Stability Control of Ball and Beam System Using Heuristic Computation Based PI-D and PI-PD Controller

Abstract

The ball & beam system (BBS) exhibits an unstable open loop response, which requires a controller to act as a stable system. In this paper, Proportional Integral-Derivative (PI-D) and Proportional Integral-Proportional Derivative (PI-PD) controllers are suggested for the stability control of BBS. The tuning of these controllers is carried out using two popular heuristic computational techniques including Simulated Annealing (SA) and Cuckoo Search Algorithm (CSA). Furthermore, four different performance indices including Integral of squared error (ISE), Integral of absolute value of error (IAE), Integral of time multiplied by squared value of error (ITSE) and Integral of time multiplied by absolute value of error (ITAE) are used for the evaluation of transientperformance of the suggested controllers. MATLAB/Simulink simulations are performed to show the closed-loop step-response achieved by the proposed controllers. The comparison of transient performance parameters including settling time (ts), % overshoot (os), rise time (tr) and steady state error (ess.)obtained by the proposed controllers is made with Hinfinity based PID and Particle Swarm Optimization(PSO) based I-PD (PSO-I-PD) controllers. It is observed that BBS system with PI-PD controller tunedby CSA (CSA-PI-PD) yields oscillation free, stable, and fast response. CSA-PI-PD controller with ITAEindex provided response of the BBS with zero % overshoot and settling time of 1.21s as compared to20.7% overshoot and 4.3s settling time yielded by Hinfinity based PID controller. Furthermore, CSA-PIPD controller yielded transient response with 72% reduction in settling time and 88% reduction in risetime in comparison to PSO-I-PD controller.