Inverse Compensation And Iterative Learning Control For Nonlinear Systems With Hysteresis

The smart materials such as piezoceramic, shape mamory alloys are widely used in someimportant area such as microelectronics manufacture, fibre-optical communication because oftheir high qualities.However, hysteresis that exists in these materials can result in the degradationof system performance and even lead to instability. So, it’s an important object to eliminate thehysteresis.In order to compensate the influence caused by hysteresis,the most common approach is toconstruct the inverse model cascaded with hysteresis. The inverse hysteresis models aredeveloped for the above-mentioned hysteresis respectively. On the other hand, it’s difficult tocontrol the systems with hysteresis using the classical control theory or modern control becauseof the special structure of hysteresis. ILC(Iterative learning control) is one of the intelligentcontrol methods with strict mathematical description. ILC don’t need the accurate model of thedynamic system,it can deal with some nonlinear, strong coupling systems. So it is used in thecontrol of hysteresis systems recently. This paper use a hysteresis inverse and design two ILCscheme to eliminate the effects caused by hysteresis:1)A new hysteresis inverse which is related to the rate is obtained for the Bouc-wen modeland used to efficiently compensate the hysteresis effects when developing the open loop withinverse compensation and PID control with inverse comensation. The results indicate that by PIDcontrol with inverse comensation we can obtain better precision.2)A complicated hysteresis adds to the canonical system, the output of the hysteresis is theinput of the canonical system. The P-type law is used to update the input of the system and aappropriate coefficient matrix is choosed to ensure the convergence of the system. This methodcan improve the tracking precision an eliminate the influence caused by hysteresis.3)Optimal iterative learning control for a class of nonlinear discrete-time systems withhysteresis is studied. In the control scheme, an approximating linearization model is given. Thismethod don’t need the inverse of the dynamic system, use the input and output data of the lastiteration. In the learning process, the learning gain and the sequence of the input are updating.