PID Control of MIMO Nonlinear Uncertain Systems With Low Relative Degrees

This letter studies control problems for a class of multi-input multi-output (MIMO) strongly coupled nonlinear uncertain systems with mixed relative degrees one and two. We will design an uncoupled PID controller, where each component of the input vector is determined only by a component of the system output regulation error. Under some suitable conditions on the system nonlinear uncertain functions, we will show that the proposed controller can ensure global stability of the closed-loop system while guaranteeing that the output regulation error converges to zero at an exponential rate. We will also demonstrate that the PID parameters can be chosen from an open and unbounded set constructed based on some prior knowledge regarding the nonlinear functions of the system, and that the designed PID controller exhibits two-sided robustness in terms of the uncertain system structure and the selection of controller parameters. A simulation will be provided to verify the theoretical findings.