Study On Fast Algorithm And Its Convergence Of Generalized Predictive Control

Generalized predictive control (GPC) is a new predictive control algorithm developed along with the research of adaptive control. It has the double advantages of adaptive control and predictive control, and has much more robustness and practicability than adaptive control, so its research is the focus in the fields of control theory and industrial control all the time. However, not only it is difficult that GPC is used in the high real-time system because of large on-line computation load, but also complex nonlinear relationship among parameters in the characteristic polynomial of the closed-loop system leads to the difficulty of stability analysis. Therefore the main study on fast algorithm and convergence of GPC is given as follows:Firstly, a fast GPC algorithm for single-input-single-output (SISO) system based on Toeplitz matrix is proposed. Under two conditions that prediction horizon is equal and not equal to control horizon, inverse matrix in the control law is transfered for Toeplitz matrix, then the Trench-Zohar algorithm and the inversion algorithm of lower triangular matrix are applied to calculate the transformed inverse matrix. Algorithm analysis indicates that the computation load of the above algorithm is one order less than that of the conventional algorithm. Moreover, the method is not only simple, but also easy to programme.Secondly, by introducing the feedforward gain matrix and input softing coefficient matrix into regular performance index function of GPC, a fast GPC algorithm for SISO system with convergence of tracking is proposed. The softness factor is adjusted on line by combining MP neural network with BP algorithm, thus the matrix inversion computation is avoided and it is convergent that the output of control system follows reference signal fast.Thirdly, the fast GPC algorithm for SISO system with convergence of tracking is extended to multi-inputs-multi-outputs (MIMO) system, so inverse matrix dimensions are decreased and it is convergent that the outputs of MIMO system follow reference signals fast.Algorithm analysis and simulations indicate that these algorithms reduce the on-line computation load, and improve the real-time character of control system, which contributes to that the GPC algorithm is applied to the high real-time system. In addition, theory proves the algorithm has convergence of tracking by introducing feedforward gain matrix, so it is of certain theoretical significance to analyze the stability of GPC algorithm.