Feedback Control of the Bending Response of Ionic Polymer Actuators

Abstract

Ionic polymers are a class of active material that exhibit large bending deflections under the application of an electric field. Previous research has demonstrated that the response of an actuator in air is characterized by a large initial deflection and a relaxation to a steady-state value. The time constant of the relaxation is of the order 5–20 s and the overshoot of the step response is typically greater than 100%. These aspects of the step response limit the actuation bandwidth of the material. In this work we explore the use of feedback control techniques to eliminate the large overshoot and reduce the settling time of cantilevered ionic polymer actuators. Control models are developed from measurements of the actuator response to a step change in the applied voltage. The models demonstrate that the dynamics relevant to the control problem can be separated into a low-frequency (< 5 Hz) range in which the response is characterized by a series of time constants, and a high-frequency range (> 10 Hz) characterized by the resonance of the actuator. For shorter polymers the resonance is sufficiently high that it can be ignored in the control design, but the resonant response becomes significant as the length of the polymer increases. Control simulations based on Linear Quadratic Regulator (LQR) theory demonstrate that feedback control eliminates the overshoot in the step response and decreases the settling time by a factor of 10. Control of the actuator oscillation is accomplished by using an LQR weighting matrix that includes the states associated with the actuator resonance, whereas a state weighting matrix that does not include these terms results in a compensator that includes a notch at the actuator resonance. Experimental results on the shorter polymer demonstrate that the overshoot in the step response is eliminated and the settling time is reduced from 12–16 s to 1–2 s, thus verifying the ability of feedback control to shape the step response of the actuator. Experimental results on the longer polymer demonstrate that incorporating the resonance terms in the LQR weighting matrix is the superior control design method. Designs that included a notch in the compensator were unstable for very low gains because of variations in the actuator resonance due to changes in surface hydration. Designs that included phase lead in the compensator produced superior closed-loop performance and resulted in reductions in overshoot and settling time of the order 6–10 s.