A Nonlinear Adaptive Switching Control Based On Unmodeled Dynamics Estimation And Compensation

Under the funding support by the National Fundamental Research Program of China (973), a nonlinear adaptive switching control method based on unmodeled dynamics estimation and compensation is studied systematically in depth in this thesis for a class of nonlinear controlled plants which can be represented by a linear model plus a higher nonlinear term (unmodeled dynamics). The proposed methods aim at solving the following existing problems of multiple-model adaptive control methods:(1) the unmodeled dynamics are globally bounded or their differential term (i.e., variation rate) are globally bounded; (2) the zero dynamics of the system are asymptotically stable; (3) the existing methods do not consider the problem that the data vector for estimating unmodeled dynamics contains the current unknown control input signal and the analysis of convergence and accuracy of the estimation algorithm have not been fully explored. In this context, the following main results are obtained:(1) By combining an adaptive-network-based fuzzy inference system (ANFIS) with "one-to-one mapping" and "regularization technique", an estimation algorithm for unmodeled dynamics is proposed. Furthermore, using the one-step ahead of optimal control strategy together with proposed estimation algorithm of unmodeled dynamics, a nonlinear switching control method based on the unmodeled dynamics estimation and compensation is proposed for a class of nonlinear systems with unstable zero dynamics which compose of linear model with known parameters and unmodeled dynamics. Based on these work, a linear controller and a nonlinear controller with compensator based on ANFIS are designed. By switching between the linear and nonlinear controllers, it is shown that both improved performance and stability can be achieved simultaneously. The analysis on stability and convergence of the proposed control method are established. The proposed method requires that the unmodeled dynamics of the systems satisfy a linear bounded condition. This relaxes the widely used global boundedness condition on the unmodeled dynamics or the globally boundedness of the difference between the current unmodeled dynamics and its one-step ahead value. Simulations and comparative studies with multiple-model adaptive control algorithms ([1]-[2]) have justified the fast convergence speed and good control effects of the proposed algorithm.With the above mentioned development, a nonlinear adaptive switching control algorithm is proposed for a class of nonlinear systems with unstable zero dynamics which compose of linear model with unknown parameters and unmodeled dynamics. The controller composes of a linear adaptive controller, a nonlinear adaptive controller with estimation and compensator of unmodeled dynamics and a switching mechanism. The adaptive switching control scheme combines the unmodeled dynamic estimation method proposed in this thesis with the least squares estimation algorithm with dead-zone, and incorporates a one-step ahead of optimal control strategy. The stability and convergence of the adaptive control method is analyzed. Through the simulation based comparative study and the experiment of the proposed control algorithm on a tank level control system, the effectiveness of the proposed method is validated.(2) For a class of nonlinear systems with unstable zero dynamics which compose of linear model with unknown parameters and unmodeled dynamics, a nonlinear adaptive generalized predictive switching control algorithm based on ANFIS, where multiple models is proposed by combining the above unmodeled dynamic estimation method proposed in this thesis with the generalized predictive control strategy. The proposed control algorithm consists of a linear adaptive generalized predictive controller, a nonlinear adaptive generalized predictive controller based on ANFIS and a switching mechanism. The stability and convergence have been analyzed. Through the simulation study and a real-time experiment on the hardware-in-the-loop-simulation (HILS) of pulverizing system in an alumina sintering process, it has been shown that the proposed method exhibits small overshoot, fast response speed and reduces setting time.(3) Since the previously mentioned estimation algorithm used the one-step delayed value of control input u(k-1) to replace its current unknown value u(k) directly, it may affect the estimation convergence and precision of the unmodeled dynamics. To solve this problem, the "decomposition estimation algorithm" for the unmodeled dynamics is proposed initially. First, u(k) is represented as the form of u(k-1) plus its increment Au(k). Based on this, the unmodeled dynamics are ingeniously divided into two parts which consist of "quasi-unmodeled dynamics" and the product of increment of controller and "variation rate of input dependence" by using the differential expansion with respect to u(k-1). Then, "quasi-unmodeled dynamics" and "variation rate of input dependence" are estimated separately by ANFIS. The convergence and precision analysis of the proposed estimation algorithm are given. Furthermore, it is proven that the data vector can be divided small enough and a large number of membership functions are chosen so that ANFIS is trained sufficiently when estimating the unmodeled dynamics. In this way, the upper bound of the estimation error can be made small than a pre-specified positive number.By combining the one-step ahead of optimal control strategy with proposed decomposition estimation algorithm of unmodeled dynamics, a nonlinear switching control method based on unmodeled dynamics decomposition estimation and compensation is proposed for a class of nonlinear systems with unstable zero dynamics which compose of linear model with known parameters and unmodeled dynamics. The stability and convergence analysis are established. Through comprehensive simulation-based comparative studies, it has been confirmed that a desired control performance is achieved because of the improved accuracy of the estimation.(4) To decompose the unmodeled dynamics into the sum of a known function depending on the one-step ahead value and current unknown increment, where only the unknown increment needs to be estimated. Based on the above representation, the estimation algorithm of unmodeled dynamic increment is studied by the proposed decomposition estimation algorithm. The analysis of the convergence and the precision of estimation algorithm are carried out. By comparing the simulation results of the proposed estimation algorithm with existing methods, it has been shown that the proposed estimation algorithm exhibits simple structure and the convenience of realization when maintaining the same estimation precision.With the above development, a nonlinear adaptive switching control method is proposed for a class of nonlinear systems. The method is based on the unmodeled dynamics increment estimation and compensation with unstable zero dynamics which compose of linear model with unknown parameters and unmodeled dynamics, where the combination is made between the proposed estimation method and the adaptive switching control algorithm based on one-step ahead of optimal control strategy. The stability and convergence are established. Simulation results confirm that the proposed control algorithm exhibits simple structure when maintaining the same control performance.