The Regulator Design And Application Study Of Multirate Sampled-data Systems

Multirate sampled-data systems have wider applications in modern industrial society and have received a great deal attention. The reason for studying multirate systems is due to their adaptability in various complicated practical situation, and due to the fact that they can improve system performance and often achieve objectives that cannot be achieved by single rate linear time invariant systems. On the basis of well-developed sampling control system theory and state-space equation, the lifting model of multirate digital control system, the design of multirate-output feedback controller and multirate optimal regulator were studied. The control strategy was applied to the inverted pendulum model and the simulation result was presented. This thesis is composed of follows:1. A lifted state-space model for a general multirate digital control system was developed. Through lifting state vector, input and output vector, multirate state-space model of plant and controller was inferred respectively. The lifted closed-loop discrete-time state-space model was derived. It's a linear time-invariant model, representing system behavior at a base sampling rate and at the model sampling rate in the system. It's convenient and effective for analysis and design of multirate systems.2. The sampling mechanism of multirate-output systems was derived. On the basis of the mechanism, a multirate-output controller was designed. If the plant satisfies specific condition, arbitrary pole assignment as state feedback can be realized by the controller and it self possess any prescribed margin of stability.3. Multirate linear quadratic optimal regulator (LQR) design was studied and a time invariant approach to multirate optimal regulator design was proposed. For general multirate sampled-data system, reduction of system dimensionality of lifted system model was done. The resulting system model is a linear time invariant system with the same state dimensionality as the continuous time system. On the basis of the regular LQR design, through mapping the continuous-time cost weighting matrices, the multirate optimal regulator was easily carried out.4. The model of the namely inverted pendulum on a cart was built. Two different Multirate controllers were designed for the linearized model, and the result of simulation was presented and analyzed.