Research On LMS Based Adaptive Inverse Control

Among many nonlinear dynamic control approaches, nonlinear adaptive inverse control (AIC) is very novel and provides significant insight into theory research and practical application. In this paper, by studying the feasibility of LMS algorithm based nonlinear AIC method, the corresponding methodologies are designed for the accurate control of a class of typical nonlinear dynamic plant. The detailed study is conducted on improvement of the structure of nonlinear AIC, the structure and algorithms of dynamic neural networks utilized to identify the model and inverse model of the controlled nonlinear systems. Also, this paper provides innovative idea for improving and developing nonlinear AIC. The main content of study and innovation are ordered as follow:1. Proved is the feasibility of LMS algorithm based AIC. The linear and nonlinear AIC are integrated by variable step size LMS adaptive algorithms for the first time. All these provide new approaches for development of nonlinear AIC methods.2. General nonlinear algorithms in modern nonlinear AIC always converge slowly and converge to local minimums easily. In order to get over these disadvantages, based on a type of neural networks nonlinear filters whose output is a linear cascade of its weights, a modified NLMS (VS MNLMS) algorithm is proposed, and then its convergence performance is studied deeply. Both theory and simulation analysis have the same results, on the one hand, the step size of the proposed algorithm is a nonlinear function with respect to the input power and learning signal (error), both its convergence speed and final MSE are better than that of other four variable step-size LMS algorithms. On the other hand, the proposed algorithm is little sensitive to noise signals and parameters of system, and it is able to drive the adaptive filter to approximate the model and its inverse of controlled plant rapidly and accurately in both linear and nonlinear AIC system.3. Regarding dynamic nonlinear system, a discrete time error -feedback-learning (DTFEL) algorithm based nonlinear adaptive inverse control method is proposed, and the stability of the whole dynamic AIC system is assured by the Lyapunov stability theory. In this method, the feedback controller that is used to deal with robustness and stability is designed to be a PD controller, the feedforward controller that is used to improve both response speed and steady state error is design to be a dynamic RBF neural network (DRBFN), whose learning signal is a linear cascade of error of closed system and the output of PD controller. As a result, the wonderful tracking, robustness and anti-noise performances of algorithm based dynamic nonlinear AIC system are obtained, and the effectivity of the proposed method is verified further.4. Both parallel and feedback function link neural network (CDFLNN), which based on VS MNLMS algorithm and Chebyschev base function, are proposed and introduced to AIC of dynamic nonlinear system firstly. Both theory and simulation analysis show that the proposed nonlinear adapitive filters are are very novel and ideal to LMS based AIC, both adptive processes in which the CDFLNN is driven to approximate four typical nonlinear plant and its inverse, and converge to its only least square solution finally. Simulation results show that the VS MNLMS based CDFLNN is a better nonlinear filter comparing with real GA based NDFLNN in nonlinear AIC.5. By introducing CDFLNN, which exhibits powerful capabiity of nonlinear function express, a nonlinear AIC approach called DTFEL-VS MNLMS-εfiltering AIC is proposed. This nonlinear AIC method inherits all advantages of both DTFEL based AIC and s filtering AIC method. In this method, if the VS MNLMS based CDFLNN can identify both the controlled plant and its inverse accurately, then the feedforward controller can approximate the ideal controller, and the accurate control to dynamic nonlinear system can be realized.