Sampled-data Output Regulation Of Linear And Nonlinear Systems

The question of output regulation is to find the control law, which makes the unforced closed-loop system asymptotically stable and the output of the forced closed loop system asymptotically track the given signal, and asymptotic interference suppression at the same time. This is one of the core issues in control theory. Sampled-data output regulation problem is to choose a sample period T which is small enough to achieve the output regulation of continuous system by use of discrete regulator. Since more and more controllers are being implemented using digital computers in practice, the sampled-data output regulation problem is becoming increasingly important and imperative.Under this background, this paper studies the sampled output regulation problem on the bases of continuous output regulation theory. Corresponding to the case of continuous output regulation, the linear system achieves global result, and the nonlinear system achieves local result. Because the corresponding conditions and conclusions are different, this paper is divided into two cases to study, includes constant signal and general signal. When the signal is constant, asymptotic regulation can be obtained, and the condition is as same as continuous situation. When the signal is not constant, asymptotic regulation cannot be obtained, we can only get a weak practical regulator and require the derivatives of the signal is bounded. In these four cases,this paper designs the state feedback regulator and error feedback sampled-data regulator for continuous linear systems, determine the range of sample period T through stability analysis, to achieve global sampled-data output regulation. In the stability analysis section, this paper inspires the sample output feedback stabilization problem raised in the stability analysis by Qian in 2012, and innovatively applied it to the asymptotic stability analysis of output regulation problem, then deduced stability analysis of practical regulation by the use of this conclusion successfully.Be different from the existing literatures which solve the output regulation problem of linear systems through the discretization of continuous system, this paper solve it of linear system through the discretization of continuous controller for the first time. Using this idea, the sampled-data output regulation problem of nonlinear affine systems is solved for the first time this paper. And then, Based on the output regulation method of linear system, this paper estimates the nonlinear term with the property of continuously differentiable function. After that, the asymptotic regulation for constant signal and practical regulation for neutral stable signal are achieved. The result of this paper provides a theoretical basis for computer implementation of many practical problems, such as dynamic tracking of cardiac surgery robot and harmonic suppression in grid, has important significance and application value.