The Identi?cation And Control For Hysteresis Hammerstein Nonlinear Systems

Hammerstein system is a nonlinear system with a nonlinearity and a linear dynamical system being connected in series. Thus, Hammerstein system can be used to describe many practical system dynamics. The typical nonlinearity of Hammerstein system is described by hysteresis, backlash, dead-zone, etc, which can degrade the performance, or even worse, can lead to the instability of these control systems. Hysteresis nonlinearities exist in electrical motor servo systems, shape memory alloys, piezoelectric actuators and magnetostrictive materials, etc. The models of hysteresis include Preisach model, Prandtl-Ishlinskii(P-I)model, Bouc-Wen model and Backlash like model, etc. Since di?erent hysteresis models have di?erent parameters, di?erent structures and di?erent scopes of applications, thus,the identi?cation and control have been investigated for the Hammerstein systems with di?erent hysteresis models in this thesis. New prescribed performance function and identi?cations are proposed, di?erent observers are implemented and adaptive controllers are designed to control these Hammerstein systems which can guarantee the stabilization of the closed-loop systems.The main contents of this thesis can be summarized as follows:(1) Identi?cation and composite control of Hammerstein system is investigated, where the Hammerstein system is composed of linear dynamics with unknown order and a static hysteresis nonlinearity modeled by Preisach operator. The order of linear dynamics is ?rstly determined by Hankel matrix approach and then a blind identi?cation method is implemented to identify the linear dynamics based on the over-sampling output measurements, which relaxes the condition of blind identi?cation. Then a novel deterministic approach is proposed to identify the Preisach model for hysteresis nonlinearity, which is devoted to identify a triangle matrix. Moreover, this novel approach not only needs less dimensions to obtain Preisach density function than other existing methods, but also avoids the wiping-out property of Preisach model. Finally, a composite control consisting of inverse model-based controller(DIMBC) and adaptive sliding mode controller(DASMC)is developed to achieve tracking control. The composite control method can reduce the reaching time of DASMC and simultaneously improve the robustness of DIMBC.(2) An adaptive neural network(NN) controller based on the online high gain extended state observer(HGESO) is investigated for Hammerstein system with P-I hysteresis dynamics. For most of Hammerstein systems, the states cannot be directly measured since the presence of the nonlinearity. Consequently, we adopt a HGESO to estimate the system states online, which requires few model information. Importantly, the tracking errors are transformed into ?ltering errors, which avoids the ”curse of dimensionality” and reduces the computational burden. Then, an adaptive NN controller is designed based on the HGESO, where the high order neural network(HONN) is applied to estimate the unknown system elements. The stability analysis of the design scheme is veri?ed through the Lyapunov stability theory. All the signals in the closed-loop system are guaranteed to be uniformly ultimately bounded(UUB) and the tracking error can be made arbitrarily small by adjusting the design parameters. Simulation results verify the reliability and e?ectiveness of the proposed approaches.(3) An adaptive fuzzy logic control strategy with high order sliding mode state observer(HOSMSO) is proposed for Hammerstein system with Bouc-Wen hysteresis nonlinearity model. The unknown system states are estimated by HOSMSO where only the system input and output are known. Considering the di?culty of parameter identi?cation for Bouc-Wen model, a fuzzy logic system is proposed to estimate the unknown system elements. Finally, an adaptive fuzzy logic controller is proposed for Hammerstein system with Bouc-Wen hysteresis nonlinearity model based on the results of HOSMSO. Meanwhile, it is demonstrated that all signals of the closed-loop system are UUB and the tracking error converges to a small compact set. Simulation results demonstrate the e?ectiveness of the proposed methods.(4) A prescribed performance function(PPF) is proposed and incorporated into the adaptive control design for Hammerstein system with backlash-like hysteresis nonlinearity.The tracking error is transformed as a prescribed performance error so that it solves the tracking error di?cult constraint, which includes two steps: ?rstly, the vector tracking error is transformed into scalar error by Laplace transformation. Then, the scalar error is converted into prescribed performance error with the proposed PPF such that the error can converge to a prescribed region. Then, a model reference adaptive control is presented and the stability is guaranteed by a Lyapunov stability theory with Lambert W function for closed-loop system. Simulation results are conducted to illustrate the e?ectiveness of the proposed control scheme.(5) Considering the in?uence of hysteresis in the turntable servo motor system, the e?ectiveness of blind identi?cation and lower triangular matrix approach are veri?ed for Hammerstein system with Preisach hysteresis nonlinearity. The comparative experiments of DIMBC, DASMC and composite control are designed, which illustrate that the composite control gives better performance than the others. Then, a Hammerstein model with P-I hysteresis nonlinearity is established for turntable servo motor system. Compared with a nonlinear PID controller, an adaptive NN controller is designed to control the turntable servo motor system. The experiment results verify that the proposed adaptive NN controller has favorable transient performance and steady-state tracking accuracy.