Performance Evaluation of Pole Placement and Linear Quadratic Regulator Strategies Designed for Mass-Spring-Damper System Based on Simulated Annealing and Ant Colony Optimization


  • Huthaifa Al-Khazraji University of Technology Iraq
  • Luay T. Rasheed Control and System Engineering Department University of Technology Baghdad, Iraq



State Feedback Controller, Pole Placement, Linear Quadratic Regulator, Mass-Spring-Damper System, Simulated Annealing Optimization, Ant Colony Optimization


This paper investigates the performance evaluation of two state feedback controllers, Pole Placement (PP) and Linear Quadratic Regulator (LQR). The two controllers are designed for a Mass-Spring-Damper (MSD) system found in numerous applications to stabilize the MSD system performance and minimize the position tracking error of the system output. The state space model of the MSD system is first developed. Then, two meta-heuristic optimizations, Simulated Annealing (SA) optimization and Ant Colony (AC) optimization are utilized to optimize feedback gains matrix K of the PP and the weighting matrices Q and R of the LQR to make the MSD system reach stabilization and reduce the oscillation of the response. The Matlab software has been used for simulations and performance analysis. The results show the superiority of the state feedback based on the LQR controller in improving the system stability, reducing settling time, and reducing maximum overshoot. Furthermore, AC optimization shows significant advantages for optimizing the parameters of PP and LQR and reducing the fitness value in comparison with SA optimization


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• AL-Khazraji, H, Cole, C. and Guo, W., 2017. Dynamics analysis of a production-inventory control system with two pipelines feedback. Kybernetes, 24(10), pp.1632-2653

• AL-MulaHumadi, R., Abbas, N.H., and Joodi, M.A., 2018. Optimum Design of Power System Stabilizer based on Improved Ant Colony Optimization Algorithm. Journal of Engineering, 24(1), pp.123-145

• Alvarez-Sánchez, E., 2013. A quarter-car suspension system: car body mass estimator and sliding mode control. Procedia Technology, 7, pp.208-214.

• Brogan, W.L., 1991. Modern control theory. Pearson Education India.

• Burns, R. S., Advanced Control Engineering, Butterworth Heinemann, Oxford, U.K., 2001.

• Di Cairano, S., Bemporad, A., Kolmanovsky, I., and Hrovat, D., 2006. Model predictive control of nonlinear mechatronic systems: An application to a magnetically actuated mass spring damper. IFAC Proceedings Volumes, 39(5), pp.241-246.

• Dorigo, M., Maniezzo, V., and Colorni, A., 1996. Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 26(1), pp.29-41.

• Dorigo, M., and Stützle, T., 2019. Ant Colony Optimization: Overview and Recent Advances. In Handbook of Metaheuristics (pp. 227-263). Springer, Boston, MA.

• Duan, H.B., Wang, D.B., and Yu, X.F., 2006. Novel approach to nonlinear PID parameter optimization using ant colony optimization algorithm. Journal of Bionic Engineering, 3(2), pp.73-78.

• Enríquez-Zárate, J., Silva-Navarro, G., and Sira-Ramírez, H., 2000, December. Sliding mode control of a differentially flat vibrational mechanical system: Experimental results. In Proceedings of the 39th IEEE Conference on Decision and Control (Cat. No. 00CH37187) (Vol. 2, pp. 1679-1684). IEEE.

• Fang, J., 2014. The LQR controller design of two-wheeled self-balancing robot based on the particle swarm optimization algorithm. Mathematical Problems in Engineering, 2014.

• Ge, S.S., Huang, L., and Lee, T.H., 2004. Position control of chained multiple mass-spring-damper systems: adaptive output feedback control Approaches. International Journal of Control, Automation, and Systems, 2(2), pp.144-155.

• GirirajKumar, S.M., Rakesh, B., and Anantharaman, N., 2010. Design of controller using simulated annealing for a real time process. International Journal of computer applications, 6(2), pp.20-25.

• Hsiao, Y.T., Chuang, C.L., and Chien, C.C., 2004, September. Ant colony optimization for designing of PID controllers. In 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No. 04CH37508) (pp. 321-326). IEEE.

• Huang, S.H., and Lin, P.C., 2010. A modified ant colony optimization algorithm for multi-item inventory routing problems with demand uncertainty. Transportation Research Part E: Logistics and Transportation Review, 46(5), pp.598-611.

• Kim, W., Voloshin, A.S., and Johnson, S.H., 1994. Modeling of heel strike transients during running. Human Movement Science, 13(2), pp.221-244.

• Kirkpatrick, Scott, C. Daniel Gelatt, and Mario P. Vecchi. "Optimization by simulated annealing." science 220, no. 4598 (1983): 671-680.

• Kouassi, B.A., Zhang, Y., Ouattara, S., and Kiki, M.J.M., 2019, September. PID Tuning Of Chopper Fed Speed Control Of DC Motor Based On Ant Colony Optimization Algorithm. In 2019 IEEE 3rd International Electrical and Energy Conference (CIEEC) (pp. 407-412). IEEE.

• Lahcene, R., Abdeldjalil, S., and Aissa, K., 2017, October. Optimal tuning of fractional order PID controller for AVR system using simulated annealing optimization algorithm. In 2017 5th International Conference on Electrical Engineering-Boumerdes (ICEE-B) (pp. 1-6). IEEE.

• Li, Z., and Yin, Z., 2017, May. Position tracking control of mass spring damper system with time-varying coefficients. In 2017 29th Chinese Control and Decision Conference (CCDC) (pp. 4994-4998). IEEE.

• Lian, R.J., and Huang, S.J., 2001. A mixed fuzzy controller for MIMO systems. Fuzzy Sets and Systems, 120(1), pp.73-93.

• Mohammed, H.A.U.Q., and Wasmi, H.R., 2018. Active Vibration Control of Cantilever Beam by Using Optimal LQR Controller. Journal of Engineering, 24(11), pp.1-17.

• Nagaraj, B., and Murugananth, N., 2010, October. A comparative study of PID controller tuning using GA, EP, PSO and ACO. In 2010 International Conference On Communication Control And Computing Technologies (pp. 305-313). IEEE.

• Nemirsky, K.K., and Turkoglu, K., 2017, October. Simulated Annealing-Based Optimal PID Controller Design: A Case Study on Nonlinear Quadcopter Dynamics. In Dynamic Systems and Control Conference (Vol. 58271, p. V001T02A002). American Society of Mechanical Engineers.

• Nikooyan, A.A., and Zadpoor, A.A., 2011. Mass–spring–damper modeling of the human body to study running and hopping–an overview. Proceedings of the institution of mechanical engineers, Part H: Journal of engineering in medicine, 225(12), pp.1121-1135

• Prasad, L.B., Tyagi, B., and Gupta, H.O., 2014. Optimal control of nonlinear inverted pendulum system using PID controller and LQR: performance analysis without and with disturbance input. International Journal of Automation and Computing, 11(6), pp.661-670.

• Priyambodo, T.K., Dharmawan, A., Dhewa, O.A., and Putro, N.A.S., 2016, July. Optimizing control based on fine tune PID using ant colony logic for vertical moving control of UAV system. In AIP Conference Proceedings (Vol. 1755, No. 1, p. 170011). AIP Publishing LLC.

• Rao, S.S, 2009. Engineering optimization: theory and practice. John Wiley & Sons.

• Rosli, R., Mohamed, Z., and Priyandoko, G., 2021, February. Simulation of Active Force Control Using MR Damper in Semi Active Seat Suspension System. In IOP Conference Series: Materials Science and Engineering (Vol. 1062, No. 1, p. 012005). IOP Publishing.

• Salem, M.M.M., and Aly, A.A., 2009. Fuzzy control of a quarter-car suspension system. World Academy of Science, Engineering and Technology, 53(5), pp.258-263.

• Valluru, S.K., and Singh, M., 2017. Metaheuristic tuning of linear and nonlinear PID controllers to nonlinear mass spring damper system. International Journal of Appled Engineering Research., 12, pp.2320-2328.

• White, R.E., Macdonald, J.H., and Alexander, N.A., 2021. A nonlinear frequency-dependent spring-mass model for estimating loading caused by rhythmic human jumping. Engineering Structures, 241, p.112229.

• Yachen, Z., and Yueming, H., 2008, July. On PID controllers based on simulated annealing algorithm. In 2008 27th Chinese control conference (pp. 225-228). IEEE.



How to Cite

Al-Khazraji, H. and Rasheed, L. T. (2021) “Performance Evaluation of Pole Placement and Linear Quadratic Regulator Strategies Designed for Mass-Spring-Damper System Based on Simulated Annealing and Ant Colony Optimization”, Journal of Engineering, 27(11), pp. 15–31. doi: 10.31026/j.eng.2021.11.02.

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