The Combination Problem On Disturbance Decoupling And Pole Placement

Generally speaking, the disturbance of the system is inevitable. By statement feedback, the system can eliminate the influence of external disturbance to the system output. That is the so called disturbance decoupling problem. In the past decades, it obtained a thorough research, also already formed very perfect theory. But the disturbance decoupling alone is a property of limited vale. Of utmost concern in the design of any control law is to guarantee that the closed loop system behaves in a reasonable way. The first requirement is clearly to insure stability of the system, but often this is not enough. A desirable asset is to place the poles of the closed loop system at arbitrary positions; the system can then have better damping, rise time and many other properties.This paper is just in the foundation of the disturbance decoupling, further requesting the designed feedback control satisfy the desired requests. This article mainly discussed these issues by using state transformation and matrix method. The main research contents include:1. Referring to the geometry research method in multivariable control, which is popularized by Wonham, this paper gives the description and proof of related proposition by matrix theory. And then gave a necessary and sufficiency condition of the disturbance decoupling with pole placement, that is existing a feedback controller with which we can eliminate the influence on outputs and simultaneously assigning all poles of a closed loop system is derived. In fact, the proof process has included the construction method of feedback matrix,2. Considering the required feedback matrix makes the matrix of close-loop system have specific structure, this paper give a simple solution of constructing the feedback matrix by using state transformation to reduce the form of input matrix.3. In the conditions of controllability and stabilizability, this paper gives the solution of the disturbance decoupling problem with stability.4. At last give an example about a solution to the problem, which is about disturbance decoupling with poles placement and stability.