Reduction, Based On The Characteristic Structure Of The Controller

The target issue for a control system is to design a controller (regulator), which makes closed-loop system stable and get to the demand for performance index. Lots of present physical systems require numerous parameters for creating real models. However, a good representation of the system generally implies high-order state-space realization. The current synthesis methods applied to control these systems such as the H_∞ or LQG methods, lead to controllers with a high order similar to the initial system. However, the higher the order is, the more difficult feedback implementation can be. On the other hand, simple linear controllers are comprehensible and need less calculation;they are easier to be carried out;they have good reliability because they have fewer faults in hardware and less bugs in software. So, whenever, if the final performance loss is within a reasonable bound, the low-order controller should be the preference.Three methos have been developed by low-order controller design. The first approach is to reduce the model before synthesizing the controller. Thus, the feedback computed on this reduced-order model gives a reduced-order controller. A second approach is firstly give the expected structure of controller such as PI or PID and then directly design the low-order controller. There's also a third approach. A initial controller is computed considering the full model to satisfy specifications without order constraint. Then, this controller is reduced to be very close to the initial controller, which can lead to a closed-loop behavior near the expected one.This paper will show that eigenstructure analysis is well adapted to reduce the order of a controller using the third method mentioned above. The proposed method is essentially based on closed-loop considerations. The aim is to obtain closed-loop responses satisfying the closed-loop specifications with the reduced-order controller. Specifically, two methods are presented whitch base on analysis of full-order controller and the closed-loop's eigenstructure: closed-loop pole assignment for SISO system and closed-loop eigenstructure assignment for MIMO system. The majordifference with existing methods lies in the fact that the reduction does not only minimize the difference between these two controllers, full-order and reduced-order ones, but takes into account the expected closed-loop performance. Some numerical examples show that the method presented in this paper is an efficacious way to perform controller reduction.