Research Of Piezoelectric Micro Positioning Platform Hysteresis Nonlinearity Modeling And Control Methods

Piezoelectric micro positioning platform, as the core component of micro/nano positioning technology, has been widely used in all kinds of precision positioning instruments. However, the inherent hysteresis nonlinearity of piezoelectric micro positioning platform has a serious influence on the positioning accuracy and stability of the system. So in this paper, in order to reduce and eliminate the hysteresis nonlinearity of piezoelectric micro positioning platform, a series of studies has been conducted in two aspects, one is to establish a high precision hysteresis model and the other one is to design a hysteresis compensating controller.Firstly, the development and research situation about piezoelectric micro positioning platform and its hysteresis modeling and control methods are introduced, summarized and analyzed. In this paper, the Krasnosel’skii-Pokrovkii(KP) model is used to describe the hysteresis nonlinearity of piezoelectric micro positioning platform. Then the parameters of KP model are identified by particle swarm optimization(PSO) algorithm. It is proved in simulation experiments that the KP model identified by PSO can describe the hysteresis nonlinearity accurately. However, there exists a disadvantage that the convergence process is slow and the algorithm is easily to trap in local optimum in the PSO identify process sometimes. In order to overcome the disadvantages mentioned above, adaptive chaos particle swarm optimization(ACPSO) algorithm is proposed. The improvement of adaptive weight and chaos optimization method makes the identification results of ACPSO much better than PSO. The contrast experiments demonstrate that the accuracy of KP model identified by ACPSO is higher than it identified by PSO, and the speed of identify process is much faster.In order to reduce and eliminate the hysteresis nonlinearity of piezoelectric micro positioning platform, a fuzzy controller is designed by the available control knowledge and experience. In the simulation research, three kinds of tracking signals are used. The results indicate that the fuzzy controller can compensate the hysteresis of piezoelectric micro positioning platform well. For improving control accuracy further, variable universe fuzzy control method is proposed. In this controller, the control universe will vary according to the error of input signals. Simulation results verify the control accuracy is improved significantly. The effectiveness of the variable universe fuzzy controller is proved. Finally, in order to overcome the disadvantages that the fuzzy control effects depend on the control experience excessively and the controllers are lack of rigorous proof of stability and convergence, an adaptive fuzzy H∞ controller is designed based on the hysteresis decomposition. The weights of the fuzzy logic system can be adjusted adaptively, therefore, the accuracy of the displacements tracking not relays too much on the control experience. In the end, the closed-loop system stability is testified by Lyapunov function method. The simulations results validate the effectiveness of the control method proposed for eliminating the hysteresis nonlinearity of piezoelectric micro positioning platform.