Researches On Ferromagnetic Hysteresis Nonlinearities In Control Systems

Hysteresis nonlinearity is a class of typical nonlinearity. Hysteresis phenomenon widely occurs in smart materials such as magnetic materials, magnetostrictives, piezoelectrics and shape memory alloys. Usually in control systems hysteresis non-linearities will affect the relationship between the input and the output, make the system control characteristic becomes worse, decrease the control accuracy, and even lead to the system unstable. The widely existence of hysteresis in control systems makes the controller design become a challenge task. This dissertation begins with a class of ferromagnetic hysteresis model, the bound property and passivity of such model are discussed, and then the adaptive tracking problems of nonlinear systems with ferromagnetic hysteresis, the absolute stability problems of continuous-time and discrete-time Lur’e type singular systems with ferromagnetic hysteresis feed-back, and the chaotification problems of a divergent second order system using the ferromagnetic hysteresis nonlinearities are researched. The main contributions of this dissertation are as follows:1. The adaptive tracking problem of uncertain nonlinear systems with ferromagnetic hysteresis nonlinearities is researched. The solution of the differential equation of the ferromagnetic hysteresis model has two terms, one is a nonlinear function term with regard to the system input, the other term is considered as a nonlinear disturbance of which the bound is unknown. The nonlinear disturbance term can be proved to have a limit bound that can also be estimated during the procedure of designing the adaptive control law. The adaptive backstepping control method is proposed in this dissertation, which fuse the hysteresis within the procedure of controller design and effectively mitigate the effect of hysteresis to the systems, and avoid the limit of constructing hysteresis inverse needs the precise hysteresis models. The designed controller guarantees that the output quickly tracks a desired signal, the tracking error fluctuate in a small bound, all signals within the whole closed loop system are bounded, and the control objective is ideally achieved. The stability of the closed loop system is proved under the Lyapunov stability theory.2. The absolute stability and stabilization problems of a class of singular sys-tems with feedback connected ferromagnetic hysteresis nonlinearities are re-searched. The circulation orientation of the ferromagnetic hysteresis loop is counter-clockwise, thus the hysteresis model satisfies the passivity conditions of hysteresis operator. Further more, the input-output relation of the transformed operator is passive. The bound condition of the solution of ferromagnetic hystere-sis model is given to establish a local Lipschitz condition. For a typical hysteresis nonlinearity, the convergence is not to a single point but rather to a stationary set. So, invariant set theory is employed to deal with the convergence of hysteresis case. Through the new differential-integral loop transformation framework pro-posed in this dissertation, an augmented singular system model is established for the stability analysis. A new extended Popov criterion for the absolute stability analysis of singular systems with hysteresis feedback is presented based on KYP method and LMIs technique. Absolute stabilization conditions of such kind of control problems are also investigated. Strict LMIs constraints for absolute sta-bility and stabilization conditions of singular systems are presented to solve the infeasible problems of non-strict LMIs.3. The absolute stability problem of discrete-time descriptor system with feedback connected ferromagnetic hysteresis nonlinearities is researched. The ferromag-netic hysteresis considered in the thesis fulfills the series of properties includ-ing passivity and boundedness. Through the difference loop transformation, an augmented discrete-time descriptor system model is established for the stability analysis. A new extended Tsypkin criterion for the absolute stability analysis of Lur’e type discrete-time descriptor system with hysteresis feedback is presented based on LMI technique. The consequence control problems are also investigated.4. The dynamical behaviors of a new chaos system with ferromagnetic hysteresis nonlinearities are investigated. A novel ferromagnetic hysteresis based chaotic attractor is generated from a simple second order linear system with the fer-romagnetic hysteresis nonlinearity. In this dissertation, the equilibrium points, dissipativity and Lyapunov exponents are discussed to analyze the chaotic dy-namical behaviors. Simulation results are given to show the chaotic, periodic, convergent and divergent trajectories with regard to the changing of the basic system parameters.