Set point tracking of Ball and Beam System Using Genetic Algorithm based PI-PD Controller

Abstract

The ball and beam system is one of the commonly used benchmark control apparatus for evaluating numerous different real systems and control strategies. It is an inherently nonlinear and open-loop unstable system. In this paper, we have suggested an Evolutionary Algorithm (EA) based Proportional Integral-Proportional Derivative (PI-PD) controller for the set point tracking of this well-known ball and beam system. A linearized model of the ball and beam system is deduced and PI-PID control methodology is employed. The popular EA technique such as Genetic algorithm (GA) is used for tuning of the controller. The optimized values of the controller parameters are achieved by solving a fitness function using GA. The transient performance of the proposed GA based PI-PD controller (GA-PI-PD) is evaluated by carrying set point tracking analysis of the ball and beam system through MATLAB/Simulink simulations. Furthermore, the performance of GA-PI-PD controller is investigated using four different performance indices such as Integral of squared value of error (ISE), Integral of time multiplied by squared value of error (ITSE), Integral of absolute value of error (IAE) and Integral of time multiplied by absolute value of error (ITAE). The comparison of transient performance including rising time, settling time and % overshoot is made with SIMC-PID and H-infinity controllers. The comparison reveals that GA-PI-PD controller yielded transient response with small % overshoot and settling time. The superior performance of the GA-PI-PD controller has witnessed that it is highly effective for maintaining good stability and the setpoint tracking of ball and beam system with fast settling time and less overshoot than SIMC-PID and H-infinity controllers.

Stabilization and tracking control of underactuated ball and beam system using metaheuristic optimization based TID-F and PIDD2–PI control schemes

“…We then consider BBS with change in its parameters as given in Eq 18, to test the robustness, step response performance, set point tracking and disturbance rejection capabilities of the proposed control schemes GWO-TID-F-ISE and WOA-PIDD-PI-IS, as well as provide the comparison with published relevant research work [21][22][23][24] as a case-02.…”

“…Case-01. In this section, a comparison is made between the proposed control strategies GWO-TID-F-ISE and WOA-PIDD 2 -PI-ISE with CSA-PI-PD [20] using the same model parameters given in Table 1 for BBS.…”

“…In Case-02. Here we consider the BBS with change in the parameters of the system as given in Eq 18 for a direct comparison with [21][22][23][24] and show the improved performance and robustness of the proposed schemes. A step response analysis, tracking performance, disturbance rejection analysis is carried out and comparison between different control schemes and optimization techniques are made.…”

“…The transfer function for the BBS [21][22][23][24] with the same values from Table 1 except the length of beam which is used as L = 0.4 m is given as…”

“…A knowledge-based particle swarm optimization (PSO) algorithm [17][18][19] adaptively controls the BBS. In comparison to H-infinity-based PIDs and Particle Swarm Optimization (PSO)-based I-PDs, they concluded that the Cuckoo Search algorithm CSA--PI-PD [20] serves as a significantly superior controller in terms of closed-loop transient response. The study of the set point tracking response of a BBS involved the employment of a PI-PD controller.…”