five LABORATORY SETUP AND EXPERIMENTAL RESULTS
 70 
Chapter (5)
Laboratory Setup and Experimental Results
Chapter (5) LABORATORY SETUP AND EXPERIMENTAL RESULTS 5.1 Introduction The purpose of this chapter to show the validity of the proposed control techniques to practical implementation. This chapter shows also, the laboratory setup of BLDC motor drive system. A data acquisition card will be used to interface between the BLDC motor drive system and the computer. The MATLAB system identification toolbox will be used to develop an approximate transfer function for BLDC motor drive system.
5.2 Laboratory Setup Figure 5.1 demonstrates the main components of BLDC motor drive system, which consists of the six power transistors MOSFET inverter, driver circuit and three hall effect sensors.
Figure 5.1: Brushless DC motor drive system [35].
 71 
Chapter (5)
Laboratory Setup and Experimental Results
The experimental setup consists of five parts as shown in Figure 5.2: 1 Maxon BLDC motor (50 watt) with three hall effect sensors that are used to detect the rotor position and speed measurements. The data sheet of motor shows in Appendix (B). 2 The ESCON 36/3 EC is a smallsized, powerful 4quadrant PWM servo controller for the highly efficient control of permanent magnetactivated brushless EC motors up to approximately 97 Watts. 3 Power supply has input (220 V,6A) and output (24 V) 4 A data acquisition card (DAQ) NI USB6008 has the following specifications: •
8 analog inputs (12bit, 10 kS/s).
•
2 analog outputs (12bit, 150 S/s).
•
12 digital I/O.
•
USB connection, No extra powersupply needed.
5 Computer used to perform the control algorithms.
Figure 5.2: Brushless DC motor experimental setup.
 72 
Chapter (5)
Laboratory Setup and Experimental Results
5.3 Data Acquisition in MATLAB Data Acquisition Toolbox in MATLAB is used for data transfer between real world and computer through a USB6008 DAQ device. Data Acquisition Toolbox software provides a complete set of tools for analog input, analog output, and digital I/O from a variety of PCcompatible data acquisition hardware. The toolbox lets you configure your external hardware devices, read data into MATLAB and Simulink environments for immediate analysis, and fast control action. Data Acquisition Toolbox also, supports Simulink with blocks that enable you to incorporate live data or hardware configuration directly into Simulink models. You can then verify and validate your model against live, measured data as part of the system development process.
Figure 5.3: Data Acquisition Toolbox.
 73 
Chapter (5)
Laboratory Setup and Experimental Results
5.4 System Identification It is difficult develop a transfer function to simulate the BLDC motor drive system which consists of nonlinear components (inverter and logic circuit). The approximate transfer function of such a system may be written as follows: 𝜔(𝑠) 1 = 𝑉𝑐 (𝑠) 𝑎. 𝑆 2 + 𝑏. 𝑆 + 𝑐
(5.1)
Where: 𝜔(𝑠): Rotor speed. 𝑉𝑐 (𝑠): Controlled voltage. a, b and c: transfer function parameters. The parameters of the approximate transfer function may be obtained using MATLAB system identification toolbox as shown in Figure 5.4, which uses the real time measurements for both input (𝑉𝑐 ) and output (𝜔) to develop the second order transfer function of the drive system.
Figure 5.4: System Identification Toolbox.
 74 
Chapter (5)
Laboratory Setup and Experimental Results
5.5 Open Loop Response Results The developed transfer function will be shown in (5.2). 𝜔(𝑠) 1 = 𝑉𝑐 (𝑠) 4.19 ∗ 10−6 𝑠 2 + 0.0041 𝑠 + 1
(5.2)
Figure 5.5 demonstrates the validity of the identified transfer function model to simulate the BLDC motor drive system. It can be noted that the developed transfer function can be simulated the real BLDC motor drive system by 90%. The small differences between the responses of identified transfer function model and the real BLDC motor drive system as a result of the system nonlinearity (inverter, switching losses and bearing friction losses) moreover, the signal noise.
Rotor Speed (RPM)
2000
1500
1000 Real BLDC Motor BLDC Motor Model
500
0 0
1
2
3
4
Time (s) Figure 5.5: Open loop response of identified model and real system.
 75 
5
Chapter (5)
Laboratory Setup and Experimental Results
5.6 Closed Loop Response Results This section illustrates the experimental results of BLDC motor drive system using different types of proposed control techniques.
5.6.1 GABased PID Control This section presents practical implementation for GAbased PID controller with three different sets of parameters. This parameters are obtained offline using the identified transfer function model as shown in Figure 5.6. The initial set of parameters are obtained using ZieglerNichols technique. The second, third and fourth set are obtained using GA according to three different cost functions as explained earlier.
Figure 5.6: The BLDC motor drive system with GA tuning system.
Table 5.1 summarizes the four sets of PID controller parameters which are obtained by ZieglerNichols rule and the GA technique based on three different cost functions. Each set of PID controller parameters will be applied on BLDC motor drive system to investigate any set of PID controller parameters will achieve the best performance.
 76 
Chapter (5)
Laboratory Setup and Experimental Results Table 5.1: Values of PID controller gains.
Optimization Method
𝑲𝑷
𝑲𝒊
𝑲𝒅
Z.N. method
1.5
1
5 × 10−7
GA based on (CF1)
1
1
8 × 10−7
GA based on (CF2)
0.42
3.424
4 × 10−8
GA based on (CF3)
0.61
5.31
3 × 10−8
Figure 5.7 shows the simulation results of the four PID controllers applied on identified T.F. model. It's can be noted that the GAbased PID controller (CF1) has almost the same performance as ZieglerNichols technique because both are based on minimizing the error only, while the GAbased PID controller (CF3) has the best performance compared to the other sets of PID controller parameters.
Figure 5.7: Response the sets of PID controller parameters applied on identified model.
 77 
Chapter (5)
Laboratory Setup and Experimental Results
Table 5.2 summarizes the performance of each set of PID controller parameters. It can be noted in Table 5.2 that the GAbased PID (CF3) has minimum rise and settling time among other techniques and zero overshoot. Table 5.2: Performance of each set using identified model.
Rise Time (sec)
Settling Time (sec)
Max. Overshoot %
Z.N. method
3.3246
6.8310
0
GA based on (CF1)
3.1743
6.2554
0
GA based on (CF2)
0.8113
1.6158
0
GA based on (CF3)
0.5582
1.1824
0
Optimization Method
Figure 5.8: Response the sets of PID controller parameters applied on the real system.
 78 
Chapter (5)
Laboratory Setup and Experimental Results
Figure 5.8 illustrates the experimental results of the four PID controllers applied on real system. It can be noted that the simulation and experimental results are identical approximately and also the GAbased PID controller (CF3) has better performance among other techniques. Table 5.3 summarizes the performance of each set of PID controller parameters using actual BLDC motor drive system. It can be noted in the Table 5.3 that the GAbased PID controller (CF3) has minimum rise and settling time, which gives it the superiority about other techniques. There are small differences between simulation results (Table 5.2) and experimental results (Table 5.3) because of the nonlinearity and the signal noise. Also, the simulation results in the previous chapter as well as the experimental results are agreed well. Table 5.3: Performance of each set using real system.
Rise Time (sec)
Settling Time (sec)
Max. Overshoot %
Z.N. method
3.3235
6.8521
0
GA based on (CF1)
3.776
7.738
0
GA based on (CF2)
0.834
1.759
0.088
GA based on (CF3)
0.53
1.096
0.1
Optimization Method
5.6.2 SelfTuning Fuzzy PID Control This section demonstrates the performance of selftuning fuzzy PID controller practically. The main role of fuzzy control adjusts the PID controller parameters according to real time measurements of the error and the change of error. The initial values of PID controller parameters are the same parameters of GAbased PID controller (CF3) to achieve good results.
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Chapter (5)
Laboratory Setup and Experimental Results
Figure 5.9: Simulink diagram of practical selftuning fuzzy PID controller.
Figure 5.9 shows the Simulink diagram for practical selftuning fuzzy PID controller, while Figure 5.10 illustrates the speed response of BLDC motor drive system using selftuning fuzzy PID controller.
3000
Rotor Speed (RPM)
2500
2000
1500
1000 Reference speed
500
Selftuning Fuzzy PID Controller 0
0
0.2
0.4
0.6
0.8
1 1.2 Time (s)
1.4
1.6
1.8
Figure 5.10: Response of selftuning fuzzy PID controller practically.
 80 
2
Chapter (5)
Laboratory Setup and Experimental Results
5.6.3 Model Reference Adaptive Control This section demonstrates the speed response of BLDC motor drive system using Model Reference Adaptive Control (MRAC). MRAC strategy is used to design the adaptive controller that works on the principle of adjusting the controller parameters so that the output of the actual plant tracks the output of a reference model having the same reference input. Figure 5.11 shows the performance of MRAC under different values of adaptation gain. It can be concluded that increasing the adaptation gain will increase the system overshoot and decreases the rise time (faster response).
Figure 5.11: Response of MRAC at different adaptation gains practically.
 81 
Chapter (5)
Laboratory Setup and Experimental Results
5.6.4 MRAC with PID Compensator This section illustrates the effect adding PID compensator to MRAC. When the adaptation gain increase, the rise time will decrease without increasing in the overshoot. The parameters of PID compensator are the same parameters of GAbased PID controller (CF3). Figure 5.12 demonstrates the performance of a modified MRAC (MRAC with PID compensator) at the above selected adaptation gains. It can be noted that increasing the adaptation gain will cause decrease in rise time (faster response) and slightly increase in the system overshoot.
Figure 5.12: Response of modified MRAC at different adaptation gains practically.
 82 
Chapter (5)
Laboratory Setup and Experimental Results
5.7. Control Techniques Performance Investigation 5.7.1. Speed Regulation Test This section presents a practical comparison between different types of control techniques at speed regulation test to investigate which one will achieve better performance as shown in Figure 5.13. It can be noted that the performance of selftuning fuzzy PID controller is better than GAbased PID controller (CF3) moreover, the performance of MRAC is better than selftuning fuzzy PID controller, but it suffers from high overshooting and high settling time. In case of MRAC with PID compensator can treat the defects of MRAC without affecting on the rapid response. It is clear that the experimental results are agreed with simulation results in previous chapter.
3000
Rotor Speed (RPM)
2500
2000
1500
1000
Reference speed Selftuning Fuzzy PID Controller Model Reference Adaptive Controllr MRAC with PID Compensator GAPID Controller (CF3)
500
0
0
0.2
0.4
0.6
0.8
1 1.2 Time (S)
1.4
1.6
1.8
Figure 5.13: Response of control techniques at speed regulation practically.
 83 
2
Chapter (5)
Laboratory Setup and Experimental Results Table 5.4: Comparison between control techniques.
Control technique
Rise Time (sec)
Settling Time (sec)
Max. Overshoot %
GAbased PID control (CF3)
0.651
1.88
1.5587
Selftuning fuzzy PID control
0.521
1.82
0.73
Model reference adaptive control
0.048
1.79
9.27
MRAC with PID compensator
0.079
1.55
1.02
Table 5.4 summarizes the performance of each controller technique. It can be noted in table 5.4 that MRAC has minimum rise, but it suffers from high overshooting and high settling time. Those defects can be alleviated using the MRAC with PID compensator where it has relatively small rise time, minimum settling time and low overshooting.
5.7.2. Speed Tracking Test The reference speed in some industrial application is changed continuously. This test investigates the performance of each control technique at different commands of reference speed. Figure 5.14 shows the speed response for three different control techniques at different commands of reference speed. It can be noted that the MRAC has faster response among other control techniques (GAPID control and selftuning fuzzy PID control) but it suffer from high overshooting and high settling time. Figure 5.15 illustrates the effect merge the PID compensator with MRAC (modified MRAC) where the high overshooting is eliminated and the faster response is kept.
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Chapter (5)
Laboratory Setup and Experimental Results
4000
Rotor Speed (RPM)
3500 3000 2500 2000 1500 Reference speed Selftuning fuzzy PID controller Model reference adaptive control GAPID controller (CF3)
1000 500 0
0
1
2
3
4
5 6 Time (S)
7
8
9
10
11
Figure 5.14: MRAC with other techniques at different commands of speed.
4000
Rotor Speed (RPM)
3500 3000 2500 2000 1500 Reference speed Selftuning fuzzy PID controller MRAC with PID compensator GAPID controller (CF3)
1000 500 0
0
1
2
3
4
5 6 Time (S)
7
8
9
10
Figure 5.15: Modified MRAC with other techniques at different commands of speed.
 85 
11
Chapter (6)
Conclusions and Recommendations
Chapter Six CONCLUSIONS AND RECOMMENDATIONS
 86 
Chapter (6)
Conclusions and Recommendations
Chapter (6) CONCLUSIONS AND RECOMMENDATIONS 6.1
Conclusions This thesis sought to treat the drawbacks in conventional PID
controller to achieve high performance BLDC motor. The main drawbacks divide into two problems. The first problem is selection the proper parameters. So, in this work Genetic Algorithm (GA) optimization technique is used to determine the proper controller parameters based on three different cost functions. From simulation and experimental results the GA based on third cost function (CF3) achieved the best performance compared to other cost functions. The second problem in conventional PID control is the fixed parameters where it is not suitable for all operating conditions. Also, it cannot deal with the high external disturbances and parameters variation. So, this work sought to design and implement three different advanced control techniques to alleviate this problem. The first technique is selftuning fuzzy PID control where the task of fuzzy control adapts the PID controller parameters online according to the error and the change of error in order to achieve the required speed tracking. The second technique is a model reference adaptive control (MRAC) where the desired performance is expressed in terms of a reference model. MRAC has a fast response as shown in this thesis, but it suffers from high overshooting and high settling time. The third technique is MRAC with PID compensator which can treat the drawbacks of MRAC technique (MRAC) where the faster response is achieved without high overshooting. The simulation and experimental results were identical and show that the superiority for MRAC with PID compensator compared to other control techniques.
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Chapter (6)
Conclusions and Recommendations
6.2 Contributions The studies conducted in this thesis yield the following conclusions:
A new methodology is used to obtain the proper PID controller parameters using GA optimization technique based on three different cost functions to achieve high performance for BLDC motor drive system.
Improving system performance by using the fuzzy logic control which is used to tune the PID controller parameters online according to error and change of error.
The model reference adaptive control (MRAC) is used to investigate the previous two control techniques. The MRAC achieves good performance (fast response) compared to GAbased PID controller and selftuning fuzzy PID controller, but it suffer from high overshooting and high settling time.
A new technique is used to improve the MRAC performance where a PID compensator is added to MRAC to become MRAC with PID compensator which its control action depends on both MRAC and PID compensator. The parameters of PID compensator are the same parameters of GAbased PID controller (CF3).
Develop an approximate transfer function to BLDC motor drive system using MATLAB system identification toolbox.
Practical implementation to four advanced control techniques applied on the laboratory setup of BLDC motor drive system to investigate which one will achieve high performance.
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Chapter (6)
Conclusions and Recommendations
6.3 Future Work The following points are candidates for investigation in the near future
It is possible use new optimization technique to tune the PID controller parameters such as particle swarm optimization (PSO) and ant colony optimization (ACO) may lead to better PID controller parameters to achieve better performance for BLDC motor drive system.
Studying the effect adding fractional order PID (FOPID) compensator to model reference adaptive control (MRAC) instead of PID compensator.
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References
References
 90 
References
References [1]
C.L. Xia, Permanent Magnet Brushless DC Motor Drives and Controls. Singapore: John Wiley & Sons Singapore Pte. Ltd., 2012.
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.
 95 
Appendix A
Appendix A 1) Rule base: A decision making logic which is, simulating a human decision process.
2) Defuzzification: This yields a non fuzzy control action from inferred fuzzy control action.
 96 
Appendix A The input e has 7 linguistic labels and ∆e has 7 linguistic labels Then we have 7×7 = 49 rule base . In this thesis the designer simplify 49 to 25 rule base we will apply the two method without simplification and with simplification and should be the results are equal.
Example 1: Without simplification if e=0.6 F1(e) =0.6(NM) & F1(e)=0.25(NB)
If ∆e=0.6 F2(e) =0.6(PM) & F2(e)=0.25(PB)
 97 
Appendix A Apply the rule base to calculate kp1 If F1(e)=0.25 (NB) Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.25(PB) If F1(e)=0.25 (NB)
Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.6 (PM) If F1(e)=0.6 (NM)
Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.25(PB) If F1(e)=0.6 (NM) Min (F1&F2)= 0.6 (VB)
F2(∆e)=0.6 (PM) Then y1(kp1)=min(0.25,0.6)=0.25 (VB) KP1(the centre of area)= 0.9
Apply the rule base to calculate KI1 If F1(e)=0.25 (NB)
Min (F1&F2)= 0.25 (M)
F2(∆e)=0.25(PB) If F1(e)=0.25 (NB) Min (F1&F2)= 0.25 (M)
F2(∆e)=0.6 (PM)
 98 
Appendix A If F1(e)=0.6 (NM)
Min (F1&F2)= 0.25 (M)
F2(∆e)=0.25(PB) If F1(e)=0.6 (NM)
Min (F1&F2)= 0.6 (M)
F2(∆e)=0.6 (PM) Then y1(ki1)=min(0.25,0.6)=0.25 (M) KI1(the centre of area)= 0.5
Apply the rule base to calculate kd1 If F1(e)=0.25 (NB) Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.25(PB) If F1(e)=0.25 (NB)
Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.6 (PM) If F1(e)=0.6 (NM) Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.25(PB) If F1(e)=0.6 (NM)
Min (F1&F2)= 0.6 (VB)
F2(∆e)=0.6 (PM)
 99 
Appendix A Then y1(kd1)=min(0.25,0.6)=0.25 (VB) Kd1(the centre of area )= 0.9
Example 2: With simplification if e=0.6 F1(e)=0.25(NB)
If ∆e=0.6 F2(e)=0.25(PB)
 100 
Appendix A
Apply the rule base to calculate kp1 If F1(e)=0.25 (NB) Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.25(PB) Then y1(kp1) =0.25 (VB) KP1(the centre of area)= 0.9
Apply the rule base to calculate KI1 If F1(e)=0.25 (NB) Min (F1&F2)= 0.25 (M)
F2(∆e)=0.25(PB) Then y1(ki1)=0.25 (M) KI1(the centre of area)= 0.5
 101 
Appendix A
Apply the rule base to calculate kd1 If F1(e)=0.25 (NB) Min (F1&F2)= 0.25 (VB)
F2(∆e)=0.25(PB) Then y1(kd1) =0.25 (VB) Kd1(the centre of area)= 0.9
Then the results of the two methods are the same .
 102 
Appendix B
Appendix B
 103 