Time-Scale Redesign-Based Saturated Controller Synthesis for a Class of MIMO Nonlinear Systems

A consideration of actuator saturation is an important aspect to study the effectiveness of a designed controller in practice. However, the conventional Lyapunov theory-based design is not always suitable to analyze the quantitative behavior of closed-loop system. This article presents a time-scale redesign-based saturated tracking controller for a class of feedback linearizable multi-input-multi-output (MIMO) nonlinear systems. The proposed controller is built upon the frameworks of contraction and partial contraction theories which ensures that bounded tracking performance as well as quantify the steady-state error bounds in terms of the various control design parameters. Notably, in contrast to the existing Lyapunov-method-based designs, the proposed approach allows to tune the controller performance without arbitrary reduction of singular perturbation parameters. Therefore, the vulnerability of the controller toward actuator saturation and noise, due to the ill-effects of high-gains stemming from the conventional high-gain controllers, are reduced. The extensive experimental results using a wheeled mobile robot are provided to demonstrate the effectiveness of the proposed controller.