A combined PID/adaptive controller for a class of nonlinear systems

This paper presents a robust control method for a class of nonlinear systems, based on a mixed PID/adaptive algorithm. The nonlinear system is considered as a second-order linear dominant model with an unmodeled dynamics that is possibly nonlinear and time-varying. The PID part of the controller is applied to stabilize the dominant model. The adaptive part of the controller is used to compensate for the deviation of the system characteristics from the dominant linear model for performance enhancement. The advantage of our controller is that it can cope with strong nonlinearities in the system without abandoning the PID controller which is well-known to many engineers. The proposed control scheme guarantees the boundedness of the system states and parameter estimation. An example is given to illustrate the effectiveness of the proposed controller.