Regulation of Nonminimum-Phase Nonlinear Systems Using Slow Integrators and High-Gain Feedback

This paper investigates the regulation problem for nonminimum-phase nonlinear systems via slow integrators and high-gain feedback. The developed methodology involves four steps: in the first step, we design a full-information feedback controller for an auxiliary system, which parallels the stabilization of the original system, as pioneered in [18]. In the second step, we use high-gain feedback to stabilize the original system, which is able to recover the performance of the auxiliary system by choosing the gain high enough. In the third step, with a condition on the dc steady-state input-output map, a slow integrator is added that enforces the objective of regulation. In the last step, we extend the methodology into the output feedback case by utilizing the extended high-gain observer to estimate the derivatives of the output as well as one unknown term including system uncertainties. The use of the observer recovers the performance under full-information feedback. The design procedure is first presented for the linear model for the clarity of the proposed methodology. The effectiveness of such methodology is demonstrated on the nontrivial translational oscillator rotating actuator example. At last, the design for minimum-phase nonlinear systems is also provided. In this case, the performance recovery of the closed-loop auxiliary system by output feedback is verified.