Comparative analysis of bioinspired algorithms for tuning a flatness-based controller: A ball and beam case study

This paper provides a comprehensive comparative analysis of the performance of four bioinspired algorithms (Differential Evolution, Grasshopper Optimization Algorithm, Moth-flame Optimization, and Particle Swarm Optimization) in designing a flatness-based controller for a ball and beam system simulated in MATLAB/Simulink environment. The assessment involves the tuning of feedback gains utilizing four distinct fitness functions: Integral Square Error, Integral Absolute Error, Integral Time Absolute Error, and an ad-hoc cost function. Hypothesis tests are employed to choose the optimal controllers from each combination for every bioinspired algorithm and a fitness function. Subsequently, a control performance analysis of these controllers for the ball and beam system is conducted, focusing on critical parameters such as overshoot, settling time, and steady-state error. This analysis demonstrates that all the controllers achieve a zero steady-state error. Noteworthy is the flatness-based controller tuned with the bioinspired Grasshopper Optimization Algorithm and utilizing the Integral Time Absolute Error fitness function, which stands out for achieving the fastest response with the lowest overshoot. This particular controller emerges as the most recommended choice for the specified application.