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.
Highlights
The ball & beam system has been used to study and analyze the stability control of many control engineering problems [1]
Genetic Algorithm (GA)-Proportional Integral-Proportional Derivative (PI-Proportional Derivative (PD)) controller is implemented for the set point tracking of ball and beam system given by equation 6
Implementation of GA-Proportional Integral (PI)-PD controller for the set point tracking is provided
Summary
The ball & beam system has been used to study and analyze the stability control of many control engineering problems [1]. Since open loop response of this system is unstable, so a controller is always required to make this system stable. For this purpose, many controllers have been used for the stabilization of ball and beam system such as Fuzzy controller, SIMC-PID, H-infinity and LQR and [2,3,4,5,6,7,8,9,10,11]. Many traditional tuning techniques have been used for the tuning of these controllers Evolutionary computational techniques such as Differential Evolution (DE) and Particle Swarm Optimization (PSO) have been explored successfully for the tuning of controllers. The comparison of the GA-PI-PD controller with SIMC based PID (SIMC-PID) and H-infinity controller is presented to evaluate the working of the proposed controller
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