Research On Direct Generalized Predictive Control

Generalized predictive control(GPC) is a kind of advance control methods that is of strong robustness, can overcome the time delay of system effectively and is suitable to unstable non-minimum phase system. But it has the shortcoming of large computation load because of online solving the Diophantine equation, inverse matrix and recursion solution by Least squares. So four kinds of fast algorithms of GPC that don't need the mathematical model of plant and are highly real-time are proposed in the paper. They have laid the rationale for the application of GPC to systems that need fast response. The main achievements are as follows:(1) A direct GPC(DGPC) method for a class of single-input-single-output linear system with unknown parameters is presented. This method directly recognizes the parameters of GPC controller, namely the controller parameters and the unknown vectors in the estimated generalized error are adjusted adaptively. Then, based on the mean value theorem a class of nonlinear system is replaced by a time varying linear system, and cubic spline functions polynomials are used to approximate the time varying coefficients and the unknown vectors in estimated generalized error, namely the DGPC of single-input-single-output linear system is generalized to single-input-single-output nonlinear systems. Finally, the DGPC is generalized to multi-inputs-multi-outputs linear systems and nonlinear systems.(2) DGPC based on Radial Basic Function(RBF) neural network method for a class of single-input-single-output linear system with unknown parameters is presented. RBF network is used to approximate the function of control increment, and both the controller parameters and the unknown vectors in the estimated generalized error are adjusted adaptively. Then, the RBF DGPC of single-input-single-output linear system is generalized to single-input-single-output nonlinear systems. Finally, the RBF DGPC is generalized to multi-inputs-multi-outputs linear systems and nonlinear systems.(3) DGPC based on fuzzy adaptation method for a class of single-input-single-output linear system with unknown parameters is presented. Fuzzy logic is used to approximate the function of control increment, and both the controllerparameters and the unknown vectors in the estimated generalized error are adjusted adaptively. Then, the fuzzy adaptation DGPC of single-input-single-output linear system is generalized to single-input-single-output nonlinear systems. Finally, the fuzzy adaptation DGPC is generalized to multi-inputs-multi-outputs linear systems and nonlinear systems.(4) A new generalized predictive control algorithm of MIMO systems based on grey model is presented. It identifies small parameters, moreover avoids online solving the Diophantine equation and inverse matrix. So the computation load of algorithm can be reduced greatly, and real-time property is advanced.The four methods above don't need the mathematical model of plant. Therefore they provide one kind of new mentality for solving the problem that in GPC the parameter of plant is uncertain. Moreover online recursion of Diophantine and matrix inversion are avoided.