Driven Variable Speed Drive (PWM Driven VSD) of an induction motor by using state space control method, focusing at the wide range of speed response.
Modeling and Simulation of PLC-based PWMDriven Variable Speed Drive via State-Space Approach Muhammad Kamarul Baharin, Nordin Saad, Taib Ibrahim and Handy Ali Munir Department of Electrical & Electronic Engineering Universiti Teknologi PETRONAS Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia. state-space control is due to its wide application in various Abstract— Intelligent control has contributed great benefits to industry in terms of increasing efficiency and productivity of industrial processes. Programmable Logic Controller (PLC) based controller is one of the control device used in industrial automation drive applications, the important aspect is to control speed of an induction motor in the presence of variable load. The plant model in this project is developed using MATLAB/Simulink and the aim is to simulate and analyze the appropriate control technique suitable for implementation onto the PLC to perform real-time implementation of the VSD (variable speed drive) control. This paper presents the work conducted in analyzing, evaluating and improving a PLCbased intelligent controller for a Pulse Width Modulation Driven Variable Speed Drive (PWM Driven VSD) of an induction motor by using state space control method, focusing at the wide range of speed response. The results show that it is possible to archive a consistent control from low till high speed range. Keywords-variable speed induction motor, state space
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I.
drive,
PLC-Based
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INTRODUCTION
Speed Drive (VSD) applications are extremely used in the industry to control wide range of speed and torque for motors, manufacturing process, machines, pumps, rolling mills etc. [1]. VSD increases the productivity in terms of quality or product system efficiency thus reduces operating cost [2]. VSD is a better alternative compared to conventional control based on mathematical model due to its complexness and not easy to be determined. It requires having the parameters of the motor itself in order to make the model for the specified motor which is not preferred. In this work, the VSD induction motor control would be implemented via V/Hz (voltage to frequency ratio) control, similar to the work reported in [3]. ARIABLE
The issue addressed in [8, 25] is to find a suitable control method and controller that could possess better dynamic performance compared to the conventional schemes which does not require explicit knowledge of motor and load dynamics thus needs to be explored for further improvement. This project explores into state-space approach to improve the controller’s performance reported in [8] where the author uses Ziegler Nichol’s approach. The selection of
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classes of systems such as multiple-input, multiple-output systems and nonlinearities. PLC proves to be efficient and reliable in applications that involve sequential and continuous control [4] that successfully implements a fuzzy control algorithm onto basic PLC for PWM-Driven motor control at constant V/Hz ratio. As a continuation, this project aims to focus on the development of control technique to improve the controller’s performance. The main objective of this project is to ensure an efficient operation of a VSD system, able to operate in wide range of speed and load conditions. The specific objective of the work presented in this paper is to improve the system’s performance in a wider speed range, from low until high threshold speed, using state-space approach. II.
BACKGROUND
This part explains some background related to this research to provide a general understanding on what is the basis of the study and also the control approach to be used. A. Intelligent Control Intelligent control is a part of automatic control discipline which has made great contribution to science and technology, and quality of life. It is a kind of automatic control that can drive self-control intelligent machines to reach its goals with least or even with no human interaction. Intelligent control is an important topic of the research area for the development of science of automatic control [5]. Control means making the plant respond to inputs in a desired manner. Table 1 shows the specifications of the best performance for a control system to run a plant. The desired behavior in response should meet the expected specifications, highly stable, obtain fast response time, high robustness, low dynamic interaction and low steady-state error [5].
2
TABLE I. Attribute
PERFORMANCE SPECIFICATION FOR A CONTROL SYSTEM [5] Desired value
Purpose
Specifications
Percentage overshoot, settling time, pole (eigenvalue) locations, time constants, phase Rise time, peak time, delay time, natural frequencies, resonant frequencies, bandwidth
Stability
High
The response does not grow without limit and decays to the desired value
Speed of response
Max
The plant response quickly to inputs
SteadyState error
Min
Robustnes
High
Dynamic interaction
Min
The offset from the desired response is negligible Accurate response under uncertain conditions (signal noise, model error, etc.) and under parameter variation One input affects only one output
Error tolerance for a step input Input noise tolerance, measurement error tolerance, model error tolerance Cross-sensitivity, crosstransfer functions
B. Variable Speed Drive (VSD) and Induction Motor VSD has explored and broaden its technology across the entire industrial revolution, from the development of the steam engine to modern microprocessor-based electronic motor controller [6]. This project deals with AC drives or usually called inverter where it can vary the motors’ speed and torque. Inverter switches the DC on and off rapidly so that the motor receives a pulsating DC that appears similar to AC thus could vary the frequency and control the speed. It is very important to keep the ratio of V/Hz constant while operating the induction motor, otherwise it could cause negative effects to the motor. By increasing the applied voltage and keeping the frequency constant, it will increase the magnetic flux and saturates the iron components of the motors. As a result, the flux causes iron losses to increase in the form of hysteresis and eddy currents. Furthermore it also increases the stator current thus could damage the motor windings. The same effect occurs if the frequency is reduced but keeping the voltage constant and excessive current will flow which will result in more heat produced [7]. An example of constant V/Hz control performed in [8] shows that voltage boosting is applied up to 20 Hz to maintain constant torque at low speed as shown in Fig. 1 [8]. Induction motors are commonly used in the industry. AC induction motors are often called squirrel-cage motors which are extensively applied due to its durability and rugged design. It can also be used in hazardous areas, do not contain any brushes and low maintenance requirements [6]. C. Fuzzy Logic Fuzzy logic is from the class of ‘intelligent control’, expert control or knowledge based control [5]. Fuzzy logic has achieved a growing interest in many motor control applications due to its complex, non-linearity handling features and sometimes mathematically intangible.
Figure 1. V/Hz pattern [8]
The meaning of the word ‘fuzzy’ is ‘not clear, vague’, indistinct, non-coherent but in the technical term, fuzzy systems are precisely defined system and fuzzy control is precisely defined method of non-linear control. Fuzzy logic relies on a set of linguistic if-then rules where the aim is to improve on the ‘human-like’ reasoning [10, 11]. Fuzzy logic is used the development of the hybrid FuzzyPID (Proportional Integral Derivative) as reported in [8, 25]. D. Programmable Logic Controller, PLC Wide application of automation in modern industries demands several strategies that have high robustness and reliability to be introduced. PLC, which is the subject of this work shows to be reliable and efficient in applications involving the synchronization and sequential control of processes and back-up elements in process and manufacturing industries [12]. The availability of PLC with basic features like calculation operations and the improvement of graphical user interface (GUI) in communication and programming, promises the means to utilize the advantages of PLC in variable speed application [13]. Successful examples of utilizing PLCs in control as the main controller are in [14-19], while PLC as a device control assistant is related in [20]. The applications of PLC in industry as a controlling and monitoring a system with multi-tasking can be found in [21-24]. E. State-space Control State-space control is a unified method for modeling, designing and analyzing different types of systems. Statespace approach can be used to represent a non-linear system, handle systems with non-zero initial conditions, multi-input and multi-outputs, time-varying systems and also to represent systems with a digital computer in the loop or to model systems for digital simulation. This project deals with ‘pole placement for plants in phase-variable form’. Equations (1) and (2) express the general state-space representation of a plant. .
x = Ax + Bu
(1)
y = Cx + Du
(2)
3 Y ( s ) = G _ 1( s ) + G _ 2( s ) G _ 1( S ) =
G _ 2( S ) =
62.62 s + 0.1783 e −0.69926 s s + 21.07 s 2 + 110.7 s + 0.339 3
− 11.1497 s + 0.834 e − 0.0259044 s s 3 + 53.5s 2 + 717.2 s + 51.51
1 0 ⎤ ⎡ x1 ⎤ ⎡0⎤ ⎡ 0 0 1 ⎥⎥ ⎢⎢ x 2 ⎥⎥ + ⎢⎢0⎥⎥u ss[G _ 1( s )] = ⎢⎢ 0 ⎢⎣− 0.339 − 110.7 − 21.07 ⎥⎦ ⎢⎣ x3 ⎥⎦ ⎢⎣1⎥⎦
Figure 2. General State-space representation of a plant
⎡ x1 ⎤ y = [0.1783 62.62 0] ⎢⎢ x 2 ⎥⎥ ⎢⎣ x 3 ⎥⎦
(4) (5) (6)
(7)
(8)
1 0 ⎤ ⎡ x1 ⎤ ⎡0⎤ ⎡ 0 ⎢ ss[G _ 2( s)] = ⎢ 0 0 1 ⎥⎥ ⎢⎢ x 2 ⎥⎥ + ⎢⎢0⎥⎥u (9) ⎢⎣− 51.51 − 717.2 − 53.5⎥⎦ ⎢⎣ x3 ⎥⎦ ⎢⎣1 ⎥⎦
Figure 3. Plant with State Feedback and Feedforward
Fig. 2 and 3 show a typical state-space representation of a plant with and without feedback respectively. The output’s control system, y, is fed back to the summing junction to compensate the error represented by vector –K. Equations (3) and (2) represent the plant Fig. 3. The gain K acts as the controller for each state feedback. These equations relates to the plant model design. .
x = Ax + Bu = Ax + B (− Kx + r ) = ( A − BK ) x + Br III.
(3)
METHODOLOGY
The plant dynamics from [25] is modeled into state-space representation and the model obtained will be used to design and analyze a suitable controller that could be implemented onto PLC controller. The plant model consists of the induction motor, PWM inverter and the load is designed using a simulation environment. The transfer function of the plant is obtained via system identification and has been discussed in [8] extensively. A. State-space Modeling The plant model is designed using state-space approach. Specifically, controller canonical form is selected to ease of modeling and solution [26]. The gains K1, K2 and K3 in Fig. 4 play an important role in controlling the plant performance. The plant transfer function model is obtained from research performed in [25] represented by equation (4), (5) and (6). However, the bias is not included in this model. The output, y (7) is obtained using canonical approach [26]. The transfer function is converted into state-space representation using canonical approach represented by (8), (9) and (10). The state space equations are used to design the signal-flow graph which can be modeled directly into the simulation environment, Matlab/Simulink in Fig. 4.
⎡ x1 ⎤ y = [0.834 − 11.1495 0] ⎢⎢ x2 ⎥⎥ ⎢⎣ x3 ⎥⎦
(10)
B. System Layout of PLC-Based Fuzzy Controller Fig. 5 are illustrates the physical system layout and the related electrical connection of the test rig. The induction motor, PWM inverter and load constitute the plant. The PWM inverter functions as an interface between the induction motor and the PLC. The personal computer (PC) acts as a terminal for developing and downloading the program to PLC whereas the connection between PC and PLC is implemented via TCP/IP Ethernet network. The PLC used is equipped with a digital and an analogue I/O modules. The input voltage of the digital input is 24V DC while for the digital output is 12 - 24 V DC. The forward/reverse can be achieved via relay contactors running at low voltage (24 V) that drive the magnetic contactors. One channel of analogue input and two channels of analogue output are used, the input channel is used to measure the analogue voltage that represents the actual speed while one of the two analogue outputs is used to send the manipulated variable (u) to the VSD and the other is to specify the load applied to the induction motor. The PWM inverter forms the main component of a VSD. The VSD is connected to a three-phase supply on its line side and produces sequences of three-phase PWM on its output side. This is arranged to drive the 3-phase squirrel cage induction motor. The VSD is rated at 0.75 kW, 415V line-to-line on its output load side and its frequency is controlled by a 0 – 10V analogue signal coming from the analogue output module of the PLC. There is a linear relation between 0 – 10V of analogue signal to the PWM inverter and 0 – 50 Hz analogue output from PWM inverter to the three phase induction motor. The modulation implemented on the PWM inverter is a sine pulse width modulation (PWM) that runs on a carrier frequency of 7.5 kHz and operates on a constant V/Hz ratio control.
4
Figure 4. Plant model in MATLAB/Simulink
induction-motor stator, depends on the controller’s output signal to the PWM inverter and the V/Hz ratio relationship. The Human Machine Interface, HMI, consists of a programmable terminal, a display and a touch panel provides interfacing between system and operator. In order to acquire a particular mechanical load, an analogue control voltage is adjusted to provide a voltage that is proportional to the speed as provided by a dynamometer. The dynamometer consists of a direct current (DC) motor that operates as a generator and is mechanically coupled to the motor. The analogue voltage is related to the speed at 500 rpm/V (revolution per minute per voltage), and the voltage is then fed to the PLC as the measured process variable. IV. RESULT & DISCUSSION Specifically, this research aims to design a controller for an induction motor using state-space approach which would be an alternative to the work conducted earlier as in [8,25]. The state space controller is designed using ‘pole placement technique’. The plant’s output response is specified to be 5% overshoot, and this is obtained by specifying the appropriate feedback gain, K values. Figure 5. Physical system layout with HMI, PLC, PWM inverter, induction motor and load
The PLC-based controller, as being interfaced to an induction motor via the PWM inverter provides a signal to the PWM inverter that corresponds to the speed and torque requirements. The PWM inverter operates on a constant V/Hz ratio control and hence the output of the PWM inverter in the form of voltage and frequency supplied to the
It is important to highlight that this control scheme has able to improve the performances for wider range of speeds, i.e. 30 rpm, 1800 rpm, from low and high threshold speeds which was not possible using the method used in [8, 25] for low speed. In this paper, the result and discussion focuses only for low threshold speed. The performance of both controllers i.e., state-space as well as the hybrid Fuzzy-PID [8, 25] are compared using step response.
5 The graphs of Fig. 6, 7 and 8 show the responses of the plant’s controller at low speed (with 100 rpm is selected at the input reference), at medium speed (1000 rpm) and at the higher speed (1800 rpm). The controller is tuned by designing using ‘pole placement technique’ the appropriate controller to obtain two types of responses: 5% and 20% overshoot by changing the feedback gain, K values. Considering at no-load condition, Fig. 6 shows that the controller’s performance is consistent for the different references input speeds requirement, i.e., when the input is increased, the output is also increased with similar trend for all speed ranges (low, medium and high).
Figure 6. Step response for 5% and 20% OS (with no-load)
Fig. 7 shows a comparison of step responses when the controller is set to give an output of 5% overshoot (OS) for different reference inputs requirements. The figure shows the response when a load is applied, first with 1 Nm and then with 2 Nm. As can be observed at the instant the load is applied at 4 seconds, the speed reduces proportionally. The speed takes sometimes to reach its settling point which is longer as compared to if no load is applied. For the design to have 20% OS, Fig. 8 shows the speed starts off with a slightly negative rotation (-ve) of the motor when no-load is applied before it gains back speed and rotate in the positive direction. At the instant when a load is applied at 4 seconds, first with 1 Nm and then with 2 Nm, the speed reduces proportionally. The speed takes nearly 6 seconds before reaching its settling point. Even though there is a delay before settling to its desired speed when a load is applied (slow settling time), however the controller’s as designed via state-space approach indicates to give good responses for all ranges of speed. This is an improved result as compared to the work in [8] that using Ziegler Nichol’s method that give a good response only for the middle range to high speed range (600 – 1800 rpm). V. CONCLUSION AND FUTURE WORK
Figure 7. Step response for 5% OS when load introduced
The results obtained using state space indicates that this approach is capable to improve the system’s response at low to high speed ranges, with the performance of the controller consistent throughout a wide input range of speed (100 – 1800 rpm). The specific new finding from this paper is to achieve a good control for all speed ranges. For future work, the state space controller’s performance should be improved to achieve a shorter settling time for any disturbances (or introduction of new load requirements) are encountered and improving the steady state error. REFERENCES [1]
[2] [3]
Figure 8. Step response for 20% OS when load introduced
N. Mohan, T. M. Undeland, and W. P. Robbins, Power Electronics: Converters, Applications and Design, pp. 2004. John Wiley & Sons, Inc. M. Barnes , Practical Variable Speed Drives and Power Electronics, pp 2003. Newnes. Arrofiq, M.; Saad, N. "PLC-based fuzzy logic controller for induction-motor drive with constant V/Hz ratio," International Conference on Intelligent and Advanced Systems, 2007. ICIAS 2007., 25-28 Nov. 2007.
6 [4]
[5] [6] [7] [8]
[9]
[10]
[11]
[12] [13] [14]
[15]
Toannides M.G., “Design and Implementation of PLC-Based Monitoring Control System for Induction Motor”, in IEEE Transactions on Energy Conversion, vol. 19, No. 3, pp. 469-476,Sep. 2004. C. W. de Silva Intelligent Control: Fuzzy Logic Applications, pp. 1995. CRC. D. W. Spttzer, Variable Speed Drives: Principles and Applications for Energy Cost Savings, pp 2004. ISA. M. E. Brumbach, Electronic Variable Speed Drives, pp 2005. Thomson Delmar Learning. M. Aroffiq, “A PLC-Based Hybrid Fuzzy PID Controller for PWMDriven Variable Speed Drive,” Ph.D. dissertation, Dept. Electrical & Electronic Eng., Univ. Teknologi PETRONAS, Perak, Malaysia, 2010. Wahyunggoro, Oyas; Saad, Nordin, "Evaluations of fuzzy-logic-based self tuning PI controller and fuzzy-scheduled PID controller for DC servomotor," Information Technology, 2008. ITSim 2008. International Symposium on , vol.4, no., pp.1-7, 26-28 Aug. 2008. Asija, D., "Speed control of induction motor using fuzzy-PI controller," Mechanical and Electronics Engineering (ICMEE), 2010 2nd International Conference on , vol.2, no., pp.V2-460-V2-463, 1-3 Aug. 2010. Aras, M.S.M. Bin Syed Salim, S.N. Hoo, E.C.S. Razak, I.A.B.W.A. Hendra Bin Hairi, M. , "Comparison of Fuzzy Control Rules Using MATLAB Toolbox and Simulink for DC Induction Motor-Speed Control," Soft Computing and Pattern Recognition, 2009. SOCPAR '09. International Conference of , vol., no., pp.711-715, 4-7 Dec. 2009. K. T. Erickson, "Programmable logic controllers," IEEE Potentials, vol. 15, pp. 14-17, Feb-Mar 1996. Kaplan, G. , "Technology 1993-industrial electronics," Spectrum, IEEE , vol.30, no.1, pp.58-60, Jan 1993. A. R. Al-Ali, M. M. Negm, and M. Kassas, "A PLC based power factor controller for a 3-phase induction motor," In: Proceedings of the IEEE Industry Applications Conference, 2000. Arrofiq, M. Saad, N. , "A PLC-based self-tuning PI-fuzzy controller for linear and non-linear drives control," IEEE 2nd International Power and Energy Conference, 2008. PECon 2008., pp.701-706, 1-3 Dec. 2008.
[16] A. S. Z. E. Din, "High performance PLC controlled stepper motor in robot manipulator," In: Proceedings of the IEEE International Symposium on Industrial Electronics, 1996. [17] A. M. Graham, and M. Etezadi-Amoli, "Design, implementation, and simulation of a PLC based speed controller using fuzzy logic," In: Proceedings of the IEEE Power Engineering Society Summer Meeting, Seattle, WA, 2000. [18] O. Karasakal, E. Yesil, M. Guzelkaya, and I. Eksin, "The implementation and comparison of different type self-tuning algorithms of fuzzy pid controllers on PLC," In: Proceedings of World Automation Congress, 2004. [19] H.-X. Li and S. K. Tso, "A fuzzy PLC with gain-scheduling control resolution for a thermal process – a case study," Control Engineering Practice, vol. 7, pp. 523-529, 1999. [20] D. Li, F. Li, X. Huang, Y. Lai, and S. Zheng, "A model based integration framework for computer numerical control system development," Robotics and Computer-Integrated Manufacturing, vol. 26, pp. 333-343, 2010. [21] M. G. Ioannides, "Design and Implementation of PLC-Based Monitoring Control System for Induction Motor," IEEE, vol. 19 no.3, pp. 469 - 476, 2004. [22] M. Fabian and A. Hellgren, "PLC-based implementation of supervisory control for discrete event systems," In: Proceedings of the 37th IEEE Conference on Decision and Control, 1998. [23] A. Hossain and S. M. Suyut, "Monitoring and controlling of a realtime industrial process using dynamic model control technology," In: Proceedings of the IEEE. Ind. Application Soc. Workshop on Dynamic Modeling Control Applications for Industry, pp. 20-25, 1997. [24] S. Akula and K. P. Karunakaran, "Hybrid adaptive layer manufacturing: An Intelligent art of direct metal rapid tooling process," Robotics and Computer-Integrated Manufacturing, vol. 22, pp. 113-123, 2006. [25] Arrofiq, M., and Saad, N. , "Control of induction motor drives using modified-fuzzy logic methods," Systems Man and Cybernetics (SMC), 2010 IEEE International Conference, pp.612-619, 10-13 Oct. 2010 [26] N. S. Nise, “Control System Engineering,” 4th Ed, United States, John Wiley & Sons, 2003
