On the Transient Response of a Nonlinear Output Regulator

In, Serrani, Isidori, and Marconi design an output feedback controller that achieves semiglobal output regulation for a class of minimum phase nonlinear systems. The controller has three components: an internal model to ensure asymptotic regulation, a high-gain partial state feedback controller to stabilize the augmented system of the plant and internal model, and a high-gain observer to implement the partial state feedback. In this note we show a property of the transient response of this controller. We consider an alternate controller that shares with the controller of the structure of high-gain partial state feedback and high-gain observer, but without internal model. Such controller can only achieve practical regulation. We show that when the controller and observer gains are large enough, the trajectories under the two controllers will be close to each other. Hence, the transient response of the controller of is not degraded by the inclusion of internal model. A similar transient response property is shown by Seshagiri and Khalil for the conditional servocompensator. Similarities and differences between the two designs are pointed out.