Discrete-time Analysis of a Robust Model Reference Adaptive Sliding Mode Control

In real-world applications, plants with parametric variations and unmodelled dynamics are very common, and, in most cases, fixed-gain controllers can not ensure global stability and hardly have high performance for large system variations. To overcome this challenge, this paper presents a Robust Model Reference Adaptive Sliding Mode Control, whose structure combines a Robust Model Reference Adaptive controller (RMRAC) and an adaptive first-order Sliding Mode controller (SMC). Its discrete-time robustness analysis and stability proofs by means of Lyapunov theory are provided. The mathematical analyses show that this hybrid adaptive controller is robust to parametric variations and unmodelled plant dynamics. Besides, it ensures that tracking error tends to a residual set in steady state, maintaining global stability. Simulation results are presented to show the controller effectiveness applied in a non-minimum phase unstable plant with unmodelled dynamics. Furthermore, a comparison with a Proportional-Resonant controller is also provided.