The Internal Model And Controller Design For The Output Regulation Problem

As one of the central problems in control theory, the output regulation problem aims to design a feedback control law for the given plant, which can achieve asymptot-ic tracking of a class of reference signals and rejecting of a class of disturbance signals while maintaining the stability of the closed-loop system. The reference or the distur-bance signals are called exosignals and are generated from an autonomous dynamical system, which is called the exosystem. Due to the uncertainties and complexities of controlled plants and exosystems, the output regulation problem has been one of most challenging issues in the control field.It is well known that, the regulator can be divided into two parts:the first one is the internal model, which can provide a feedforward term to eliminate the steady-state error; the second one is the stabilizer, which can stabilize the overall system. In linear systems, the internal model is a copy of the exosystem; while in nonlinear case, the internal model not only provide a copy of exosystem, but also need to generate a number of high-order nonlinear deformations of the trajectories of the exosystem. However, due to the complicated structure of the plant and the exosystem, it is difficult to construct a suitable internal model. Thus, how to design a suitable internal model not only is a key point, but also is a difficult point in solving the output regulation problem.In the thesis, we attempt to probe into the internal model design by considering three types of output regulation problems of output feedback systems. The first one is the robust output regulation problem of an infinite dimensional system with an unknown exosystem; the second one is the globally robust output regulation problem of output feedback nonlinear systems with an unknown exosystem; the last one is the globally robust output regulation problem with a nonlinear exosystem. The main contributions of the thesis are summarized as follows.1. The output regulation problem for a class of infinite dimensional systems with an uncertain exosystem is considered. For these systems, a concept of relative degree is firstly introduced and used to construct a transformation which leads to the canonical form of output feedback systems. Then, based on this canonical form, by means of an internal model and a recursive adaptive control, we obtain an adaptive regulator which solves the problem. It should be pointed out that the proposed regulator is finite dimensional while it is usually infinite dimensional in existing literatures.2. The global output regulation problem of output feedback nonlinear systems with an unknown exosystem is studied via a new internal model. The main feature of the proposed internal model is that, based on a nonlinear observer, the unknown parameters is estimated without relying on the traditional nonlinear adaptive techniques. So it can be viewed as a nonlinear internal model in a non-adaptation scheme. Furthermore, the dimension of the unknown parameter vector is as many as the sinusoids in the steady-state input of the systems, while, in the existing literatures, this dimension is twice as many as the sinusoids in the steady-state input. Then, an output feedback control law is proposed to solve the problem. Finally, a disturbance rejection problem of Duffing’s system is utilized to illustrate the effectiveness of the new internal model.3. The global output regulation problem of output feedback nonlinear systems with a nonlinear exosystem is considered. From the viewpoint of contraction theory, a suf-ficient condition for the existence of internal models is that all trajectories of the steady state generator are the trajectories of an internal model which is a contracting system. The new internal model can avoid complicated Lyapunov analysis as well as remove structure restrictions of some existing nonlinear internal models. Finally, the robust output regulation problem for output feedback systems with nonlinear exosystems is solved by a recursive solution which is independent of state variables of the exosystem.