A Dissertation On
An Adaptive, Robust Control of DC motor using Fuzzy-PID Controller Submitted in the partial fulfillment of the requirement for the award of degree of
Master of Technology in
Electrical Engineering (Power Electronics and ASIC Design) Submitted By
RISHABH ABHINAV Reg. No. 2010PE07 Under the Guidance of
Dr. SATYA SHEEL Professor, EED MNNIT
ELECTRICAL ENGINEERING DEPARTMENT MOTILAL NEHRU NATIONAL INSTITUTE OF TECHNOLOGY ALLAHABAD- 211004, INDIA JUNE 2012
माँ को सम पत
Certified that the Thesis entitled “An Adaptive, Robust Control of DC motor
using Fuzzy-PID Controller” submitted by Mr. Rishabh Abhinav in partial fulfillment of the requirement for the award of the Degree of Master of Technology in Electrical Engineering with specialization in Power Electronics and ASIC Design of Motilal Nehru National Institute of Technology, Allahabad has not been submitted elsewhere for the award of any other degree.
Electrical Engineering Department June 2012
(Dr. Satya Sheel) Professor
UNDERTAKING I, Rishabh Abhinav, hereby submit the thesis, as approved by my thesis supervisor Dr. Satya Sheel, Professor, EED, MNNIT Allahabad. I hereby declare that the work presented in this thesis is an authentic work carried out by me during July 2011-June 2012. Where appropriate, I have made acknowledgements to the work of others. I also declare that, to the best of the knowledge and belief, this thesis has not been submitted earlier for the award of any other degree.
June, 2012 Allahabad
RISHABH ABHINAV (Power Electronics and ASIC Design)
ACKNOWLEDGEMENT I am extremely grateful to my thesis supervisor Dr. Satya Sheel Sir, who guided me at every stage of preparation of this dissertation. His support, encouragement, valuable ideas and many excellent comments have been crucial for accomplishing this thesis work. I am truly thankful for his guidance and many interesting analytical discussions. He provided me with all the necessary resources and guidance during the thesis which helped me to complete the thesis successfully. It is a great pleasure to thank all those who helped me directly or indirectly in carrying out this term paper thesis work. I am thankful to our friends for their support. I wish to thank all Electrical Engineering department staffs for their kind co-operation throughout the thesis work. Last but not least, I want to acknowledge my gratitude towards my parents and brother, for their great support, encouragement and kind understanding.
Date:
RISHABH ABHINAV
Place:
(Power Electronics and ASIC Design)
ABSTRACT
DC motor is the most common choice if the wide range of adjustable speed drive operation is desired. The separately excited DC motor has nonlinear dynamics in the field weakening area, and even more the system parameters can vary. Although the conventional cascade PID technique is widely used in DC motor speed and position control, it is not suitable when the system model is complicated or unknown. For a non-linear system, the parameters of PID controller may not give satisfactory performance and therefore need to be tuned frequently. Fuzzy logic may be used to tune the parameters of a PID controller corresponding to the changes that may occur during the system operation or due to data imprecision or uncertainty or due to nonlinearity in behavior. In many studies, the DC motor controllers have been implemented without considering the final control element (FCE), leading to a non-realistic performance. Also, the effect of speed sensor on the motor performance is neglected. In this thesis, a new approach to obtain the adaptive and robust control of DC motor has been discussed in detail. A separately excited dc motor with buck converter as FCE has been considered in this study. The duty cycle of the Buck converter is obtained from PID controller and PWM technique is used for the generation of pulses for converter switch. Ziegler-Nichols method is applied to the combined system of dc motor and buck converter, to get the initial settings of PID controller. Using fuzzy logic, these settings are updated online corresponding to the changes that may occur during system operating conditions. The presented dc drive has been simulated in MATLAB/SIMULINK and results have been discussed. A comparative study of the results has been done for PID controller and adaptive fuzzy-PID controller for both tracking and regulatory type of control problems. The drive has also been simulated for the case of parameters variations or uncertainties in data and it is observed that this approach has a robust performance against disturbance/parameter variations.
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CONTENTS
ABSTRACT CONTENTS LIST OF FIGURES LIST OF TABLES
Chapter 1: Introduction
1
1.1.Literature Survey 1.2.Thesis Organization
Chapter 2: Development of Fuzzy-PID controller
4
2.1.Fuzzy Logic system 2.1.1. Fuzzification 2.1.2. Defuzzification 2.1.3. Fuzzy Inference System 2.1.3.1.Mamdani Inference mechanism 2.1.3.2.Sugeno inference mechanism 2.2.Fuzzy Logic Controller 2.2.1. Assumptions in fuzzy logic controller design 2.3.Fuzzy-PID Controller 2.3.1. Steps involved in designing a Fuzzy-PID controller
Chapter 3: Modeling of dc motor and Buck converter 3.1.Separately excited dc motor 3.1.1. Modeling of Separately excited dc motor 3.2.Buck Converter 3.2.1. State space averaging model 3.2.2. Small Signal model 3.3. Modelling of speed sensor
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14
Chapter 4: Implementation aspect of Fuzzy-PID control of dc motor
22
4.1.Transfer function of DC motor 4.2.Design of buck converter as final control element 4.3.PID controller settings by Z-N method 4.4.Design of fuzzy-PID controller 4.4.1. Fuzzy rules 4.4.2. Fuzzy rule surface 4.4.3. Membership functions 4.4.4. Inference mechanism 4.5.Pulse generation for buck converter switch
Chapter 5: Simulation Results
31
5.1.Tracking Control
5.2. Regulatory control 5.3. Robust control Chapter 6: Conclusion
39
Scope for Future work
40
References
41
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LIST OF FIGURES
Fig. 2.1
Fuzzy logic system
5
Fig. 2.2
Membership function for speed of motor
6
Fig. 2.3
Centroid method of defuzzificztion
7
Fig. 2.4
Mamdani Inference Scheme
9
Fig. 2.5
Sugeno Inference Scheme
10
Fig. 2.6
Fuzzy logic controller
11
Fig. 2.7
PID controller
12
Fig. 2.8
Fuzzy-PID controller
12
Fig, 3.1
DC motor speed control scheme
14
Fig. 3.2
Separately excited DC motor
14
Fig. 3.3
Buck Converter: Circuit diagram
16
Fig. 3.4
Buck Converter: Waveforms
17
Fig. 3.5
Buck Converter: On mode
18
Fig. 3.6
Buck Converter: Off mode
19
Fig. 4.1
Block diagram of Fuzzy-PID controlled, buck converter driven DC motor 22
Fig. 4.2
Fuzzy Rule surface for change in KP
27
Fig. 4.3
Fuzzy Rule surface for change in KI
27
Fig. 4.4
Fuzzy Rule surface for change in KD
28
Fig. 4.5
Membership function for input variables (E and ED)
28
Fig. 4.6
Membership function for output variables ( ∆KP, ∆KI and ∆KD)
29
Fig. 4.7
Pulse generation for IGBT
30
Fig. 5.1
Motor speed for +5% step change in reference speed
31
Fig. 5.2
Motor speed for -5% step change in reference speed
32
Fig. 5.3
Motor speed for +10% step change in reference speed
32
Fig. 5.4
Motor speed for -10% step change in reference speed
32
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Fig. 5.5
Speed Error for +10% step change in reference speed
33
Fig. 5.6
Electromagnetic torue for +10% step change in reference
33
Fig. 5.7
Duty ratio for +10% change in reference speed
33
Fig. 5.8
Armature current for +10% change in reference speed
34
Fig. 5.9
Armature current during starting
34
Fig. 5.10
Pulse generation for buck converter
34
Fig. 5.11
Motor speed with +10% change in load torque
36
Fig 5.12
Motor speed for -10% change in load torque
37
Fig. 5.13
Motor speed for +5% change in load torque
37
Fig. 5.14
Motor speed for -5% change in load torque
37
Fig. 5.15
Motor speed for +2% change in parameters
38
Fig. 5.16
Motor speed for -2% change in parameters
38
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LIST OF TABLES
Table 2.1
Linguistic variables for fuzzy-PID controller
13
Table 3.1
Nomenclature of symbols
15
Table 4.1
DC motor Ratings and Specifications
23
Table 4.2
PID gain settings
24
Table 4.3
Rules for incremental change in KP
26
Table 4.4
Rules for incremental change in KI
26
Table 4.5
Rules for incremental change in KD
26
Table 5.1
Results for PID and Fuzzy-PID controller for Tracking Control
35
Table 5.2
Results for PID and Fuzzy-PID controller for Regulatory Control
37
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CHAPTER 1 INTRODUCTION DC motor is the most common choice if the wide range of adjustable speed drive operation is desired. It is controllable over a wide range with stable and linear characteristics. DC motors are used in many applications such as lathes, drills, boring mills, weaving machines, electric trains, cranes, elevators etc in which either constant speed or constant load operation is required. For tracking control problems DC motor is ideally suited and this can be achieved by varying the motor input voltage easily and over a wide range. In many studies, the DC motor controllers have been considered without modeling of final control element (FCE) such as converters. The underlying hard switching strategy causes unsatisfactory dynamic behavior. In practical applications, the effect of dynamics and nonlinearity of FCE affects the performance of the system. The effect of speed sensor is also often neglected which lead to non-realistic behavior. So it is necessary to consider these for a dependable simulation study of the drive performance. The buck converter is often used as a final control element (FCE) to provide the power to armature to affect the speed of motor as per desired tracking or to offer a good disturbance rejection property under load variations. In this study, the inaccuracies noted in earlier studies have been considered and an adaptive, robust Fuzzy-PID controller has been developed. A buck converter driven separately excited DC motor has been considered for the study. The dc motor model is developed using the dynamic equations and the speed to voltage transfer function is obtained. The transfer function of the buck converter is obtained by considering a small linear region near its operating point. Using the state space averaging model and small signal model the transfer function of the converter is derived. The transfer function of the buck converter has been obtained only to get the initial settings of PID controller, and for simulation a practical model of buck converter is implemented using Sim-Power library of MATLAB. The buck converter is driven by the high frequency PWM signal obtained from the PID controller. The voltage input to the motor is directly proportional to the duty cycle of the buckconverter generated by the controller. Ziegler-Nichols tuning method is applied to the overall EED, MNNIT
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transfer function including dc motor along with buck converter and speed sensor, to get the initial settings of PID controller. Then fuzzy logic is used to update these controller settings online, corresponding to the changes that may occur in the system operating conditions. The dynamics of speed sensor is also considered for more realistic performance. The DC motor is started manually using a starter, to limit the starting current within the safe limit. When motor achieves steady state, the controller is switched-in. Bumpless transfer is achieved while switching from manual to automatic mode. Both tracking control and regulatory control problems have been considered for simulation purpose. The simulation work has been carried out in MATLAB/SIMULINK. Comparative results have been shown for PID controller and FuzzyPID controller. Results are also shown for speed control under system parameters variation i.e. robust control with Fuzzy-PID controller.
1.1. Literature Review DC drives are known to have stable and linear characteristics and dc motors are controllable over a wide range of speed. Therefore, they are the most common choice in the industries for both constant speed and constant load operations. Separately excited DC motors are most suited for tracking control problems [15,17]. In many studies [2,19], the dc motor controllers are designed without the modeling of a final control element. A dc-dc converter, generally buck converter is used as final control element. In [20], authors have conducted a comparative study of buckconverter driven dc motor for PI and fuzzy-PI, PI and LQR controllers. In [9], authors have suggested various control strategies for dc motor using PID and fuzzy-PID controllers. In [14], the authors have proposed a fuzzy logic based speed control of dc shunt motor in which speed control is accomplished by adjusting the field current. The input variables to the fuzzy controller are motor speed and field current, while the field current is also an output variable. The fuzzy system is represented by a fuzzy associative memory (FAM) mapping that associates the input variables to the output variable. In [18], a FLC has been implemented for DC motor speed control on a fuzzy logic microcontroller. Heuristic knowledge is applied to define fuzzy membership functions and rules are modified after initially borrowing the knowledge from a PI controller developed from a simple linear model. A linear model of dc motor has been developed to obtain the initial EED, MNNIT
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parameters of the PI controller. The FLC has been implemented on microcontroller, Motorola 68HC812A4. In [8], fuzzy logic motor speed controller has been implemented with real-time interface using an 8-bit embedded processor. This paper, describes a hybrid approach that implements a generic fuzzy logic algorithm based solely on error. In [4], the authors have presented a Universal fuzzy logic controller using a personal computer. [9], the authors are using PWM technique for controlling the speed of the dc motor. The motor has been considered with a dc-dc converter as FCE. In [10], speed control of a buck converter driven dc motor has been considered using PI and PI type fuzzy controller. Fuzzy logic controllers have been widely used in industries and process control systems. In [4,6], fuzzy-PID controller techniques have been discussed in detail with examples. In [7,21], various techniques for self-tuning PID controllers have been discussed.
1.2. Organization of Thesis This thesis report is organized as follows: Chapter 1 gives brief introduction about the work carried out in this thesis and literature review on DC motor drives using PID and fuzzy-PID controllers. Chapter 2 describes the basic concepts of fuzzy logic, fuzzy logic controller and development of fuzzy-PID controller. Chapter 3 presents the modeling of DC motor and buck converter, and their transfer functions. Chapter 4 describes the implementation aspects of fuzzy-PID controller for DC motor, wherein a separately excited dc motor with practical parameters, is considered for tracking and regulatory control problems. Chapter 5
shows the
simulation results
for
the dc drive
being
simulated
in
MATLAB/SIMULINK. Chapter 6 includes the conclusions of this thesis work. Scope for future work and References are presented in the last.
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CHAPTER 2 DEVELOPMENT of FUZZY-PID CONTROLLER The conventional control techniques require linear and accurate plant model. In many cases, the plant is non-linear or it becomes very difficult to obtain a linear model. Additionally, there may be some uncertainties in the system parameters which lead to imprecision. For such cases, the conventional control techniques do not provide satisfactory performance. Therefore, emerging intelligent techniques have been developed and extensively used to improve or replace the conventional control techniques. These intelligent techniques do not require a precise model. Some of these techniques are:
Fuzzy logic
Neural Network
Particle Swarm Optimization (PSO)
Genetic Algorithm (GA)
Ant Colony Optimization
Out of the above techniques, Fuzzy logic is very popular and is extensively used. Fuzzy logic is conceptually easy to understand. It is tolerant of imprecise data and based on the experience of experts. Fuzzy logic can model nonlinear functions of arbitrary complexity and can be blended with conventional control techniques. Fuzzy control provides a convenient method for constructing non-linear controllers. While conventional controllers depend on the accuracy of the system model and parameters, Fuzzy Logic Controllers (FLCs) use a different approach to control the system operation. Instead of using a system model, the operation of a FLC is based on heuristic knowledge and linguistic description to perform a task. The effect of inaccurate parameters and models are reduced because a FLC does not require a system model. The separately excited DC motor has nonlinear dynamics in the field weakening area, and even more the system parameters can vary. Generally, an accurate model of an actual DC motor is difficult to find, and parameter values obtained from system identifications may be only EED, MNNIT
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approximated values. Although the conventional cascade PID technique is widely used in DC motor speed and position control, it is not suitable for the non-linear systems or when the system model is complicated or unknown. PID controllers can be made adaptive with the help of Fuzzy logic to improve performance.
2.1. Fuzzy Logic system Fuzzy logic was introduced by Zadeh (65), is a mathematical tool for dealing with uncertainties and imprecision in modeling and data available. The fuzzy logic provides an inference structure that enables appropriate human reasoning capabilities. The traditional binary set theory describes crisp events, events that either do or do not occur. Fuzzy logic uses probability theory to explain if an event will occur, measuring the chance with which a given event is expected to occur. The theory of fuzzy logic is based upon the notion of relative graded membership. A fuzzy logic system accepts imprecise data and vague statements and provides decisions. It provides means to model the uncertainty associated with vagueness, imprecision, and lack of information regarding a problem or a plant. The basic elements of a fuzzy logic system, as shown in figure 2.1, are Fuzzifier, Fuzzy inference system, and Defuzzifier.
Fig. 2.1 Fuzzy logic system Input data are most often crisp values. The task of the fuzzifier is to map crisp inputs into fuzzy. Inference system consists of a decision making unit based on knowledge base and rule base. Models based on fuzzy logic consist of “If-Then” rules. The fact following “If” is called a
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premise or hypothesis or antecedent. Based on this fact, one can infer another fact that is called a conclusion or consequent (the fact following “Then”). A set of a large number of rules of the type: IF (antecedent) THEN (consequent) is called a fuzzy rule base. Knowledge base contains the information about the model based on the experience of the experts. Defuzzifier converts inferred fuzzy actions into crisp output action.
2.1.1. FUZZIFICATION Fuzzification is the process where the crisp quantities are converted to fuzzy values. By identifying the uncertainties in the crisp values, the fuzzy values are formed. The conversion of fuzzy values is represented by membership functions. In any practical application, there may be error in the measured variable. This causes imprecision in the data. This imprecision may be represented by membership functions. Thus, fuzzification process involves assigning membership functions to the fuzzy values. For example, speed of dc motor can be considered in several speed bands, identified as membership functions. The shape of universe of speed is shown in fig. 2.2.
Fig. 2.2 Membership function for Speed of motor [14] The range of speed is splitted into low, medium and high. The curves represent membership functions corresponding to various fuzzy variables. These curves differentiate the range of speed, decided by a certain person. Different persons can decide the range differently. The placement of curves is approximated over the universe of discourse. The number of curves and the overlapping of curves are important criteria to be considered while defining membership functions. EED, MNNIT
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2.1.2. DEFUZZIFICATION The fuzzy results generated cannot be used as such to applications; hence it is necessary to convert fuzzy quantities to crisp quantities for further processing. Defuzzification is the process of making inferred fuzzy outputs to crisp value. It is the conversion of a fuzzy quantity to a precise quantity, just as fuzzification is the conversion of a precise quantity to a fuzzy quantity. The output of a fuzzy process can be the logical union of two or more fuzzy membership functions defined on the universe of discourse of the output variable. Defuzzification reduces the collection of membership functions to single sealed scalar quantity. Following are some of the methods for defuzzification:
Max membership principle
Centroid method
Weighted average method
Mean max membership
Among the above methods, Centroid method is the most widely used. It is also called center of gravity or center of mass method. It can be explained by the algebraic expression: ∗
where,
( )=
=
∫ ∫
( ). ( )
membership function for fuzzy set C.
Fig. 2.3 shows the graphical representation of the centroid method of defuzzification.
Fig. 2.3 Centroid method of defuzzificztion EED, MNNIT
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2.1.3. Fuzzy Inference System Fuzzy inference systems (FISs) are also known as fuzzy rule-based systems. Fuzzy inference system consists of a rule base, a database and a decision-making unit. Rule base consists of a number of If-Then rules. Database defines the membership functions of the fuzzy sets used in the fuzzy rules and the decision-making unit performs the inference operations on the rules. FIS formulates suitable rules and based upon the rules, the decision is made. This is based mainly on the concepts of fuzzy set theory, fuzzy IF-THEN rules and fuzzy reasoning. The most important two types of fuzzy inference methods are:
Mamdani fuzzy inference method
Sugeno or Takagi-Sugeno-Kang method of fuzzy inference
The main difference between the two methods lies in the consequent of fuzzy rules. Mamdani method uses fuzzy sets as rule consequent whereas Sugeno method employs linear function of input variables as rule consequent. Mamdani inference expects the output membership functions to be fuzzy set whereas the Sugeno output membership functions are either constant or linear. In Sugeno method, a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. Sugeno controllers usually have far more adjustable parameters in the rule consequent and the number of parameters grows exponentially with increase in number of input variables.
2.1.3.1.
Mamdani Inference Mechanism
This method was introduced by Mamdani and Assilian (74). The concept of Mamdani inference mechanism can be explained with the help of an example explained in fig. 2.4. There are two inputs, x0 and y0. These inputs are mapped into fuzzy numbers by assigning membership functions to them. The fuzzy “AND” is used to combine the membership functions to compute the rule strength. The outputs of all of the fuzzy rules are combined to obtain one fuzzy output distribution. This is usually, but not always, done by using the fuzzy “OR.” .If it is desired to come up with a single crisp output from an FIS, it is obtained from the process of defuzzification.
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Fig. 2.4 Mamdani Inference Scheme [14]
2.1.3.2.
Sugeno Inference Mechanism
The Sugeno fuzzy model was proposed by Takagi, Sugeno, and Kang. A typical fuzzy rule in a Sugeno fuzzy model has the format “IF x is A and y is B THEN z = f(x, y)”, where A,B are fuzzy sets in the antecedent; Z = f(x, y) is a crisp function in the consequent. Usually f(x, y) is a polynomial in the input variables x and y, but it can be any other function that can approximate the output within the fuzzy region specified by the antecedent of the rules. When f is constant, it is a zero order Sugeno fuzzy model. When f(x,y) is a first order polynomial, then it is first order Sugeno fuzzy model and so on. Fig. 2.5 explains Sugeno inference mechanism with an example. EED, MNNIT
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Fig. 2.5 Sugeno Inference mechanism[14]
Advantages of Mamdani Method
It is intuitive.
It has widespread acceptance.
It is well suited to human input.
It is easy to form compared to Sugeno method.
Advantages of Mamdani Method
It is computationally efficient and well suited to mathematical analysis
It works well with linear techniques.
It works well with optimization and adaptive techniques.
It has guaranteed continuity of the output surface.
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2.2. Fuzzy Logic Controller Fuzzy logic controllers are used to reduce the development time or to improve the performance of an existing controller. Fig 2.6 shows the basic construction of a fuzzy logic controller. It consists of a fuzzification unit, a knowledge base and rule based inference system and defuzzication unit.
Fig. 2.6 Fuzzy logic controller
Scaling factors map input/output values to the domain of fuzzy variables. The values of input scaling factors connect input values to suitable rules, and the values of output scaling factors adjust the amplitude of a control action.
2.2.1. Assumptions in a Fuzzy Control System Design A number of assumptions are implicit in a fuzzy control system design. Following basic assumptions are commonly made whenever a fuzzy rule-based control policy is selected.
The plant is observable and controllable: state, input, and output variables are usually available for observation and measurement or computation.
There exists a body of knowledge comprised of a set of linguistic rules, engineering common sense, intuition, or a set of input – output measurements data from which rules can be extracted.
A solution exists.
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The control engineer is looking for a ‘‘good enough’’ solution, not necessarily the optimum one.
The controller will be designed within an acceptable range of precision.
2.3. Fuzzy-PID controller The PID controller is mainly to adjust an appropriate proportional gain (KP), integral gain (KI), and differential gain (KD) to achieve the optimal control performance. Figure 2.7 shows a basic structure of PID controller.
Fig. 2.7 PID controller PID controllers work efficiently with the linear system but for a non-linear system, the parameters of PID controller may not give satisfactory performance and therefore need to be tuned frequently. Fuzzy logic may be used to tune the parameters of a PID controller corresponding to the changes that may occur during the system operation or due to data imprecision or uncertainty or due to nonlinearity in behavior. Fig. 2.8 shows the basic construction of a fuzzy-PID controller.
Fig. 2.8 Fuzzy-PID controller EED, MNNIT
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2.3.1. Steps involved in designing a Fuzzy-PID controller Following steps are involved during the development of a fuzzy-PID controller: Tuning of a crisp PID controller This is the first step involved in the development of a fuzzy-PID controller. The parameters of the PID controllers are tuned as it is done in the conventional controller. This can be done by Zieglar-Nichols method or any other tuning method.
Designing a linear fuzzy controller The first step in designing linear fuzzy controller involves identification of the input and output variables. Input variables are selected as: error between desired and actual values of output (e) and rate of change of error (ė ) and output variables as incremental changes in gain parameters (∆KP, ∆KI and ∆KD). The input and output variables are normalized by using appropriate scaling factors to map them in the domain of fuzzy variables. Universe of discourse of each variable is defined and linguistic label is assigned to each one. The linguistic variables defined in this study are shown in Table 2.1.
NL
Table 2.1 Linguistic variables for fuzzy-PID controller NM NS ZE PS PM
Negative
Negative
Negative
Large
Medium
Small
Zero
PL
Positive
Positive
Positive
Small
Medium
Large
Once linguistic variables are defined, membership functions are assigned to them. Then a rule base is formed by assigning relationship between input and output. Then the inference method is chosen. In this study, Mamdani inference mechanism is considered for the development of the fuzzy-PID controller. The fuzzy output generated from the inference system is defuzzified to obtain a crisp value. Here, Centroid method is chosen for defuzzification. The output value is de-normalized by choosing appropriate scaling factor to adjust the amplitude of control action. The output from the fuzzy controller i.e. ∆KP, ∆KI and ∆KD are combined with the initial PID parameters to update them corresponding to the changes
that occur during system operation. In the next chapter, modeling of DC motor and buck converter has been done and their transfer functions are obtained. EED, MNNIT
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CHAPTER 3 MODELLING and CONTROL of DC MOTOR with BUCK CONVERTER as FINAL CONTROL ELEMENT The control loop shown in fig. 3.1 consists of an armature voltage controlled dc motor with buck converter as final control element (FCE). The duty ratio of the buck converter is controlled according to the error between the desired speed and the actual speed sensed with speed sensor.
Fig. 3.1 DC motor speed control scheme
3.1.
Separately Excited DC Motor
Figure 3.2 shows the configuration of a separately excited dc motor with armature voltage V and constant field flux supplied from a fixed voltage source Vf.
Fig 3.2 Separately excited dc motor EED, MNNIT
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3.1.1. Modelling of separately excited dc motor [3] In this section, transfer function model of a separately excited dc motor has been derived with the assumption that field is maintained constant and any distortion that may arise in field flux is neglected. The effect of armature reaction has also not been taken into the consideration. Table 3.1 shows the nomenclature of symbols used in the derivation. Table 3.1 Nomenclature of symbols La
Armature Inductance
Va
Motor terminal voltage
Ra
Armature Resistance
ia
Armature current
J
Moment of Inertia
E
Back EMF
Coefficient of Viscous Friction
T
Electromagnetic Torque
Bm
Motor Speed TL
Armature circuit time constant
Load Torque
K
Torque constant
The voltage equation of the armature circuit under transient is given by:
or,
V =R i + L
+ E
(3.1)
V =R i + L
+ Kω
(3.2)
From the dynamics of motor- load system
J
= T − T − Bω
(3.3)
here,
T = Ki
(3.4)
so,
J
(3.5)
= Ki − T − Bω
Differentiating the above equation (3.5):
K
=J
+B
+
(3.6)
Substituting for di /dt into above equation, and rearranging the terms gives:
+ 1+
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+
(
)
ω =
−
T +
(3.7)
Page 15
or,
τ
+ 1+
+
ω =
−
T +τ
(3.8)
where,
τ =
(3.9)
τ
=
(3.10)
τ
=(
(3.11)
)
Taking Laplace transform of equation (3.8):
( )= ( )
( ⁄
)
−
( )
(3.12)
Equation 3.12 represents the motor speed as a function of input voltage and load torque.
3.2.
Buck Converter
A buck converter is a dc-dc step down converter. It consists of dc input voltage source Vd, controlled switch S, diode D, filter inductor L, filter capacitor C, and load resistance R. The circuit diagram of a buck converter is shown in the fig 3.3.
Fig 3.3 Buck Converter: circuit diagram The output voltage of the buck converter is given by:
=
(3.13)
where, D = duty cycle of the switch EED, MNNIT
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Fig. 3.4 shows the waveforms for a buck converter in continuous conduction mode. During this mode, the current in the inductor never falls to zero maintaining a unidirectional flow.
Fig 3.4 Buck Converter: waveforms
3.2.1. State space Averaging model [1] The transfer function of the buck converter is obtained by considering a small linear region near the operating point. In state space averaging model both the modes of operation (i.e. switch ON and OFF modes) are considered and an averaging model is developed so as to take both modes into consideration.
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ON Mode: When switch is ON, the diode behaves like an open circuit. The circuit configuration is shown in Fig 3.5.
Fig 3.5 Buck converter circuit: ON mode The dynamic equations can be written as:
= =
or,
= =
or,
−
(3.14)
−
(3.15)
−
(3.16)
−
(3.17)
So the state-space form in the ON mode of the buck converter will be: 0 = 1
̇ ̇
̇= =
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−1 −1
+
1 0
+ =
(3.18)
(3.19)
=
= [0
1]
(3.20)
Page 18
OFF Mode: The diode behaves like a short-circuited path when switch is in OFF mode and the input source appears disconnected from the circuit. Fig 3.6 shows the circuit diagram of the buck converter in OFF mode.
Fig 3.6 Buck Converter circuit diagram: OFF mode The dynamic equations in this mode can be written as:
=−
(3.21)
=−
or,
(3.22)
= =
or,
−
(3.23)
−
(3.24)
So the state-space form in the OFF mode of the buck converter will be: −1 −1
0 = 1
̇ ̇ ̇= =
+
0 0
+ =
(3.25) (3.26)
=
= [0
1]
(3.27)
Let the duty ratio of converter to be d. Then one can define: =
+
(1 − )
(3.28)
=
+
(1 − d)
(3.29)
C = C + C (1 − d)
(3.30)
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Page 19
In case of buck converter: 0 −1 L A=A =A = 1 1 C − RC 1 L d B=B d= 0 C = C = C = [0
1]
(3.31)
(3.32) (3.33)
3.2.2. Small Signal Model Using small signal model of the converter the input transfer function and the control transfer can be obtained. ẋ = Ax + Bu
(3.34)
ẋ = [A + A (1 − d)]x + [B + B (1 − d)]u
(3.35)
y = Cx
(3.36)
y = [C + C (1 − d)]x
(3.37)
Considering small perturbations in duty-ratio and input voltage, as: d =D+d Hence, x = X + x
v = V +v and
v=V+v
(3.38) (3.39)
Under steady-state condition, Ẋ = AX + BV = 0
(3.40)
By putting these values into above equations with assumption that the products of perturbations are neglected, it is possible to obtain ẋ = Ax + Bv + Fd
(3.41)
F = [(A − A )X + (B − B )V
(3.42)
v = cx + (C − C )Xd
(3.43)
where,
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Control Transfer Function would be given by: ( ) ( )
= c(sI − A) F
(3.44)
Substituting the values, the buck converter transfer function is obtained as: or,
( ) ( )
=
(3.45)
Equation 3.45 represents the ratio of buck-converter voltage to the control input duty cycle.
3.3. Modelling of Speed Sensor There are various types of sensors being used to sense the speed of a motor such as tachogenerator, Hall Effect sensor, eddy current sensor etc. For the purpose of simulation, a speed sensor can be considered as a first order filter with the following transfer function:
H(s) =
τ
(3.46)
where, τ = Sensor time constant The time constant of the sensor depends on the time constant of the system and is generally larger than it.
In the next chapter, a separately excited dc motor with practical parameters has been considered for the case study. A suitable buck converter is designed to meet the requirement of the motor. The fuzzy-PID controller has been designed and implemented on the motor.
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Page 21
CHAPTER 4 IMPLEMENTATION ASPECTS OF FUZZY PID CONTROLLER FOR DC MOTOR In this chapter, an adaptive, robust control of DC motor has been developed using Fuzzy-PID controller. A buck converter driven separately excited DC motor has been considered for both tracking control and regulatory control problems. The developed fuzzy-PID controller is also capable of controlling dc motor under parameters variation. The overall concept can be understood with the help of the block diagram of the control scheme presented in fig 4.1.
Fig. 4.1 Block diagram of Fuzzy-PID controlled, buck converter driven DC motor
4.1. Transfer function of DC motor For the conduct of a case study of the performance of the proposed fuzzy-PID approach, a separately excited dc motor with following ratings and specifications has been used in simulation.
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Page 22
Table 4.1 DC motor Ratings and Specifications Rated Power
5 HP (3.73 KW)
Rated Voltage
240 V
Rated Speed
1750 rpm (183.26 rad/s)
Rated Torque, TL
20.345 N-m
Moment of Inertia, J
0.2215 Kg/m2
Coefficient of Viscous Friction, B
0.002953 N-m-sec
Armature Resistance, Ra
0.2592 Ω
Armature Induction, La
0.028 Henry
Torque Constant, K
0.002953 V/rad/sec
The transfer function of the separately excited DC motor derived in Chapter 3 is given by: ω (s) = V(s)
(K⁄R ) τ J s τ +s 1+ τ
+τ
1
− T (s)
1 + sτ τ J s τ +s 1+ τ
+τ
1
where, τ =
;
τ
= ;
τ
=(
)
By substituting the parameters from Table 4.1, the speed of motor can be expressed as a function of input voltage and load torque as: ω (s) = V(s)
1647.92 0.48s + 45.14 − T (s) [ s + 92.708s + 1696.76 ] [ s + 92.708s + 1696.76 ]
4.2. Design of Buck Converter as final control element [12] The design of buck converter is based on the output voltage (V), maximum allowed ripple in the output voltage (△Vc) and maximum allowed ripple in the output current (△IL) [9]. The buck converter parameters i.e. inductance and capacitance can be derived as: L=
DV (1 − D) f∆I
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C=
DV (1 − D) 8Lf ∆V
Page 23
For continuous conduction of the converter there must be a check, which can be performed by verifying the values of inductance and capacitance. i.e. (1 − D)R 2f (1 − D) C> 16Lf L>
Based on the specifications to be met, following values have been taken: Vd = 480V
D = 0.5
f = 10 KHz
∆I = 0.05 Amp
∆V = 0.5 Volts
The values of inductor and capacitor are calculated as: L = 240 mH
C = 1.25 µF
The full load converter current for a given load of 5 HP (3.73 KW), is given by: I
=
R=
= 15.53 Amp = 15.44
The Buck converter transfer function obtained in chapter 3 is given by: V LC = d(s) s + s + 1 RC LC v(s)
Substituting above values, the buck converter transfer function is obtained as: v(s) d(s)
=
1.6 × 10 s + 5.18 × 10 s + 3.33 × 10
The transfer function of speed sensor has been considered as: H(s) =
1 1 + sτ
where, τ = Sensor time constant = 0.05 sec
The overall speed to voltage transfer function of the dc motor along with buck converter and speed sensor is obtained by multiplying the three transfer functions and is given by: G(s). H(s) =
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2.637 × 10 s + 5.189 × 10 s + 8.137 × 10 s + 3.97 × 10 s + 5.67 × 10 s + 2.825 × 10
Page 24
4.3. PID controller settings by Z-N method Ziegler-Nichols method is an empirical approach to determine the PID controller settings for a system. It is perfected over a long period in process control systems, and used successfully in large number of industrial problems. The initial setting of the controller is obtained by applying Ziegler-Nichols method to the overall transfer function of the system. The three parameters KP, KI and KD are obtained using the PID tuning software developed by Sheel and Gupta. The PID gain settings are given in table 4.2. Table 4.2 PID Gain settings Kp
Ki
0.015
0.4
Kd 1.5× 10
4.4. Design of Fuzzy-PID controller The fuzzy logic is used to update the initial controller settings on-line, corresponding to the changes that may occur in the system operating conditions. A linear fuzzy logic controller has been designed involving the steps discussed in chapter 2.
4.4.1.
Fuzzy Rules
The philosophy of generating rules for fuzzy-PID can be different according to the requirement. Here these rules have been created by considering the concept given by Kha and Ahn, in which the rule surfaces are given for PID tuning. Using these rules, the fuzzy rule tables have been developed. The inputs of the fuzzy logic are the speed error (e) and derivative of error( ̇ ). Using these inputs and after applying the fuzzy rules, it provides the outputs ∆KP, ∆KI and ∆KD, which are used to update the PID controller gains online. A total of 49 rules have been used in this study. Each rule uses an If – Then logic of the following form: If e is PL and ̇ is PL then ∆KP is PL, ∆KI is NL and ∆KD is NL. Table 4.3-table 4.5 shows the fuzzy rules for ∆KP, ∆KI and ∆KD
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Page 25
Table 4.3 Rules for incremental change in KP
/ ̇
NL
NM
NS
ZE
PS
PM
PL
NL
PL
PL
PL
PL
PL
PL
PL
NM
PS
PM
PM
PM
PM
PM
PS
NS
ZE
ZE
PS
PS
PS
ZE
ZE
ZE
NL
NS
ZE
ZE
ZE
NS
NL
PS
ZE
ZE
PS
PS
PS
ZE
ZE
PM
PS
PM
PM
PM
PM
PM
PS
PL
PL
PL
PL
PL
PL
PL
PL
Table 4.4 Rules for incremental change in KI
/ ̇
NL
NM
NS
ZE
PS
PM
PL
NL
NL
NL
NL
NL
NL
NL
NL
NM
NM
NL
NL
NL
NL
NL
NM
NS
PM
ZE
NM
NL
NM
ZE
PM
ZE
PL
PM
PS
NL
PS
PM
PL
PS
PM
ZE
NM
NL
NM
ZE
PM
PM
NM
NL
NL
NL
NL
NL
NM
PL
NL
NL
NL
NL
NL
NL
NL
Table 4.5 Rules for incremental change in KD
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/ ̇
NL
NM
NS
ZE
PS
PM
PL
NL
NL
NL
NL
NL
NL
NL
NL
NM
ZE
NS
NM
NM
NM
NS
ZE
NS
PS
ZE
ZE
ZE
ZE
ZE
PS
ZE
PL
PL
PM
PS
PM
PL
PL
PS
PS
ZE
ZE
ZE
ZE
ZE
PS
PM
ZE
NS
NM
NS
NM
NS
ZE
PL
NL
NL
NL
NL
NL
NL
NL Page 26
4.4.2. Fuzzy Rule surface Fuzzy rule surface shows the region in which the fuzzy rules have been made more effective. Fuzzy rules can be understood by the fuzzy rule surface, it shows the values of PID gains at the various points of inputs. The inputs and outputs are normalized to -1 to +1. Normalization of e and ė is done by dividing them by their largest value obtained during the operation with conventional PID controller. Rule surface is helpful to see the effect of change in input to output in each direction (positive and negative). In other words how the output changed corresponds to change in input. Figures (4.2-4.5) show the rule surfaces for ∆KP, ∆KI and ∆KD.
Fig. 4.2 Fuzzy Rule Surface for change in KP
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Fig. 4.3 Fuzzy Rule Surface for change in KI
Fig. 4.4 Fuzzy Rule Surface for change in KD It is clear that near error zero region (or near stable region) most of the fuzzy rules are made. The rules are almost same for all values of rate of change of error (ė ) as error increases in either direction.
4.4.3. Membership function Triangular membership functions have been chosen for inputs and outputs. Mamdani type of fuzzy inference system has been adapted for controller designing. Centroid method is chosen for defuzzification. Figures (4.5-4.6) show the membership functions for e, ė , ∆KP, ∆KI and ∆KD.
Fig. 4.5 Membership function for input variables (e and ė ) EED, MNNIT
Page 28
Fig. 4.6 Membership function for output variables (∆KP, ∆KI and ∆KD)
4.4.4. Inference Mechanism In this study, Mamdani type of fuzzy inference system has been implemented and centroid method is applied for defuzzification. This process is achieved using Fuzzy logic toolbox in MATLAB. The output variables ∆KP, ∆KI and ∆KD are de-normalized to fit in the desired range of control action. The final control action is achieved by the following equations: KP1 = KP + ∆KP KI1 = KI + ∆KI KD1 = KD + ∆KD where, KP, KI, KD are the initial values of gain parameters obtained from Z-N method, ∆KP, ∆KI, ∆KD are fuzzy outputs; and KP1, KI1, KD1 are the settings of the PID controller being updated online corresponding to the changes that occur during the system operation. The output of the PID controller is given by: u ( t) = K . e + K
edt + K . ė + u(0)
where, u(0) = initial controller output when system was under steady state. The output of the controller is saturated in the range of 0 to 1 which corresponds to the duty ratio of the buck converter.
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Page 29
4.5. Pulse generation for buck converter switch IGBT has been used as the controlled switch for the buck converter. The gating pulses for IGBT are generated using pulse width modulation (PWM) technique. Fig. 4.7 explains the PWM technique.
Fig. 4.7 Pulse generation for IGBT The output of fuzzy-PID controller (duty ratio) is the modulating signal and high frequency saw tooth signal (10 KHz) has been chosen as career signal. The two signals are compared and whenever the modulating signal is greater than the career signal, the output is high, else low. Hence, the gating pulses are generated which controls the output voltage of the buck converter. Armature voltage control method is applied to the dc motor for controlling the speed. The armature voltage which is output of the buck converter varies according to the duty cycle of converter. The duty cycle, is controlled by the PID/fuzzy-PID controller, input to which is the error between the desired and actual speed and its derivative. Thus the closed loop operation of the dc motor is performed. The dc drive is simulated in sim-power system library of MATLAB/SIMULINK and various cases of regulatory and tracking control problems have been considered. The drive has also been observed for robust control against the parameter variations. The simulation results have been shown in the next chapter and the results have been discussed.
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Page 30
CHAPTER 5 SIMULATION RESULTS
The motor considered in section 4.1 has been simulated in MATLAB/SIMULINK for tracking control as well as regulatory control. Motor is started normally under full load, by using the starter to keep the starting current within limits of safety and when motor achieves steady state; the controller is switched-in. Following are the results of case study shown for both the reference speed tracking control and load disturbance rejection control.
5.1. Tracking control In this problem the tracking performance of the system with controller in closed loop has been investigated. It is also known as Reference speed tracking control. The motor has been put on full load condition and the motor is running in steady state at its rated speed. It is desired to study the performance of the drive for a change in the desired speed. Here the reference speed changes by ±5% and ±10% of its rated value of 1750 rpm have been considered and the performance evaluated. All the changes have been considered to be sudden or step change. Fig. 5.1- fig. 5.10 show various simulation results for tracking control problem.
2500
Motor Speed (rpm)
Fuzzy-PID 2250
PID
2000
1750
1500
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.1 Motor speed for +5% step change in reference
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Page 31
Motor Speed (rpm)
2000 1900
PID Fuzzy-PID
1800 1700 1600 1500
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.2Motor speed for -5% change in reference speed
Motor Speed (rpm)
2500 Fuzzy-PID 2250
PID
2000
1750
1,500
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
Fig. 5.3 Motor speed for +10% step change in reference speed 2000
Motor Speed (rpm)
1900 Fuzzy-PID PID
1800 1700 1600 1500 1400 1300 1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig 5.4 Motor speed for -10% change in reference speed
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Page 32
200 150
Fuzzy-PID PID
Error (rpm)
100 50 0 -50 -100 -150
1
1.05
1.1
1.15
1.2 1.25 Time(sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.5 Speed Error for +10% step change in reference speed
Electromagnetic Torque (N-m)
100 Fuzzy-PID PID
80 60 40 20 0
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.6 Electromagnetic torue for +10% step change in reference
2 1.5
Duty ratio
1 0.5 0 -0.5 -1
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.7 Duty ratio for +10% change in reference speed
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Page 33
Armature Current (Amp)
50 40
Fuzzy-PID PID
30 20 10 0
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.8 Armature current for +10% change in reference speed
Armature current (Amp)
40 35 30 25 20 15 10 5 0 0
0.1
0.2
0.3
0.4
0.5 Time (sec)
0.6
0.7
0.8
0.9
1
Fig. 5.9 Armature current during starting 2 0 -2 0
0.1
0.2
0.3
0.4
0.5 Time (sec)
0.6
0.5 Time (sec)
0.6
0.7
0.8
0.9
1 x 10
-3
2 1 0 -1 0
0.1
0.2
0.3
0.4
0.7
0.8
0.9
1 x 10
-3
Fig. 5.10 Pulse generation for buck converter
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Page 34
Table 5.1 Results for PID and Fuzzy-PID controller for Tracking Control
Change in Reference Speed
+5%
-5%
+10%
-10%
Percentage
PID
4.08
2.7
10.2
4.21
overshoot
Fuzzy-PID
3.29
2.2
6.83
3.14
PID
0.0426s
0.0513s
0.0384
0.0584s
Fuzzy PID
0.0315s
0.0493s
0.0295s
0.0487s
2% Settling
PID
0.0612s
0.0235s
0.0834s
0.0738s
time
Fuzzy-PID
0.0492s
0.0156s
0.0824s
0.0463s
Rise time
Table 5.1 shows the comparative analysis of time domain performance of both PID and fuzzyPID controller under reference speed tracking problem. It is observed that the maximum overshoot is less than 5 % for both the controller when ± 5% change in reference speed is applied and it is less than 10% when step change of + 10% is applied to the reference. Steady state error reaches to zero with the fuzzy-PID controller. It can be clearly seen that the presented controller improves the performance of the drive. Rise time has been improved up to 35% in case of +5% change in reference and 2% settling time improves up to a factor of 69% in case of -10% change in speed. In all other cases, there is considerable improvement in both rise time and settling time with the presented fuzzy approach. Fig. 5.7 shows the control effort of the controller in which it can be observed that the duty ratio is maintained at constant value before and after applying changes in the reference. Fig. 5.9 shows the starting current of the motor when started using starter. It can be seen that the starter keeps the armature current within the safe limits. Fig. 5.10 shows pulse generation for buck converter by using PWM technique.
5.2. Regulatory Control In this study the motor has been started and full load applied when it reaches at steady state, then following cases have been taken into consideration:
Change in the load by ±5%
Change in the load by ±10
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Page 35
In each case the load change has been considered as sudden or step change. It is also called disturbance rejection problem as the controller is expected to control the system such that, when a disturbance enters the system, the transient in speed due to the disturbance is minimized and the drive system regains the steady state every such occasion. Fig.5.11- fig.5.14 show motor speed response under the influence of load disturbance. 2000
Motor Speed (rpm)
1950
Fuzzy -PID PID
1900 1850 1800 1750 1700 1650 1600
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.11 Motor Speed with +10% change in load torque
2000
Fuzzy-PID PID
Speed (rpm)
1900
1800
1700
1600
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig 5.12 Motor speed for -10% change in load torque
Motor Speed (rpm)
2000 Fuzzy -PID PID
1900
1800
1700
1600
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.13 Motor speed for +5% change in load torque EED, MNNIT
Page 36
Motor Speed (rpm)
2000 Fuzzy-PID PID
1900
1800
1700
1600
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig. 5.14 Motor speed for -5% change in load torque Table 5.2 Results for PID and Fuzzy-PID controller for Regulatory Control
Change in Load Torque
+5%
-5%
+10%
-10%
Percentage
PID
0.77
0.92
1.08
1.17
overshoot
Fuzzy-PID
0.6
0.72
0.54
0.88
Load disturbance
PID
0.041s
0.048s
0.055s
0.052s
Rejection time
Fuzzy-PID
0.032s
0.035s
0.045s
0.048s
Table 5.2 shows the results for both types of controller under regulatory control. It is observed that the maximum overshoot due to introduction of load disturbance in the system in all the four cases considered, is less than 2% for both the controllers. The load disturbance rejection time is less than 0.06 seconds in all the cases. The performance of the drive improves when fuzzy-PID controller is applied. The maximum overshoot is less than 1% by fuzzy-PID approach. Disturbance rejection time is less than 0.35s when ±5% change in load is applied and is less than 0.05 s in case of ±10%.
4.3. Robust control The system parameters such as armature resistance and inductance may vary under certain physical conditions viz. change in temperature or there may be some uncertainty in parameter values. These variations may be small, but may disturb the system steady state equilibrium. Therefore a robust control is required against these variations and uncertainties. A step change of ± 2% has been considered in armature resistance and inductance and the motor speed response for both cases are shown in fig.5.16 and fig.5.17 respectively.
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Page 37
1800 Fuzzy-PID
Motor Speed (rpm)
1780 1760 1740 1720 1700
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
Fig.5.15 Motor Speed with +2% change in parameters
Motor Speed (rpm)
1800 Fuzzy-PID
1780 1760 1740 1720 1700
1
1.05
1.1
1.15
1.2 1.25 Time (sec)
1.3
1.35
1.4
1.45
1.5
Fig.5.16 Motor Speed with -2% change in parameters The above figures show the speed response of the motor when ±2% change is made in the armature resistance and inductance value. It can be observed that the fuzzy- PID controller maintains constant speed of the motor in case of parameter variations or uncertainties in data. The controller does not allow the system to deviate from its desired output as overshoot in each case is less than 1%. From the above results, it clear that the presented fuzzy-PID approach improves the performance of the drive system in each of the cases considered.
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Page 38
CHAPTER 6 CONCLUSION
In this thesis work, an adaptive and robust controller for DC drive has been simulated and results have been shown. Both control problems (tracking and regulatory) have been discussed. It becomes necessary to consider the final control element when the practical study of any system has to be performed. It is clear that the final control element changes the system dynamics and non-linearity also affects the system response in each case. In this regard it can be said that the study about to control any plant is incomplete and incorrect if we neglect the final control element (FCE). Control of dc drive has been studied with realistic PID controller and results show the effect of FCE. Fuzzy adaptation has been used to tune the PID gains in real time or online, which improves the performance of the drive. Comparative results have been shown for PID controller and adaptive fuzzy-PID controller for both tracking and regulatory type of control problems. In tracking control problem, zero steady state error is achieved with the presented fuzzy-controller. In regulatory type of problem also, the overshoot is minimum. The performance of fuzzy-PID controller is better than the conventional PID controller as the presented controller allows less overshoot in the system and the response settles fast. This configuration of controller has also been observed to have robust performance against parameter variations and uncertainties. Under this situation, the controller does not allow the system to deviate much from its reference value. Thus it can be concluded that the presented fuzzy-PID controller efficiently controls the buckconverter driven dc motor. Due to its adaptive nature, it improves the closed loop performance of a DC drive.
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Page 39
SCOPE FOR FUTURE WORK
Following points can be brought out for future work: 1. The presented DC drive can be implemented on hardware with PC based controller to achieve real time control. 2. The DC drive can be investigated in discrete time to get an improved digital control.
EED, MNNIT
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REFERENCES
[1] A. Simon, O. Alejandro, Power-Switching Converters, Chapter-6, continuous-time modeling of switching converters, Third Edition, CRC Press. [2] C. K. Lee, “W. H. Pang, Adaptive Control to Parameter Variations in a DC Motor Control System Using Fuzzy Rules”, Intelligent Systems Engineering', 5-9 September 1994, Conference Publication No. 395, IEE. [3] G. K. Dubey, Fundamentals of Electrical Drives, Second Edition, Narosa Publishing House, (2001), pp. 75-76 [4] I-Hai Lin, P.; Ellsworth, C.; “Design and Implementation of A PC-Based Universal Fuzzy logic controller system” International IEEE/IAS Conference on industrial Automation and Control: Emerging Technologies,1995,pp 399-408 [5] Ibrahim A M, “Fuzzy Logic for Embedded Systems Applications”, 2004, Elsevier Science (USA), pp 73-79 [6] Kha N B & Ahn K K, “Position Control of Shape Memory Alloy Actuators by Using Self Tuning Fuzzy PID Controller”, First IEEE Conference on Industrial Electronics and Applications, 2006. [7] Mann G K I, Hu B G, and Gosine R G, “Two-Level Tuning of Fuzzy PID Controllers”, IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, vol. 31, No. 2, April 2001, pp. 263-269 [8] Mountain Jeffrey R., “Fuzzy Logic Motor Speed Control with Real-Time Interface using an 8-bit Embedded Processor”, 42nd South Eastern Symposium on System Theory, March 7-9, 2010, pp 307-312 [9] Muruganandam M. And Madheswaran M, “Modeling and Simulation of Modified Fuzzy Logic Controller for Various Types of Dc Motor Drives”, International Conference on Control, Automation, Communication and Energy Conservation -2009, 4th-6th June 2009. [10]Oscar M, Roberto S, Patricia M, Oscar C,Miguel Á P, Iliana M M, “Performance of a Simple Tuned Fuzzy Controller and a PID Controller on a DC Motor”, Proceedings of the 2007 IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), pp 532,537 [11] Raja Ismail, R. M. T.; Ahmad, M. A. and Ramli,M. S. “Speed control of buck-converter driven dc motor based on smooth trajectory tracking” 2009 Third Asia International Conference on Modelling & Simulation, pp.97-101. [12] Rashid M H, “Power Electronics Circuits, Devices and Applications”, Third Edition, Pearson Prentice Hall, pp. 186-190 [13] Ross Timothi J. “Fuzzy logic with Engineering Applications”, Third Edition, John Wiley & Sons,2010. [14] S. Shivanandam, S. Sumathi, S.N.Deepa, “Introduction to Fuzzy logic using MATLAB”, Springer 2007 [15] Saneifard, S.; Prasad, N.R.; Smolleck, H.A.and Wakileh, J.J. “Fuzzy-logic-based speed control of a shunt DC motor” IEEE Transactions on Education, Vol. 41 , NO. 2, May 1998, pp: 159 – 164. [16] Sheel S, Chandkishore R. and Gupta O, “Speed Control of DC drive using MRAC Technique”, International Conference on Mechanical and Electrical Technology, 10-12 September, 2010, Singapore, pp. 135-139. EED, MNNIT
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[17] Sheel S and Gupta S, “Advanced techniques of PID controller tuning–development of a toolbox”, First International conference on Control, Instrumentation and Mechatronics CIM ‘07 at Persada Johor, Malaysia. [18] Thadiappan K and Bellamkonda R, “A Fast-Response DC Motor Speed Control System”, IEEE Transactions on Industry Applications, vol. IA-10, no. 5, September/October 1974, pp 843851. [19] Tipsuwan, Y. and Mo-Yuen Chow; “Fuzzy logic microcontroller implementation for DC motor speed control” The 25th Annual Conference of the IEEE Industrial Electronics Society, 1999.IECON '99 Proceedings vol.3, pp 1271 - 1276 [20] Vineet Kumar, A. P. Mittal, Parallel Fuzzy P + Fuzzy I + Fuzzy D Controller: Design and Performance Evaluation, International Journal of Automation and Computing, 7(4), November 2010, 463-471. [21] Weerasooriya S & Sharkawi M.A., “Development and Implementation of Self-Tuning Controller for DC Motor”, IEEE Transactions on Energy Conversion, Vol.5, No.1, March 1990 pp 122-128.
EED, MNNIT
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BIODATA
Name
:
Rishabh Abhinav
Father’s Name
:
Sri Ashok Kumar
D.O.B.
:
November 23rd, 1987
Address
:
C/O Karmveer Shiromani, Lodi Katra, Patna City, Patna-800008, Bihar
Email
:
[email protected]
Contact No.
:
+91-9336548352
Area of Interest
:
Electric motor Drives, Control Theory
Publication
:
Paper submitted in IEEE International Conference on Power Electronics, Drives and Energy systems (PEDES 2012)
EED, MNNIT
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