Improving the Tracking Precision of a Robust Sliding Mode Controller Using Steffensen's Convergence Accelerator Strategy

The primary objective of control system design is to ensure that the system functions effectively, even in the presence of modeling inaccuracies. The Robust Sliding Mode Control is a systematic approach that helps maintain stability and consistent performance accuracy in situations with even considerable dynamic and parameter uncertainties. However, overestimating the control force can cause the system to chatter leading to good tracking accuracy at the cost of high wear of moving mechanical parts, and high heat losses. Smoothing the control signal can reduce chattering, which may result in deteriorated tracking accuracy. The Steffensen Convergence Accelerator Strategy is employed to improve tracking precision and the smoothness of the applied control signal by speeding up the convergence of the controller. Numerical simulations were conducted to analyze the strategy's effectiveness in controlling the van der Pol oscillator. This oscillator is a well-known example of a strong nonlinear system that exhibits nonlinear oscillations and an unstable equilibrium state. The results of the simulations demonstrate that Steffensen's accelerator considerably improved the control quality in terms of accuracy, simplicity, and smoothness of the applied control signal.