Research On Control Strategies For Nonlinear Systems

The paper is concerned with the control strategies of uncertain nonlinear systems and the application on the AC speed adjustable systems. Its main contents includes neural network control, differential geometry control and algebra control.Basically not relying on the model of controlled object, neural network control has become an important branch in the field of intelligent control. Being a local approximating neural network, Cerebellar Mode Arculation Controller(CMAC) has the distinctive ability of disposing nonlinear mapping and building nonlinear relationship. The paper proposes a CMAC-based control scheme in which learning and controlling are alternately processed. The method is applied to the AC servo control system and obtain high quality output. The direct adaptive control system that being composed of neural network has a simple structure and can fast trace the given object which taking advantage of the convergence of BP algorithm. Neural network STC has the capacity of restrain the disturbance on the feedforward loop and essentially is applied to the controlled object that probably disturbed by the environment.Being the major research work in the field of nonlinear analysis and design, differential geometry has achieved some success. Being aimed at the drawbacks that state feedback of nonlinear affine systems depends on parameters, the paper give an adaptive control scheme on the basis of feedback linearization. In this method, the parameters of system are estimated adaptively and applied in nonlinear state feeback so that the goal of robust feedback linearization is achieved. The emphasis research in this paper is giving the process from theory to application. After applying the method to the AC servo system and using the real-time estimated parameters in the process of adaptive control, we discover the strategy can make the AC servo system has a good property through the computer simulation. At the same time, we discuss the zero dynamic problem of nonminimum phase systems. An approximate system of original nonlinear system is obtained by expanding the original system on the dynamic state on the basis of analyzing the decouplled matrix of original nonminimum phase system with small nonlinearity. Then the approximate system is feedback linearization controlled.To overcome the shortcomings of differential geometry method in the respect of invertibility and dynamic state feedback, this paper discuss algebra control method. Combining linear algebra with dynamic expansion, one method can decouple the nonlinearity through construct the root of nonlinear system by dynamic expanding. Another method that combines Singh algorithm with differential algebra also can decouple nonlinear systems. The method can find the certain part of output be decouplled structure of original system by Singh algorithm calculating essentiality of the decouplled system matrix. Being an example, the paper deduce the process of AC servo motor controlled by the method. In addition, we discuss the relationshipof affine nonlinear system and differential system in the respect of state feedback linearization and draw a conclusion that the differential system can be converted to extended Goursat normal form if and only if the distribution of affine nonlinear system be involutive.