The Application Of Wavelet Transform To The Order Identification Of System And Controller Design

This thesis puts the particular emphasis on the study and application of wavelet transform to the order identification of linear system, the integrated performance index of control system and the adaptive Control. The main contributions of the thesis are as follow.The developing history of wavelet analysis theory is systematically summarized, the current situation of its application to the field of automatic control is thoroughly investigated. The prospects of combining wavelet analysis theory with automatic control theory are also explored.The application of wavelet transform in the singularity detection of signal is studied. The relationship between the singularity of impulse response of system and the order of linear system is analyzed in this paper. A new method based on CWT to detect the singularity of the impulse response of linear TI system is proposed here to identify the order of the system. The effective of this method is proved by theory and the simulation results.With a lot of simulations, the wavelet transform's character of second-order system is studied. Furthermore, two performance indexes based on wavelet transform are proposed, details as (5-1) and (5-2). Optimizing the parameter of the PID controller with the aid of genetic algorithm, the simulation result shows that these two integrated performance indexes based on wavelet transform are feasible.Applying the new order identification method based on wavelet transform to detect the positions of step disturbances, a new adaptive PID controller of perturbation based on the new order identification method is designed. The simulation shows that the controller can not only track the set point accurately, but also suppress the step disturbance appeared in different position in time. This controller is effective and useful.