Robust Adaptive Control For Multivariable Bilinear System

The control theory has experienced the stages of classic control theory and modern control theory. The pertaining research objects include linear SISO system, linear multivariable system and nonlinear system. Strictly speaking, almost all the controlled plants are nonlinear, linearity is the approximation for the practical plant in a certain scope and degree. Today, the hot points of control theory research have been turned to problems about essential nonlinearity and uncertainty. It is not proper to deal with the essential nonlinearity problem by utilizing linearity methods. Presently, there are few methods for direct resolving nonlinear control problems; the results obtained are rather complex; therefore, it is difficult for application. Bilinear system is the simplest nonlinear system; it can not only describe many phenomena in biology, chemical industry, social economy and population, but also be the approximation for many nonlinear processions. If the procession can be properly modeled by bilinear system, the bilinear model obtained has higher precision than the linear model and less complexity than nonlinear model. Furthermore, most of the control method designs are based on certain mathematical model, while the model can only describe part of performances of the plant in a certain scope. For this, the uncertainties and unmodeled dynamics which probably occur during operation must be considered in designing control system; so robust stability must be included in controller design.The simulation results show that: for a class of MIMO uncertain bilinear system with unmodeled dynamics, it can not obtain satisfactory control results only by using adaptive decoupling control law. In the paper, based on the robust adaptive control law for SISO bilinear system, a new modified robust adaptive decoupling control algorithm for multivariable bilinear system has been presented. By combining the multivariable decoupling control and robust parameter estimation method with relative dead-zone and introducing the estimation of the unmodeled dynamics and uncertain signal, the algorithm can reduce both the effects of uncertainties resulting from disturbances and high-order unmodelled dynamics, and multivariable coupling.The comparison of the control results between the robust control law and non-robust control law shows that: the algorithm is effective for a class of multivariable, bilinear systems with unmodeled dynamics and disturbances. The control system can not only quickly track the required reference signal, but also achieve dynamical and steady decoupling property of the closed loop system approximately. The global convergence of the algorithm is also established.