Piezoceramic Micro-positioning Platform Control Method Based On Hammerstein-like Model

Since modern times,precise driving positioning technology has been developed in many high-tech fields,such as microelectronics technology,fluid machinery,ultra-precision processing and manufacturing,micro-nano operation and micro-nano assembly,biotechnology and modern medical treatment.Among the devices that realize the precise driving and positioning technology,the micro-positioning platform with the piezoelectric ceramic actuator as the driving element has unique advantages,such as fast response speed,high displacement resolution,good stiffness,good frequency characteristics and high positioning accuracy.However,in the application of precise positioning,due to the hysteresis characteristics of piezoelectric ceramic materials,the nonlinear characteristics will affect the positioning accuracy of the piezoelectric ceramic micro-positioning platform and make the control accuracy worse.In order to ensure that the positioning accuracy of the platform is not affected or to reduce the degree of influence,the hysteresis characteristics of the piezoelectric ceramic micro-positioning platform are studied and compensated from the aspects of modeling and control.Firstly,the composition and principle of piezoelectric ceramic micro-positioning platform are introduced,and the research on hysteresis model and hysteresis compensation control by domestic and foreign scholars is summarized.Then,a Hammerstein-like model is established to accurately describe the input-output relationship of the piezoelectric micro-displacement positioning platform.Finally,based on the established model,a two-step generalized prediction controller and a generalized prediction controller considering system constraints are designed to realize precise positioning control.In the case that the traditional static hysteresis model such as KP model cannot describe the rate-related hysteresis characteristics of the piezoelectric ceramic micro-positioning platform,this paper designs a Hammerstein-like model to describe the hysteresis nonlinearity and the rate correlation.The model is composed of the static hysteresis model described by KP model and the dynamic nonlinear sub-model described by least squares support vector machines in tandem.The parameters of KP model were identified by cuckoo optimization algorithm and cuckoo genetic hybrid optimization algorithm respectively,and the static hysteresis submodel was obtained.The dynamic nonlinear submodel is obtained by online identification.The accuracy of the model is verified by voltage driven experiments.In order to realize the positioning control of the piezoelectric micro-positioning platform,the inverse KP model is used as the feedforward controller to form an open-loop control system in series with the platform to compensate for the influence of hysteresis characteristics on the positioning control.It is proved that the inverse KP model controller can compensate the hysteresis.However,since open-loop control cannot solve the influence of modeling errors on the system and considering the special structure of Hammerstein-like block connection model,a more flexible two-step generalized predictive control strategy is designed.The first step is to linearize the dynamic nonlinear sub-model and obtain the intermediate control quantity by using the generalized predictive control method.The second step is to apply the inverse KP model to eliminate the hysteresis effect and obtain the direct control quantity.Compared with the inverse KP model,the trajectory tracking experiment proves that the generalized predictive control strategy based on the two-step method is higher and more accurate.In the actual control,due to the limitation of physical structure and mechanical characteristics,when the maximum driving voltage or the maximum driving voltage change rate is exceeded,the working performance of the piezoelectric ceramic micro-positioning platform will be affected,and unexpected response may be generated,or even damage to the platform.In order to solve the effects of constraints and hysteresis on the system,the input constraints and the input rate of change constraints are added to the design of GPC.Particle swarm optimization(pso)algorithm is used to replace the optimal control rate in rolling optimization.Moreover,the stability of the constrained hysteresis system is proved by using the objective function as the Lyapunov function.Finally,the trajectory tracking control experiment proves the effectiveness of the constrained generalized prediction controller under the expected displacement of different frequencies.