Open Access Open Access  Restricted Access Subscription or Fee Access

Optimal PID Design Approaches for an Inverted Pendulum System

(*) Corresponding author

Authors' affiliations



Instability may cause a system to move dangerously and suffer bodily damage, which can become costly. One of the reasons for designing control systems is to stabilize an unstable system. However, control of unstable systems is primarily more difficult either due to lack of precise description of the system or incompletely modelled disturbances. Application of a classical control algorithm does not mostly yield the desired results. Advanced control is expensive and intelligent control has parameters' choice/tuning issues. This paper presents a comparison of optimal Proportional Integral Derivative (PID) controller design techniques for an inverted pendulum. The optimization approaches considered are the swarm intelligent based algorithm (Particle Swarm Optimization [PSO]) and Enhanced Nonlinear PID (EN-PID). The performances of the controllers were evaluated based on stabilizing the angle of the pendulum and disturbance rejection. Simulation results revealed that the PSO-PID outperformed the EN-PID and PID in maintaining the pendulum vertically and demonstrated an attractive ability in rejecting disturbances as compared to the PID and EN-PID. The PSO-PID may serve as a useful control algorithm for the system.
Copyright © 2016 Praise Worthy Prize - All rights reserved.


Pendulum; PID; Nonlinear; Optimization; Particle; Swarm; Gain

Full Text:



M. A. Saeed, S. Tahir, H. Rizvi, and M. Y. Javed, “Optimize Algorithm for Motion Control of Inverted Pendulum , with Real Time Assessment Using MATLAB.”

“CTM Example State-space design for the inverted pendulum,” Control Tutorials for MATLAb & SIMULINK, 2016.

T. R. Krishnan, “On Stabilization of Cart-Inverted Pendulum System: An Experimental Study,” National Institute of Technology, India, 2012.

M. Askari, H. A. F. Mohamed, M. Moghavvemi, and S. S. Yang, “Model predictive control of an inverted pendulum,” International Conference for Technical Postgraduates (TECHPOS), 2009, pp. 1–4.

A. Mills, A. Wills, and B. Ninness, “Nonlinear model predictive control of an inverted pendulum,” American Control Conference, 2009, pp. 2335–2340.

J. Yi and N. Yubazaki, “Stabilization fuzzy control of inverted pendulum systems,” Artif. Intell. Eng., vol. 14, no. 2, pp. 153–163, 2000.

Y. Becerikli and B. K. Celik, “Fuzzy control of inverted pendulum and concept of stability using Java application,” Math. Comput. Model., vol. 46, pp. 24–37, 2007.

Yusuf, L., Magaji, N., Comparison of Fuzzy Logic and GA-PID Controller for Position Control of Inverted Pendulum, (2014) International Review of Automatic Control (IREACO), 7 (4), pp. 380-385.

N. Valeri Mladenov, Georgi Tsenov, Lambros Ekonomou and P. K. Harkiolakis, “Neural Network Control of an Inverted Pendulum on a Cart,” in Proceedings of the 9th WSEAS International Conference on Robotics, Control and Manufacturing Technology, 2007, pp. 3–8.

C. W. Anderson, “Learning to control an inverted pendulum using neural networks,” Control Systems Magazine, IEEE, vol. 9, no. April, pp. 31–37, 1989.

K. Williams Victor, Matsuoka, “Learning to balance the inverted pendulum using neural networks,” in IEEE International Joint Conference on Neural Networks, 1991, pp. 214 – 219.

Gaya, M., Bature, A., Yusuf, L., Madugu, I., Abubakar, U., Abubakar, S., Comparison of Control Strategies Applied to Nonlinear Quarterly Car Passive Suspension System, (2015) International Review of Automatic Control (IREACO), 8 (3), pp. 203-208.

Y. X. Su, D. Sun, and B. Y. Duan, “Design of an enhanced nonlinear PID controller,” Mechatronics, vol. 15, pp. 1005–1024, 2005.

J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Neural Networks, 1995. Proceedings., IEEE International Conference on, 1995, vol. 4, pp. 1942–1948 vol.4.

A. Banks, J. Vincent, and C. Anyakoha, “A review of particle swarm optimization . Part I: background and development,” Nat Comput, vol. 6, pp. 467–484, 2007.

V. Ramos, C. Fernandes, and A. Rosa, “Social Cognitive Maps, Swarm Collective Perception and Distributed Search on Dynamic Landscapes,” 2006.

“ENGM646 III. Global Unconstrained Optimization,” Particle Swarm Optimization, p. 646.

A. . Engelbrecht, Computational intelligence: An introduction, 2nd Editio. John Wiley & Sons Ltd, 2007.

S. Sumathi and S. Paneerselvam, Computational intelligence paradigms: theory & applications using MATLAB. 2010.


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2023 Praise Worthy Prize