Multivariable Compensation of Hysteresis, Creep, Badly Damped Vibration, and Cross Couplings in Multiaxes Piezoelectric Actuators

This paper presents the control of a two-degree-of-freedom piezoelectric actuator that exhibits hysteresis nonlinearity, creep nonlinearity, badly damped vibration, and cross couplings without using feedback sensors. The principle consists in compensating first the hysteresis, then the creep, and finally the vibration. The proposed compensation technique is multivariable and therefore is also able to reduce the cross couplings that are unwanted phenomena. The experimental tests demonstrate that the hysteresis that initially exceeds 19% is reduced to about 0.01%, while the creep is reduced from 5.5% to 0.04%. Regarding the vibration, the related overshoot that was initially 45% is completely removed. Note to Practitioners-This paper describes an approach to control and to automate dexterous precise positioning systems based on multiaxes piezoelectric actuators (PEAs). Two problems have motivated the approach investigated in this paper: 1) the presence of nonlinearities (hysteresis and creep), of badly damped vibration and of cross couplings in the multiaxes PEAs and 2) the lack of convenient sensors to feedback control them. Therefore, this paper proposes multivariable and complete feedforward control approach that does not require external sensors. This sensorless control architecture permits a low-cost and a high integration feature additionally to the fact that it is of great interest in applications at small scales where implementation of real-time measurement system is often difficult.