Random vibration control for multi-degree-of-freedom mechanical systems with soft actuators

Soft robotics include soft actuators and possess the capacity of large deformation and environmental compatibility. Weak environmental disturbances may deteriorate the operating performance of soft robotics due to the low stiffness of soft actuators. This manuscript investigates multi-degree-of-freedom nonlinear mechanical systems with dielectric elastomer actuators and establishes the bounded/unbounded optimal control strategies to suppress the random vibration around the equilibrium position by adjusting the imposed voltage in real time. First, the constitutive relation of a plan-type dielectric elastomer actuator and then the vibrating equation of the multi-degree-of-freedom nonlinear system around the equilibrium position are derived successively. The bounded/unbounded optimal control problems are then established by adopting the corresponding performance indexes. The bounded/unbounded optimal control strategies are then derived by combining the stochastic averaging technique and stochastic dynamic programming principle. Numerical results on a two-degree-of-freedom nonlinear system illustrate the application and efficacy of the proposed optimal control strategies.