Proxy-based sliding-mode tracking control of dielectric elastomer actuators through eliminating rate-dependent viscoelasticity

Dielectric elastomer actuators (DEAs) usually suffer from rate-dependent
viscoelastic nonlinearity, which manifests as hysteresis in their deformation cycles, leading to huge challenges in their modeling and control. In this work, we
propose a model-free, proxy-based, sliding-mode tracking control approach to mitigate viscoelastic nonlinearity, achieving high-precision tracking control of DEAs. To this end, we first investigate the viscoelastic nonlinearity of DEAs, revealing its asymmetric and rate-dependent characteristics. Then, by combining the benefits of the PID control for small positioning errors and sliding-mode control for large errors, a proxy-based, sliding-mode tracking controller (PBSMC) is established. Finally, the stability of the controller is analyzed. To verify the effectiveness of the controller, several experiments are conducted to demonstrate the performance of DEAs in tracking sinusoidal trajectories under different frequencies. The experimental results demonstrate that with the PBSMC, the DEA can precisely track sinusoidal trajectories within a frequency range of 0.1 Hz to 4.0 Hz by effectively minimizing the effect of inherent viscoelastic nonlinearity. Compared with open-loop tracking performance, the
proxy-based, sliding-mode controlled DEA performance shows a significant reduction in maximum tracking error from 45.87% to 8.72% and in root-mean-square (RMS) error from 24.46% to 3.88%. The main advantages of the proxy-based, sliding-mode control are: i) it adopts a model-free approach, avoiding the need for complex dynamic modeling; ii) it can achieve high-precision tracking control of DEAs, thereby paving the way for the adoption of DEAs in several emerging applications.