Adaptive control using stochastic approach for unknown but bounded disturbances and its application in balancing control

This paper presents a simultaneous perturbation stochastic approximation (SPSA) approach for unknown but bounded disturbances in a typical closed loop system. These random disturbances are represented by a sequence of uncertainties along with the measured system output. Further, the proposed approach constructs a sequence of estimates and formulates an optimization problem which is minimized to achieve the adaptive control. In addition, the convergence conditions and additional generalizations are proposed to enhance the operation of SPSA algorithms for trail perturbation properties. To address the major challenges with unknown disturbances on the closed loop system, a balancing control problem with two degree of freedom (2DoF) ball balancer system and proportional integral derivative (PID) controller is considered. The proposed SPSA method minimizes the optimization problem to obtain the gain values of the PID controller. Simulation and experimental analysis are carried out, and the results substantiate that the PID gains optimized using SPSA provide better control when compared to conventional control approach in terms of tracking response under random uncertainties.