Controller design for high-order descriptor linear systems based on requirements on tracking performance and disturbance rejection

In this paper, controller design for high-order descriptor linear systems based on requirements on tracking performance and disturbance rejection is addressed. The proposed controller is composed of a decoupling controller and a disturbance term observer. When designing the controller, a new tracking performance index is first defined, which reflects the desired modes of tracking error of the closed-loop system. Based on this index, a decoupling controller with a disturbance term is derived. A disturbance term observer is then designed to estimate the disturbance term. Stability is proved for the closed-loop system and it is shown that the speed and shape of response of the closed loop tracking error can be conveniently regulated with only two parameters; furthermore the closed-loop system has robust disturbance compensation property. The attitude control of a spacecraft is used as an example to demonstrate the effectiveness of the controller.