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PID Controller Design for Electro-hydraulic Servo Valve System with Genetic Algorithm
Available online at www.sciencedirect.com
ScienceDirect Procedia Computer Science 86 (2016) 91 – 94
2016 International Electrical Engineering Congress, iEECON2016, 2-4 March 2016, Chiang Mai, Thailand
PID Controller Design for Electro-hydraulic Servo Valve System with Genetic Algorithm Tanasak Samakwong a, Wudhichai Assawinchaichoteb, * 0F0F0F0F0F
a, b
King Mongkut's University of Technology Thonburi, Bangkok, Bangkok 10140, Thailand
Abstract The proportional-integral-derivative (PID) controller are widely applied with the electro-hydraulic servo system since it is easily to implement and highly efficient. The optimal tuning PID parameter that can increase the performance of the control system. Thus, this paper is considered the optimization technique of Genetic Algorithm (GA) for tuning PID controller parameter for electro-hydraulic servo system. The other techniques are compared, that is the obtained results are shown the genetic algorithm optimized PID controller provide an improved closed-loop are performed than the Ziegler- Nichols, tuning method automatic tuning method and particle swarm optimization (PSO). © TheAuthors. Authors.Published Published Elsevier © 2016 The byby Elsevier B.V.B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of iEECON2016. Peer-review under responsibility of the Organizing Committee of iEECON2016 Keywords: PID Controller, Genetic Algorithm, Particle Swarm Optimization, Ziegler- Nichols, Electro-hydraulic Servo Valve System ;
1. Introduction The hydraulic servo valve system is important in the industry because it has many advantages such as high power, high-speed response and lightweight when compared other devices [1]. However, the hydraulic servo valve system is actually nonlinear dynamic systems. Therefore, it may be difficult to control a system when the controller is a linear format. Electro-hydraulic servo system has problem about high swing response. The tuning method of PID controller has been used for the hydraulic servo valve system. For examples, Ziegler-Nichols [2] that is a simply method, but it provides high overshoot response. Meanwhile the PSO tuning method [3] and automatic tuning can solve these problems of high overshoot response of Ziegler-Nichols method. However, the controlled systems are remained with
* Corresponding author. Tel.: +662-470-9056; fax: +662-470-9070. E-mail address: [email protected].
1877-0509 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of iEECON2016 doi:10.1016/j.procs.2016.05.023
92
Tanasak Samakwong and Wudhichai Assawinchaichote / Procedia Computer Science 86 (2016) 91 – 94
problem about a long-time settling time response and a rise time response. These problems have affected to delay production process. To solve aforementioned problems, this paper proposes the tuning method by Genetic Algorithm which approached the optimal PID parameters so that it can increase the efficiency control of the system because it can be reduced settling time response and rise time response. Therefore, the system which is faster work than old PIDs tuned methods. However, Genetic Algorithm is has highly maximum overshoot, but it is an accuracy and powerful searching technique, so that they are widely used in science, business and engineering circles. 2. PID controller design for electro-hydraulic servo valve system Firstly, the considered of the electro-hydraulic servo valve system shown in Fig. 1
Fig.1.Block diagram of an electro-hydraulic servo valve system with a PID controller.
where C(s) is the actual output, E(s) is the error signal, U(s) the control input, and kp, ki, and kd are the proportional, integral and derivative gains respectively. Transfer function of plant has given as below. ࡳ(࢙) =
.ૡ࢙ା.࢙ା
(1)
࢙ା.࢙ା.࢙ା ૠ.࢙ା࢙ା
Transfer function of a PID controller is written as: ࡳ(࢙) =
ࢁ(࢙) ࡱ(࢙)
= +
ࡷ ࢙
+ ࢙ࡷࢊ
(2)
3. The process of work GA
Fig.2.The flowchart of Genetic algorithm
93
Tanasak Samakwong and Wudhichai Assawinchaichote / Procedia Computer Science 86 (2016) 91 – 94
3.1. Initial Population is generated randomly. These values haven’t occurred more than define values. The best values are distributed randomly and the numbers format hasn’t repeatedly as shown below. ܲ݊݅ݐܽݎ݁݊݁݃ ݉݀݊ܽݎ = ݈݅݀
(3)
3.2. Selection Population is selected from populations pass genetic process which using method of select random population .This function will select from old group population that amount two people. Copying are right become a new population as Pnewi and Pnewj as shown below. [ܲ݊݁ ݓ, ܲ݊݁)݈݀ܲ( ݊݅ݐ݈ܿ݁݁ݏ ݊݅ݐܿ݊ݑ݂ = ] ݓ ݅ ݆
(4)
3.3. Genetic operators are genetic processes have two steps. First step Crossover is the process divided into groups and exchanged with another groups. This process, with two new lines at different, it will create a new group is randomly. The crossover is shown as below. [ܲ݊݁ ݓ, ܲ݊݁ ݓ݁݊ܲ(ݎ݁ݒݏݏݎܿ ݊݅ݐܿ݊ݑ݂ = ] ݓԢ, ܲ݊݁ ݓԢ) ݅ ݆ ݅ ݆
(5)
Finally step Mutation is a change from the original group as a new group. Mutations that occur with dissimilar characteristics depend on beginning of manner not possible from the perspective of optimization problem. It can be explained as shown as equation (6). ܲ݊݁ݓ݁݊ܲ(݊݅ݐܽݐݑ݉ ݊݅ݐܿ݊ݑ݂ = ݓԢ)
(6)
3.4. Replacement is with the appropriate population in the next generation. As per Equation 7. Total population in Pold and Pnew, they will be considered only suitable value with the right to Pold a next generation population. ݈ܲ݀ܲ( ݐ݈݊݁݉݁ܿܽ݁ݎ ݊݅ݐܿ݊ݑ݂ = ݈݀, ܲ݊݁ݓԢ)
(7)
3.5. Termination is determined when the results were higher value than or equal to the desired output then to stop working 4. Simulation Results The results of optimization parameters Kp Ki Kd are shown in Table 1. Genetic algorithm method that applied in this paper has shown the better performances when compared with other techniques. Table1. Optimal of PID Parameters are obtained by each tuning techniques Tuning Methods
Kp
Ki
Kd
Ziegler-Nichols
3.9563
4.1688
0.9384
PSO Automatic Tuning Genetic Algorithm
2.2573 3.9716 5.9179
1.7794 1.1276 6.2483
3.333 3.4517 6.2838
As shown in Figure 3, the simulation results are indicated, the Genetic Algorithm tuning method is more effective than Ziegler-Nichols method, PSO method and automatic tuning for the Electro-hydraulic servo valve system.
94
Tanasak Samakwong and Wudhichai Assawinchaichote / Procedia Computer Science 86 (2016) 91 – 94
Fig.3.The step response of the electro-hydraulic servo valve system with representative GA-PID solutions
The compared value of percentage peak overshoot, rise time (sec) and settling time (sec) are shown in Table 2. According to Table 2, the settling time (sec) of Genetic Algorithm method is better results than the settling time (sec) of PSO method about 68.1 %. Table2. Comparative performance in transient responses of different tuning techniques Tuning Methods
Ziegler-Nichols
PSO
Automatic Tuning
Genetic Algorithm
Overshoot (%)
58.3
1.23
6.5
6.5
Rise Time(sec)
0.386
0.282
0.243
0.152
Settling Time(sec)
10.2
4.64
6.35
1.48
3. Conclusion The performance of the Genetic Algorithm (GA) with the PID controller system is faster convergence when compared the performance of the other tuned algorithm are Ziegler-Nichols, Particle Swarm Optimization and Automatic turning. However, the incremental speed of system by the Genetic Algorithm method it has a high peak overshoot when the system starts. It is the most seriously situation because the system can be damaged by the high peak overshoot. Therefore, the system which using with Genetic algorithm, it should be had a better characteristic system. But the system may be high maintenance cost because high peak overshoot. Acknowledgements The authors would like to acknowledge the Department of Electronic and Telecommunication Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi for their supports in this research work. References [1] A. Rangel-Merino, J. L. López-Bonilla and R. Linares y Miranda, October 2005,“ Optimization Method based on Genetic Algorithms,” Apeir, Vol.12, No.4, pp. 398-399. [2] Neha Tandan and Kuldeep Kumar Swarnkar, April 2015, “ Tuning of PID Controller using PSO and ITS Performances on Electro- Hydraulic Servo System,” International Journal of Modern Trends in Engineering and Research (IJMTER), Vol. 02, Issue 04, pp. 233-235. [3] Supakit Nootyaskool, JUL-DEC 2011, “ Evolutionary computation between Genetic Algorithm and Particle Swarm Optimization,” Journal of Information Science and Technology, VOL. 2, Issue 02, pp. 15-16.
ScienceDirect Procedia Computer Science 86 (2016) 91 – 94
2016 International Electrical Engineering Congress, iEECON2016, 2-4 March 2016, Chiang Mai, Thailand
PID Controller Design for Electro-hydraulic Servo Valve System with Genetic Algorithm Tanasak Samakwong a, Wudhichai Assawinchaichoteb, * 0F0F0F0F0F
a, b
King Mongkut's University of Technology Thonburi, Bangkok, Bangkok 10140, Thailand
Abstract The proportional-integral-derivative (PID) controller are widely applied with the electro-hydraulic servo system since it is easily to implement and highly efficient. The optimal tuning PID parameter that can increase the performance of the control system. Thus, this paper is considered the optimization technique of Genetic Algorithm (GA) for tuning PID controller parameter for electro-hydraulic servo system. The other techniques are compared, that is the obtained results are shown the genetic algorithm optimized PID controller provide an improved closed-loop are performed than the Ziegler- Nichols, tuning method automatic tuning method and particle swarm optimization (PSO). © TheAuthors. Authors.Published Published Elsevier © 2016 The byby Elsevier B.V.B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of iEECON2016. Peer-review under responsibility of the Organizing Committee of iEECON2016 Keywords: PID Controller, Genetic Algorithm, Particle Swarm Optimization, Ziegler- Nichols, Electro-hydraulic Servo Valve System ;
1. Introduction The hydraulic servo valve system is important in the industry because it has many advantages such as high power, high-speed response and lightweight when compared other devices [1]. However, the hydraulic servo valve system is actually nonlinear dynamic systems. Therefore, it may be difficult to control a system when the controller is a linear format. Electro-hydraulic servo system has problem about high swing response. The tuning method of PID controller has been used for the hydraulic servo valve system. For examples, Ziegler-Nichols [2] that is a simply method, but it provides high overshoot response. Meanwhile the PSO tuning method [3] and automatic tuning can solve these problems of high overshoot response of Ziegler-Nichols method. However, the controlled systems are remained with
* Corresponding author. Tel.: +662-470-9056; fax: +662-470-9070. E-mail address: [email protected].
1877-0509 © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the Organizing Committee of iEECON2016 doi:10.1016/j.procs.2016.05.023
92
Tanasak Samakwong and Wudhichai Assawinchaichote / Procedia Computer Science 86 (2016) 91 – 94
problem about a long-time settling time response and a rise time response. These problems have affected to delay production process. To solve aforementioned problems, this paper proposes the tuning method by Genetic Algorithm which approached the optimal PID parameters so that it can increase the efficiency control of the system because it can be reduced settling time response and rise time response. Therefore, the system which is faster work than old PIDs tuned methods. However, Genetic Algorithm is has highly maximum overshoot, but it is an accuracy and powerful searching technique, so that they are widely used in science, business and engineering circles. 2. PID controller design for electro-hydraulic servo valve system Firstly, the considered of the electro-hydraulic servo valve system shown in Fig. 1
Fig.1.Block diagram of an electro-hydraulic servo valve system with a PID controller.
where C(s) is the actual output, E(s) is the error signal, U(s) the control input, and kp, ki, and kd are the proportional, integral and derivative gains respectively. Transfer function of plant has given as below. ࡳ(࢙) =
.ૡ࢙ା.࢙ା
(1)
࢙ା.࢙ା.࢙ା ૠ.࢙ା࢙ା
Transfer function of a PID controller is written as: ࡳ(࢙) =
ࢁ(࢙) ࡱ(࢙)
= +
ࡷ ࢙
+ ࢙ࡷࢊ
(2)
3. The process of work GA
Fig.2.The flowchart of Genetic algorithm
93
Tanasak Samakwong and Wudhichai Assawinchaichote / Procedia Computer Science 86 (2016) 91 – 94
3.1. Initial Population is generated randomly. These values haven’t occurred more than define values. The best values are distributed randomly and the numbers format hasn’t repeatedly as shown below. ܲ݊݅ݐܽݎ݁݊݁݃ ݉݀݊ܽݎ = ݈݅݀
(3)
3.2. Selection Population is selected from populations pass genetic process which using method of select random population .This function will select from old group population that amount two people. Copying are right become a new population as Pnewi and Pnewj as shown below. [ܲ݊݁ ݓ, ܲ݊݁)݈݀ܲ( ݊݅ݐ݈ܿ݁݁ݏ ݊݅ݐܿ݊ݑ݂ = ] ݓ ݅ ݆
(4)
3.3. Genetic operators are genetic processes have two steps. First step Crossover is the process divided into groups and exchanged with another groups. This process, with two new lines at different, it will create a new group is randomly. The crossover is shown as below. [ܲ݊݁ ݓ, ܲ݊݁ ݓ݁݊ܲ(ݎ݁ݒݏݏݎܿ ݊݅ݐܿ݊ݑ݂ = ] ݓԢ, ܲ݊݁ ݓԢ) ݅ ݆ ݅ ݆
(5)
Finally step Mutation is a change from the original group as a new group. Mutations that occur with dissimilar characteristics depend on beginning of manner not possible from the perspective of optimization problem. It can be explained as shown as equation (6). ܲ݊݁ݓ݁݊ܲ(݊݅ݐܽݐݑ݉ ݊݅ݐܿ݊ݑ݂ = ݓԢ)
(6)
3.4. Replacement is with the appropriate population in the next generation. As per Equation 7. Total population in Pold and Pnew, they will be considered only suitable value with the right to Pold a next generation population. ݈ܲ݀ܲ( ݐ݈݊݁݉݁ܿܽ݁ݎ ݊݅ݐܿ݊ݑ݂ = ݈݀, ܲ݊݁ݓԢ)
(7)
3.5. Termination is determined when the results were higher value than or equal to the desired output then to stop working 4. Simulation Results The results of optimization parameters Kp Ki Kd are shown in Table 1. Genetic algorithm method that applied in this paper has shown the better performances when compared with other techniques. Table1. Optimal of PID Parameters are obtained by each tuning techniques Tuning Methods
Kp
Ki
Kd
Ziegler-Nichols
3.9563
4.1688
0.9384
PSO Automatic Tuning Genetic Algorithm
2.2573 3.9716 5.9179
1.7794 1.1276 6.2483
3.333 3.4517 6.2838
As shown in Figure 3, the simulation results are indicated, the Genetic Algorithm tuning method is more effective than Ziegler-Nichols method, PSO method and automatic tuning for the Electro-hydraulic servo valve system.
94
Tanasak Samakwong and Wudhichai Assawinchaichote / Procedia Computer Science 86 (2016) 91 – 94
Fig.3.The step response of the electro-hydraulic servo valve system with representative GA-PID solutions
The compared value of percentage peak overshoot, rise time (sec) and settling time (sec) are shown in Table 2. According to Table 2, the settling time (sec) of Genetic Algorithm method is better results than the settling time (sec) of PSO method about 68.1 %. Table2. Comparative performance in transient responses of different tuning techniques Tuning Methods
Ziegler-Nichols
PSO
Automatic Tuning
Genetic Algorithm
Overshoot (%)
58.3
1.23
6.5
6.5
Rise Time(sec)
0.386
0.282
0.243
0.152
Settling Time(sec)
10.2
4.64
6.35
1.48
3. Conclusion The performance of the Genetic Algorithm (GA) with the PID controller system is faster convergence when compared the performance of the other tuned algorithm are Ziegler-Nichols, Particle Swarm Optimization and Automatic turning. However, the incremental speed of system by the Genetic Algorithm method it has a high peak overshoot when the system starts. It is the most seriously situation because the system can be damaged by the high peak overshoot. Therefore, the system which using with Genetic algorithm, it should be had a better characteristic system. But the system may be high maintenance cost because high peak overshoot. Acknowledgements The authors would like to acknowledge the Department of Electronic and Telecommunication Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi for their supports in this research work. References [1] A. Rangel-Merino, J. L. López-Bonilla and R. Linares y Miranda, October 2005,“ Optimization Method based on Genetic Algorithms,” Apeir, Vol.12, No.4, pp. 398-399. [2] Neha Tandan and Kuldeep Kumar Swarnkar, April 2015, “ Tuning of PID Controller using PSO and ITS Performances on Electro- Hydraulic Servo System,” International Journal of Modern Trends in Engineering and Research (IJMTER), Vol. 02, Issue 04, pp. 233-235. [3] Supakit Nootyaskool, JUL-DEC 2011, “ Evolutionary computation between Genetic Algorithm and Particle Swarm Optimization,” Journal of Information Science and Technology, VOL. 2, Issue 02, pp. 15-16.