Control of a hysteretic actuator using inverse hysteresis compensation

The accurate control of a system that exhibits hysteresis requires a control strategy that incorporates some form of compensation for the hysteresis. One approach is to develop an accurate model P of the hysteresis and then use the inverse P-1 as a compensator (inverse compensation). This paper focuses on the problem of determining P and P-1 for a piezoelectric stack actuator. The KP operator is used to formulate the hysteresis operator P and from this an approximation Pm is derived. Compensation is then defined in terms of the inverse of the approximation, Pm-1. Experimental data collected on an unloaded piezoelectric stack actuator is used to demonstrate the concept of inverse compensation. The parameters of Pm are identified using only major hysteresis loop data and results are given that show Pm provides an accurate model for both major and minor hysteresis loops. Results are then presented that demonstrate the capability of the inverse Pm-1 to compensate for the actuator hysteresis.