Performance comparison of optimization algorithms in LQR controller design for a nonlinear system

CAKAN, Abdullah; İlhan, İlhan; Önen, Ümit

doi:10.3906/elk-1808-51

Performance comparison of optimization algorithms in LQR controller design for a nonlinear system

Ümit ÖNEN, (Necmettin Erbakan Üniversitesi)

Abdullah ÇAKAN, (Konya Teknik Üniversitesi)

İlhan İLHAN (Necmettin Erbakan Üniversitesi)

Turkish Journal of Electrical Engineering and Computer Sciences

4 0

Yıl: 2019 Cilt: 27 Sayı: 3 Sayfa Aralığı: 1938 - 1953 Metin Dili: İngilizce DOI: 10.3906/elk-1808-51 İndeks Tarihi: 15-05-2020

Performance comparison of optimization algorithms in LQR controller design for a nonlinear system

Öz:

The development and improvement of control techniques has attracted many researchers for many years.Especially in the controller design of complex and nonlinear systems, various methods have been proposed to determinethe ideal control parameters. One of the most common and effective of these methods is determining the controllerparameters with optimization algorithms.In this study, LQR controller design was implemented for position control ofthe double inverted pendulum system on a cart. First of all, the equations of motion of the inverted pendulum systemwere obtained by using Lagrange formulation. These equations were linearized by Taylor series expansion around theequilibrium position to obtain the state-space model of the system. The LQR controller parameters required to controlthe inverted pendulum system were determined by using a trial and error method. The determined parameters wereoptimized by using five different configurations of three different optimization algorithms (GA, PSO, and ABC). The LQRcontroller parameters obtained as a result of the optimization study with five different configurations of each algorithmwere applied to the system and the obtained results were compared with each other. In addition, the configurations thatyielded the best control results for each algorithm were compared with each other and the control results were evaluatedin terms of response speed and response smoothness.

Anahtar Kelime:

Konular: Mühendislik, Elektrik ve Elektronik Bilgisayar Bilimleri, Yazılım Mühendisliği Bilgisayar Bilimleri, Sibernitik Bilgisayar Bilimleri, Bilgi Sistemleri Bilgisayar Bilimleri, Donanım ve Mimari Bilgisayar Bilimleri, Teori ve Metotlar Bilgisayar Bilimleri, Yapay Zeka

Belge Türü: Makale Makale Türü: Araştırma Makalesi Erişim Türü: Erişime Açık

[1] Hong H, Kim S, Kim C, Lee S, Park S. Spring-like gait mechanics observed during walking in both young and older adults. Journal of Biomechanics 2013; 46 (1): 77-82.
[2] Koolen T, De Boer T, Rebula J, Goswami A, Pratt J. Capturability-based analysis and control of legged locomotion, Part 1: Theory and application to three simple gait models. International Journal of Robotics Research 2012; 31 (9): 1094-1113.
[3] McGrath M, Howard D, Baker R. The strengths and weaknesses of inverted pendulum models of human walking. Gait & Posture 2015; 41 (2): 389-394.
[4] Pratt J, Koolen T, De Boer T, Rebula J, Cotton S et al. Capturability-based analysis and control of legged locomotion, Part 2: Application to M2V2, a lower-body humanoid. International Journal of Robotics Research 2012; 31 (10): 1117-1133.
[5] Suzuki Y, Nomura T, Casadio M, Morasso P. Intermittent control with ankle, hip, and mixed strategies during quiet standing: a theoretical proposal based on a double inverted pendulum model. Journal of Theoretical Biology 2012; 310: 55-79.
[6] Nasir A, Ismail R, Ahmad M. Performance comparison between sliding mode control (SMC) and PD-PID controllers for a nonlinear inverted pendulum system. World Academy of Science, Engineering, and Technology 2010; 71: 400- 405.
[7] Prasad LB, Tyagi B, Gupta HO. Optimal control of nonlinear inverted pendulum dynamical system with disturbance input using PID controller & LQR control system. In: 2011 IEEE International Conference on Control System, Computing and Engineering; 25–27 November 2011; Penang, Malaysia. pp. 540-545.
[8] Zhang J, Zhang W. LQR self-adjusting based control for the planar double inverted pendulum. Physics Procedia 2012; 24: 1669-1676.
[9] Ibanez CA, Frias OG, Castanon MS. Lyapunov-based controller for the inverted pendulum cart system. Nonlinear Dynamics 2005; 40 (4): 367-374.
[10] Jabbar A, Malik FM, Sheikh SA. Nonlinear stabilizing control of a rotary double inverted pendulum: a modified backstepping approach. Transactions of the Institute of Measurement and Control 2017; 39 (11): 1721-1734.
[11] Lee J, Mukherjee R, Khalil HK. Output feedback stabilization of inverted pendulum on a cart in the presence of uncertainties. Automatica 2015; 54: 146-157.
[12] Landry M, Campbell SA, Morris K, Aguilar CO. Dynamics of an inverted pendulum with delayed feedback control. SIAM Journal on Applied Dynamical Systems 2005; 4 (2): 333-351.
[13] Ashok Kumar M, Kanthalakshmi S. H∞ tracking control for an inverted pendulum. Journal of Vibration and Control 2018; 24: 3515–3524. doi: 10.1177/1077546317750977
[14] Wai RJ, Chang LJ. Adaptive stabilizing and tracking control for a nonlinear inverted-pendulum system via slidingmode technique. IEEE Transactions on Industrial Electronics 2006; 53 (2): 674-692.
[15] Wang JJ. Stabilization and tracking control of X–Z inverted pendulum with sliding-mode control. ISA Transactions 2012; 51 (6): 763-770.
[16] Tao CW, Taur JS, Wang C, Chen U. Fuzzy hierarchical swing-up and sliding position controller for the inverted pendulum–cart system. Fuzzy Sets and Systems 2008; 159 (20): 2763-2784.
[17] Roose AI, Yahya S, Al-Rizzo H. Fuzzy-logic control of an inverted pendulum on a cart. Computers & Electrical Engineering 2017: 61: 31-47.
[18] Jung S, Cho HT, Hsia TC. Neural network control for position tracking of a two-axis inverted pendulum system: experimental studies. IEEE Transactions on Neural Networks 2007; 18 (4): 1042-1048.
[19] Messikh L, Guechi EH, Benloucif M. Critically damped stabilization of inverted-pendulum systems using continuoustime cascade linear model predictive control. Journal of the Franklin Institute 2017; 354 (16): 7241-7265.
[20] Jung S, Wen JT. Nonlinear model predictive control for the swing-up of a rotary inverted pendulum. Journal of Dynamic Systems, Measurement, and Control 2004: 126 (3): 666-673.
[21] Mahmoodabadi M, Taherkhorsandi M, Talebipour M, Castillo-Villar K. Adaptive robust PID control subject to supervisory decoupled sliding mode control based upon genetic algorithm optimization. Transactions of the Institute of Measurement and Control 2015; 37 (4): 505-514.
[22] Lin CM, Mon YJ. Decoupling control by hierarchical fuzzy sliding-mode controller. IEEE Transactions on Control Systems Technology 2005: 13 (4): 593-598.
[23] Soltanpour MR, Khooban MH, Khalghani MR. An optimal and intelligent control strategy for a class of nonlinear systems: adaptive fuzzy sliding mode. Journal of Vibration and Control 2016; 22 (1): 159-175.
[24] Saifizul A, Zainon Z, Osman NA, Azlan C, Ibrahim UU. Intelligent control for self-erecting inverted pendulum via adaptive neuro-fuzzy inference system. American Journal of Applied Sciences 2006; 3 (4): 1795-1802.
[25] Oh SK, Jang HJ, Pedrycz W. A comparative experimental study of type-1/type-2 fuzzy cascade controller based on genetic algorithms and particle swarm optimization. Expert Systems with Applications 2011; 38 (9): 11217-11229.
[26] Jesus IS, Barbosa RS. Genetic optimization of fuzzy fractional PD+ I controllers. ISA Transactions 2015; 57: 220-230.
[27] Sabzi HZ, Humberson D, Abudu S, King JP. Optimization of adaptive fuzzy logic controller using novel combined evolutionary algorithms, and its application in Diez Lagos flood controlling system, Southern New Mexico. Expert Systems with Applications 2016; 43: 154-164.
[28] Martínez R, Castillo O, Aguilar LT. Optimization of interval type-2 fuzzy logic controllers for a perturbed autonomous wheeled mobile robot using genetic algorithms. Information Sciences 2009; 179 (13): 2158-2174.
[29] Zamani M, Karimi-Ghartemani M, Sadati N, Parniani M. Design of a fractional order PID controller for an AVR using particle swarm optimization. Control Engineering Practice 2009; 17 (12): 1380-1387.
[30] Liu CH, Hsu YY. Design of a self-tuning PI controller for a STATCOM using particle swarm optimization. IEEE Transactions on Industrial Electronics 2010; 57 (2): 702-715.
[31] Saleem A, Taha B, Tutunji T, Al-Qaisia A. Identification and cascade control of servo-pneumatic system using particle swarm optimization. Simulation Modelling Practice and Theory 2015; 52: 164-179.
[32] Dhillon SS, Lather J, Marwaha S. Multi objective load frequency control using hybrid bacterial foraging and particle swarm optimized PI controller. International Journal of Electrical Power & Energy Systems 2016; 79: 196-209.
[33] Ufnalski B, Kaszewski A, Grzesiak LM. Particle swarm optimization of the multioscillatory LQR for a three-phase four-wire voltage-source inverter with an LC output filter. IEEE Transactions on Industrial Electronics 2015; 62 (1): 484-493.
[34] Ata B, Coban R. Artificial bee colony algorithm based linear quadratic optimal controller design for a nonlinear inverted pendulum. International Journal of Intelligent Systems and Applications in Engineering 2015; 3 (1): 1-6.
[35] Karaboga D, Basturk B. A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. Journal of Global Optimization 2007; 39 (3): 459-471.
[36] Karaboga D, Basturk B. On the performance of artificial bee colony (ABC) algorithm. Applied Soft Computing 2008; 8 (1): 687-697.
[37] Karaboga D, Gorkemli B, Ozturk C, Karaboga N. A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artificial Intelligence Review 2014; 42 (1): 21-57.
[38] Rajasekhar A, Abraham A, Pant M. A hybrid differential artificial bee colony algorithm based tuning of fractional order controller for permanent magnet synchronous motor drive. International Journal of Machine Learning and Cybernetics 2014; 5 (3): 327-337.
[39] Bououden S, Chadli M, Karimi HR. An ant colony optimization-based fuzzy predictive control approach for nonlinear processes. Information Sciences 2015; 299: 143-158.
[40] Castillo O, Neyoy H, Soria J, Melin P, Valdez F. A new approach for dynamic fuzzy logic parameter tuning in ant colony optimization and its application in fuzzy control of a mobile robot. Applied Soft Computing 2015; 28: 150-159.
[41] Debbarma S, Saikia LC, Sinha N. Automatic generation control using two degree of freedom fractional order PID controller. International Journal of Electrical Power & Energy Systems 2014; 58: 120-129.
[42] Pradhan PC, Sahu RK, Panda S. Firefly algorithm optimized fuzzy PID controller for AGC of multi-area multisource power systems with UPFC and SMES. Engineering Science and Technology International Journal 2016; 19 (1): 338-354.
[43] Dash P, Saikia LC, Sinha N. Automatic generation control of multi area thermal system using bat algorithm optimized PD–PID cascade controller. International Journal of Electrical Power & Energy Systems 2015; 68: 364- 372.
[44] Premkumar K, Manikandan B. Bat algorithm optimized fuzzy PD based speed controller for brushless direct current motor. Engineering Science and Technology International Journal 2016; 19 (2): 818-840.
[45] Abd-Elazim S, Ali E. Load frequency controller design via BAT algorithm for nonlinear interconnected power system. International Journal of Electrical Power & Energy Systems 2016; 77: 166-177.
[46] Rahmani M, Ghanbari A, Ettefagh MM. Robust adaptive control of a bio-inspired robot manipulator using bat algorithm. Expert Systems with Applications 2016; 56: 164-176.
[47] Sharma Y, Saikia LC. Automatic generation control of a multi-area ST–Thermal power system using Grey Wolf Optimizer algorithm based classical controllers. International Journal of Electrical Power & Energy Systems 2015; 73: 853-862.
[48] Lal DK, Barisal A, Tripathy M. Grey wolf optimizer algorithm based fuzzy PID controller for AGC of multi-area power system with TCPS. Procedia Computer Science 2016; 92: 99-105.
[49] Guha D, Roy PK, Banerjee S. Load frequency control of interconnected power system using grey wolf optimization. Swarm and Evolutionary Computation 2016; 27: 97-115.
[50] Raju M, Saikia LC, Sinha N. Automatic generation control of a multi-area system using ant lion optimizer algorithm based PID plus second order derivative controller. International Journal of Electrical Power & Energy Systems 2016; 80: 52-63.
[51] Jin Q, Qi L, Jiang B, Wang Q. Novel improved cuckoo search for PID controller design. Transactions of the Institute of Measurement and Control 2015; 37 (6): 721-731.
[52] Berrazouane S, Mohammedi K. Parameter optimization via cuckoo optimization algorithm of fuzzy controller for energy management of a hybrid power system. Energy Conversion and Management 2014; 78: 652-660.

APA	Önen Ü, CAKAN A, İlhan İ (2019). Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. , 1938 - 1953. 10.3906/elk-1808-51
Chicago	Önen Ümit,CAKAN Abdullah,İlhan İlhan Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. (2019): 1938 - 1953. 10.3906/elk-1808-51
MLA	Önen Ümit,CAKAN Abdullah,İlhan İlhan Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. , 2019, ss.1938 - 1953. 10.3906/elk-1808-51
AMA	Önen Ü,CAKAN A,İlhan İ Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. . 2019; 1938 - 1953. 10.3906/elk-1808-51
Vancouver	Önen Ü,CAKAN A,İlhan İ Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. . 2019; 1938 - 1953. 10.3906/elk-1808-51
IEEE	Önen Ü,CAKAN A,İlhan İ "Performance comparison of optimization algorithms in LQR controller design for a nonlinear system." , ss.1938 - 1953, 2019. 10.3906/elk-1808-51
ISNAD	Önen, Ümit vd. "Performance comparison of optimization algorithms in LQR controller design for a nonlinear system". (2019), 1938-1953. https://doi.org/10.3906/elk-1808-51

APA	Önen Ü, CAKAN A, İlhan İ (2019). Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. Turkish Journal of Electrical Engineering and Computer Sciences, 27(3), 1938 - 1953. 10.3906/elk-1808-51
Chicago	Önen Ümit,CAKAN Abdullah,İlhan İlhan Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. Turkish Journal of Electrical Engineering and Computer Sciences 27, no.3 (2019): 1938 - 1953. 10.3906/elk-1808-51
MLA	Önen Ümit,CAKAN Abdullah,İlhan İlhan Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. Turkish Journal of Electrical Engineering and Computer Sciences, vol.27, no.3, 2019, ss.1938 - 1953. 10.3906/elk-1808-51
AMA	Önen Ü,CAKAN A,İlhan İ Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. Turkish Journal of Electrical Engineering and Computer Sciences. 2019; 27(3): 1938 - 1953. 10.3906/elk-1808-51
Vancouver	Önen Ü,CAKAN A,İlhan İ Performance comparison of optimization algorithms in LQR controller design for a nonlinear system. Turkish Journal of Electrical Engineering and Computer Sciences. 2019; 27(3): 1938 - 1953. 10.3906/elk-1808-51
IEEE	Önen Ü,CAKAN A,İlhan İ "Performance comparison of optimization algorithms in LQR controller design for a nonlinear system." Turkish Journal of Electrical Engineering and Computer Sciences, 27, ss.1938 - 1953, 2019. 10.3906/elk-1808-51
ISNAD	Önen, Ümit vd. "Performance comparison of optimization algorithms in LQR controller design for a nonlinear system". Turkish Journal of Electrical Engineering and Computer Sciences 27/3 (2019), 1938-1953. https://doi.org/10.3906/elk-1808-51