Extended High-Gain Observer Based Regulation Control For Non-Minimum-Phase Nonlinear Systems

Non-minimum phase nonlinear systems have unstable zero dynamics or internal dynamics,which are widely applied to practical engineering.There is no causal stable inversion for non-minimum systems due to the existence of unstable zeros,thus usual feedback control methods,such as back-stepping,solid model control,are not applicable.In fact,the control of non-minimum phase systems is one of the challenging issues in the control theory and engineering applications,and there has been some theoretical results reported.However,with the continuous development of modern industrial technology,the controlled system has become more and more complex,such as model uncertainties,unknown external disturbances and unknown system states,those features require the controller to be more powerful and the existing methods fail to satisfy.Therefore,the research on such kind of non-minimum phase nonlinear systems is of great theoretical and practical significance.This thesis,by using(slow)integral control and high-gain feedback control method,mainly investigates the problem of output regulation for non-minimum phase nonlinear systems,which can be concluded as follows.?Providing a method for output regulation problem of minimum phase nonlinear systems,which may involve model uncertainties and be subjected to external disturbances.By choosing a suitable auxiliary system and design a corresponding controller to stabilize it,we are able to design a high gain feedback controller for the original system,which is able to make the original system to be exponentially stable at some equilibrium point and recover the performance of the auxiliary closed-loop system as long as the gain is high enough.With a condition on the dc steady-state input-output map,an integrator is added that enforces the objective of regulation.In output feedback case,by using the extension of high-gain observer to estimate the unpredictable state and uncertainties,and saturating the output controller to avoid the phenomenon of “peak”,the output feedback semi-global exponential stability of the original system is achieved.When the gain of the high gain feedback and the gain of high gain observer are high enough,we are able to recover the transient performance of the auxiliary closed-loop system.?Addressing the problem of output regulation for non-minimum phase nonlinear systems,involved with model uncertainties and subjected to external disturbances.The developed methodology involves four steps: In the first step,we design a state feedback controller for an auxiliary system,which parallels the stabilization of the original system.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(EHGO)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 state 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 non-trivial Translational Oscillator Rotating Actuator(TORA)example as well as the linearized inverted pendulum on a cart model.?Studying the output regulation problem for a class of uncertain non-minimum phase system with time-varying disturbances,which are generated by a neutral and stable exogenous system.By designing a state feedback controller for an auxiliary system,the stability of the original system is ensured.Under a condition on the steady-state input-output map,a servo compensator is added into a high-gain feedback controller,which is able to guarantee that the system is exponentially stable at the origin.The effectiveness of this method is verified via proper Lyapunov function,singular perturbation theory and the averaging theory.