Stability and Tracking Performance of PID Controlled Nonlinear Uncertain Systems

This paper considers the global stability and tracking problem for a class of MIMO nonlinear uncertain systems controlled by the well-known classical PID control. In contrary to most of the existing literature on PID controlled nonlinear uncertain systems, the reference signal is not assumed to be a constant or have a constant limit. First, we will show that the PID parameters can be chosen to ensure the global stability of the closed-loop control systems, as long as some prior knowledge about the partial derivatives of the nonlinear functions and the control gain matrix are available. In addition, the tracking error is proved to be bounded in the whole time interval, with an ultimate upper bound proportional to the change rate of the reference signal. This implies that the ultimate bound of the tracking error will be small, if the reference signal is slowly varying. Furthermore, even if the reference signal is not slowly varying, we will show that the tracking error can still be made arbitrarily small by choosing the PID parameters suitably large.