Research On Control Algorithm Of Nonlinear Systems With Hysteresis

With the rapid development of micro/nano technology, the traditional positioning accuracy has been unable to reach the demand of the precision positioning for many industries, so the research of ultra precision positioning system has been valued by scholars. In the ultra precision positioning systems, it usually uses the drive which based on the intelligent materials(such as piezoelectric ceramic, magnetostrictive materials, shape memory alloy, etc.). However, these intelligent drive exist the inherent hysteresis characteristics. The hysteresis is one kind of nonlinear with non-smooth, multiple mapping and memory which can cause the system error and oscillation even cause the instability of the system. Meanwhile, it is difficult to use conventional methods to control it accurately. In order to eliminate the adverse effects caused by the hysteresis nonlinearity of the system and need to model the hysteresis, and design effective controller to realize the precise control.The dissertation is organized as follows:(1)An adaptive iterative learning controller(ILC) is proposed for a class of nonlinear systems with hysteresis described by Bouc-Wen model.First, the property of Bouc-Wen mode is discussed and the upper bound is derived.Then through the Lyapunov-like function, design a adapting iterative learning controller(ILC),which eliminates the adverse effects of hysteresis by iterative term that based on the classical PD feedback control theory. This method eliminates the oscillation and overshoot caused by hysteresis effectively. Finally, the simulation results prove that this control method is practicable.(2)A controller is designed of nonlinear system with hysteresis based on neural network modeling.A class of hysteretic nonlinear systems based on Neural Networks. First, a hysteretic operator is employed to construct an augmented input space for transforming the multi-valued mapping of hysteresis into a one-to-one mapping which enables neural networks to model the hysteresis. Then an adaptive iterative learning controller(ILC) based on Lyapunov-like function is proposed for a class of nonlinear systems with hysteresis described by neural networks model. And the result is compared with the traditional PID control, the simulation results prove that this method eliminates the oscillation and overshoot caused by hysteresis effectively. And implements the system output gradual tracking expected trajectory. Moreover, the controller increases the response speed and improves the control precision.(3)A controller is designed of output-constrained nonlinear systems with hysteresis, and comparing with other control schemes.A backstepping controller is proposed for a class of output-constrained nonlinear system with hysteresis described by Bouc-Wen model. First, the property of Bouc-Wen mode is discussed and the upper bound is derived. Then the symmetric Barrier Lyapunov Function(BLF) is proposed to ensure the boundedness of the closed-loop system and achieve the output-constrained conditions. Finally, the backstepping controller is proposed to eliminate oscillation and overshoot caused by hysteresis. Furthermore, it constrains the output of system in set range. This controller solves the in?uence of hysteresis and constrained output simultaneously. Moreover, the controller can improve the control precision. The simulation and experimental results prove that this control method is practicable.