1 School of Automation, China University of Geosciences, Wuhan 430074, China; Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex System, Wuhan 430074, China; Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan 430074, China.
2 Gina Cody School of Engineering and Computer Science, Concordia University, Montreal H3G 1M8, Canada.
3 School of Automation, China University of Geosciences, Wuhan 430074, China; Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex System, Wuhan 430074, China; Engineering Research Center of Intelligent Technology for Geo-Exploration, Ministry of Education, Wuhan 430074, China. Electronic address: wangyawu@cug.edu.cn.

Dielectric elastomer actuators (DEAs) show broad application prospects in the area of soft robots since they offer merits of fast response, large deformation, light weight and high energy conversion efficiency. Practical soft robot applications would usually require the study on the modeling and control of the DEA. However, the DEA has a memory property, which results in a highly nonlinear characteristics, bringing difficulties to the subject. To address this issue, an effective strategy is the utilization of the fractional order model, which is a type of modeling approach that can accurately characterize the memory property of a material with a small amount of parameters. Meanwhile, the fractional order controller can better handler the memory property, and it owns a better flexibility than traditional integer order controllers. With the above considerations, this paper proposes a modeling strategy and a tracking control strategy for the DEA on the basis of the fractional calculus. In the proposed strategy, a fractional order model is established to characterize the complicated nonlinear characteristics of the DEA. Then, to facilitate the computer simulation, the Oustaloup filter is used to construct an integer order approximation model (IOAM) of the fractional order model. Since the IOAM is difficult to be employed in the system controller design due to its high order, the IOAM is further simplified into a reduced order model based on the square root balance truncation algorithm. To realize the high accuracy control of the DEA, a feedforward-feedback combined controller is devised, which is composed of a feedforward controller and a fractional order proportional integral feedback controller (FOPIFC). Among which, the feedforward controller is devised based on the analytical inverse of the reduced order model to compensate the complicated nonlinear characteristics of the DEA, and the FOPIFC is devised to handle the bad influence from the modeling error and uncertainties on the control performance. Based on the proposed strategy, control experiment was conducted, and the root-mean-square errors in experiment are all below 0.7%, indicating the superiority of the presented modeling and tracking control strategies.