State Feedback Control Based On Passivity Theory

In practical engineering, many physical systems are nonlinear systems with uncertainties because of various reasons, so robust tacking control of nonlinear systems with uncertainties is a class important question. At present, nonlinear state feedback stable controller is usually designed by differential geometry and Backstepping in the study of nonlinear state feedback stabilization, but it mainly aims at a class of nonlinear system with triangle structure, and there are a little productions about dynamic output feedback for the other kind nonlinear systems.Passive theory is widely using for the study of nonlinear system, and we gain a mass of production in the problem of nonlinear stabilization. But the sufficient and necessary conditions to make system passivity are relative degree one and weakly minimum phase (zero dynamic stabilization). It is difficult to satisfy these conditions for common nonlinear systems, so that the application of passive is largely constrained in the field of nonlinear control.Firstly, this paper analyzes the development status of nonlinear uncertain systems control, and presents the great significance of studying the stability and tracking control of nonlinear uncertain systems. Next, for a class of essence nonlinear systems with unknown parameters, a passivity-based control(PBC) strategy based on state feedback is proposed, it overcomes the astriction of relative degree one, and it solves the stabilization and the output tracking problems of the nonlinear system. In this paper, it respectively analyzes adaptive state feedback and non-adaptive state feedback, and respectively designs non-adaptive stabilization controller, output tracking controller and adaptive stabilization controller, output tracking controller by using PBC. Just using the output signal as a control signal, it can guarantee the closed-loop system stability, and can achieve global output tracking and the overall system signals global uniform boundedness. Simulation examples verify the validity of the control scheme, show that the system has strong stabilization and tracking characteristics. Finally, this paper compares the dynamic adjustment performance of two controllers by tracking the step signal. The simulation results show that the adaptive control system has a stronger tracking and dynamic regulation.