Observer-based Multi-rate Sampling Control

With the rapid development of computer technology since 1950s, sampling system is paid more and more researcher’s attention in industrial applications and theoretical analysis due to its advantages such as high control accuracy, well stability, powerful interference suppression, strong universal property, and so on. For convenience to design and analysis in the most traditional research, all system state variables are sampled by a uniform period. Yet the more small sampling period leads a high device cost and more resource requirement, the more large one will degrade system performance even instability if there is much difference in change-rates of system states. In this way, choosing different sampling periods for different states is necessary, such a sampling system is called multi-rate sampling system. In the recent half century, the main interests of those researchers include two aspects:modeling multi-rate sampling system and multi-rate sampling controller design.This thesis investigates modeling and H∞ control for a class of multi-rate sampling system. Tak-ing into consideration the influence of the system with a network, some random disturbances and nonlinear terms, a multi-rate sampling system is difficultly modeled as a discrete-time system with a common single-rate by the lifting technique. Under some assumptions, it can be modeled here as a continuous-time delay system by constructing a class of observer-based controller. It will turn out to be convenient to analyze theoretically and generalize further. And the main results in this thesis consist of three parts as follows:(1) In the second chapter, we consider the modeling and observer-based control for a class of dual-rate sampling system. The states of the dual-rate sampling system are assumed to be measurable and sampled by two different sampling periods respectively. So they can be just viewed as output signals switched periodically. Based on the above consideration, the Luenberger state observer.evaluating the states of the controlled plant, is used to feed back control the controlled plant. Then the dual-rate system is modeled as a continuous system with two time-varying time-delays of different bounds. A stability criterion and stabilization condition are obtained by using linear matrix inequalities (LMIs) technique. At last, some numerical examples show the effectiveness of the proposed approach.(2) In the third chapter, we consider the modeling and H∞ control for a class of dual-rate sampling system with one-side network. A unilateral networked dual-rate sampling system, where the sensor and the controller are connected via a network channel, is investigated. The network channel has a network-induced time-varying delay and bounded package dropout. The dual-rate sampling is modeled as a continuous system with three time-varying delays of different bounds after some buffers are utilized to synchronize the time stamps of the state signals between the controlled plant and the observer. The stability criterion and stabilization condition are obtained in terms of LMIs. Finally, some numerical examples are proposed to test the effectiveness of the proposed method in this chapter.(3) In the fourth chapter, we consider the modeling and H∞ control for a class of multi-rate sam-pling system with two-side network. Being different form the above chapters, It’s assumed that the system is state immeasurable and the sensor, controller, actuator are connected by a com-mon network. Then the multi-rate sampling is modeled as a continuous system with several time-varying delays of different bounds by combining previous chapter ideals and approaches. Sufficient conditions of stability and stabilization are given by a group of LMIs. In the end, some numerical examples show the effectiveness of the proposed method.