L₁ Optimal Design Method Study Of Given Order Controller

After concisely describing the developmental course of control theory, the paper then educes the l₁ optimal control theory that is regarded as one of many branches in modern control theory. Consequently, aside from presenting the basic idea and framework of l₁ optimal control problem, a systemic overview of the approximate solution methods to the l₁ optimal control problem, as well as the analysis of the advantage and disadvantage of these approximate methods is given in this paper.This paper, whose background is practical engineering applications and its investigative objectives are coprime factor perturbations and unknown external disturbances systems, studiesthe l₁ optimal design method of given order controller based on multiple input-multiple outputdiscrete-time systems. For given order n controller, it optimizes the corresponding objective function and schemes out the optimal controller in order that the l\ optimal controller can meet its optimal configuration with respect to all kinds of robustness performance specifications under given order n. It divides the free parameter Q obtained from Youla parameterization into the cases of polynomial and rational to discuss, and translate the rational case into polynomial. Eventually, it solves the problem via finite-dimensional linear programming. In the paper, it obtains a linear time-invariant discrete-time controller that minimizes the l₁ norm of close-loop internally stabilizing system under given the controller's order. Finally, an example is presented and is showed by experimental simulation to illustrate the availability of the algorithm. Farther exploring, it put forward that applying l₁ optimal control theory and their relative algorithms into the virtual environment of computers and Internet as a development direction in the future.Comparing to other existing algorithms, the algorithm came from this paper doesn't via relative converting of double theory. Therefore, it is more straightforward and concise. Furthermore, it avoids the trouble of zeros and poles cancellation causing by zeros interpolation. So, it is a more practical approach.