Atom Search Optimizer-driven Lead Compensator Design for Unstable Ball and Beam System

This study proposes a novel framework for stabilizing the inherently unstable ball and beam system by combining a classical lead compensator with the atom search optimizer (ASO). The ball and beam setup, widely recognized as a benchmark for evaluating control strategies, poses significant challenges due to its open-loop instability and nonlinear dynamics. To address these issues, we formulate the design of a lead compensator in terms of an integral of absolute error (IAE) cost function, with constraints that ensure a genuine phase-lead characteristic. ASO automatically tunes the compensator parameters by iteratively minimizing the IAE criterion while respecting the required pole–zero placement. Simulation results compare the ASO-based controller against genetic algorithm, sine-cosine algorithm, and a root locus–based method. The ASO-driven design consistently achieves faster settling, lower overshoot, and reduced IAE under both linearized and nonlinear plant representations. Overall, the proposed scheme demonstrates not only robust tracking performance but also adaptability to the system’s nonlinearities, confirming the effectiveness of metaheuristic optimization for real-world control applications.