Fractional order modeling and internal model control method for dielectric elastomer actuator

The dielectric elastomer actuator (DEA) is widely used in the field of soft robots due to its large deformation, light weight, fast response, and high-energy conversion efficiency. The high-precision control of the DEA is the precondition for soft robots to perform complicated tasks. In early studies, researchers usually employed integer order modeling and control methods to build the dynamic model of the DEA and to achieve its tracking control. However, these methods are not good at handling the complicated memory property of the DEA. In addition, the number of required parameters in integer order models and control methods is enormous, which hinders their practical applications. To solve these problems, the fractional order modeling method and fractional order internal model control method of the DEA are proposed in this paper. Firstly, a fractional order transfer function (FOTF) model of the DEA is built to depict its complicated memory property. Then, to achieve the computer control, an integer order approximation model (IOAM) of the FOTF model is built by using the Oustaloup filter. Considering that the order of the IOAM is too high, a reduced integer order approximation model is established by using the square root balance truncation algorithm to facilitate the system controller design. Next, a fractional order internal model controller is designed. Finally, tracking control experiments are exerted to demonstrate the effectiveness of the proposed method. Since the root-mean-square errors of all experimental results are less than 2%, the proposed modeling method and control method are superior from the perspective of the practical application.