Linear-quadratic regulator for control of multi-wall carbon nanotube/polydimethylsiloxane based conical dielectric elastomer actuators

Abstract

Conventional rigid actuators, such as DC servo motors, face challenges in utilizing them in artificial muscles and soft robotics. Dielectric elastomer actuators (DEAs) overcome all these limitations, as they exhibit complex and fast motions, quietness, lightness, and softness. Recently, there has been much focus on studies of the DEAs material's non-linearity, the non-linear electromechanical coupling, and viscoelastic behavior of VHB and silicone-based conical DEAs having compliant electrodes that are based on graphite powder and carbon grease. However, the mitigation of overshoot that arises from fast response conical DEAs made with solid electrodes has not received much research focus. In this paper, we fabricated a conical configuration of multiwalled carbon nanotube/polydimethylsiloxane (MWCNT/PDMS) based DEAs with a rise time of 10 ms, and 50% peak overshoot. We developed a full feedback state-based linear-quadratic regulator (LQR) having Luenberger observer to mitigate the DEAs overshoot in both the voltage ON and OFF instances. The cone DEA's model was identified and a stable and well-fitting transfer function with a fit of 94% was obtained. Optimal parameters Q = 70,000, R = 0.1, and Q = 7000, R = 0.01 resulted in the DEA response having a rise time value of 20 ms with zero overshoot, in both simulations and experiments. The LQR approach can be useful for the control of fast response DEAs and this would expand the potential use of the DEAs as artificial muscles in soft robotics.