Abstract
The ball and balancer system is a popular research platform for studying underactuated mechanical systems and developing control algorithms. It is a well-known two-dimensional balancing problem that has been addressed by a variety of controllers. This research work proposes two controllers that are proportional integral derivative-second derivative-proportional integrator (PIDD2-PI) controller and tilt integral derivative with filter (TID-F) controller in a multivariate, electromechanical, and nonlinear under-actuated ball and balancer system. Integral Time Absolute Error (ITAE) is an objective function used for designing controllers because of its ability to be more sensitive to overshooting as well as reduced settling time and steady-state error. As part of the analysis, four metaheuristic optimization algorithms are compared in the optimization of proposed control strategies for cascaded control of the ball and balancer system. The algorithms are the Grey Wolf optimization algorithm (GWO), Cuckoo Search algorithm (CSA), Gradient Base Optimization (GBO), and Whale Optimization Algorithm (WOA). The effectiveness of proposed controllers PIDD2-PI and TID-F is investigated to be better in terms of transient time response than proportional integral derivative (PID), proportional integral-derivative (PI-D), proportional integral-proportional derivative (PI-PD) and proportional integral derivative-second derivative-proportional derivative (PIDD2-PD). Moreover, these two proposed controllers have also been compared with recently published work. During the analysis, it is shown that the proposed control strategies exhibit significantly greater robustness and dynamic responsiveness compared to other structural controllers. The proposed controller WOA-PIDD2-PI reduced the 73.38% settling time and 88.16% rise time compared to classical PID. The other proposed controller GWO-TID-F reduced 58.06% the settling time and 26.96% rise time compared to classical PID. These results show that proposed controllers are particularly distinguished in terms of rise time, settling time, maximum overshoot, and set-point tracking.