A Kiefer-Wolfowitz algorithm based adaptive PID for magnetic levitation ball system with experimental verification

The magnetic levitation system is a class of valuable research subject due to its potentially wide applications. However, this class of system is open-unstable and strongly nonlinear, increasing the difficulty to control. Traditional proportional-integral-differential (PID) control is still the mainstream in practical magnetic levitation applications due to its model-free nature and simplicity. However, tuning PID gains is a challenging task, especially in the presence of system and measurement noises. From a data-driven view of point, this paper introduces a Kiefer-Wolfowitz or simultaneous perturbation stochastic algorithm (SPSA) to adjust PID gains online to improve the system performance. The gradient information of the control performance loss function is estimated via practical outputs to search possible improvement direction. With the estimated gradient information, each component of the PID gains is updated simultaneously. Experiments results verify the effectiveness of the proposed method.