Multirate Fuzzy Control Theory And Its Application Research On Direct Torque Control

Owing to the rapid development of the modern microprocessor and its interfacing hardware, the digital controller is popularly utilized for controlling complicated dynamical systems such as aircrafts, robots, hard disc drivers and chaotic systems. Especially, some research results on digital control for nonlinear systems based on the Takagi-Sugeno (T-S) fuzzy model have been published. However, these researches are mostly limited to single-rate digital control systems. In practical engineering applications, it is unreasonable, or even impossible that single-rate sampling scheme is utilized to sample and control complex multi-input multi-output nonlinear systems that include various frequency characteristics signals in input and (or) output channels. Therefore, this paper aims at merging multirate sampling control scheme and T-S fuzzy model based control technology, and putting them into a model-based fuzzy digital control framework for a class of nonlinear systems. The following aspects of digital control for nonlinear systems are discussed and studied:Firstly, in order to construct the more accurate discretized model of nonlinear systems, a global multirate discretization method for fuzzy systems based on linear matrix inequality (LMI) technology is proposed. Employing discrete lifting technique and system equivalence scheme, a equivalent multirate discretized T-S fuzzy model which maintains the polytopic structure like the general T-S fuzzy system, is obtained by solving some generalized eigenvalue minimization problems (GEVPs) subject to a series of linear matrix inequalities (LMIs).Secondly, combining region pole assignment with quadratic optimum control, a multirate input fuzzy optimal control method on the basis of optimum Disc-pole (D-pole) placement is presented in the paper. The fuzzy optimal control law is determined by solving some algebraic Riccati equations. The stability of the closed fuzzy digital control systems is guaranteed by Lyapunov stability theory. Moreover, when considering multi-objective and multi-restriction problems such as limited control input and response decay rate, a multirate input fuzzy control method based on LMI technique is addressed. Campared with single-rate fuzzy control system, the multirate input fuzzy control system is equivalent to increasing the available input dimension and augmenting the redundancy degree of the digital controller design such that the control capacity of the closed systems is much enhanced.Next, a multirate output feedback control strategy without causality constraint based on fuzzy observer is addressed to avoid the causality constraint of the multirate output controller in this paper. In this approach, all the poles of the closed systems are placed into the proper disc region so that the closed systems get the good performance. The control law and observer gain of the multirate output feedback controller are obtained by solving a series of LMIs. The multirate output fuzzy control system is far superior to the single-rate fuzzy control system in various aspects due to its time-varying nature. Particularly, the multirate output feedback controllers can fully achieve the control capacity of the state feedback ones when the output sampling multiplicities is properly increased.Finally, for Instability problem encountering for adaptive flux observer in the regenerating mode at low speeds, a new speed and flux observer based on T-S fuzzy model is proposed in this paper. The observer gain is a nonlinear time-varying matrix which is composed of some constant matrices via fuzzy membership function. It has the stronger adaptiveness and robustness because the gain changes automatically along with the operating speed of induction motor (IM). Furthermore, by multirate sampling stator currents during a control period of stator voltages, a fuzzy state observer based on multirate output control scheme is represented to estimate rotor speed and stator flux directly. In the end, a direct torque control method for IM based on the multirate output fuzzy observer is implemented. The simulation results indicate that the proposed IM drive could work stably in whole range of speed with preferable precision of speed and flux estimation. The steady-state and dynamic performance of the IM drives are improved at low speeds.