Modeling and Discrete-Time Terminal Sliding Mode Control of a DEAP Actuator with Rate-Dependent Hysteresis Nonlinearity

Abstract

Dielectric electro-active polymer (DEAP) materials, also called artificial muscle, are a kind of EAP smart materials with extraordinary strains up to 30% at a high driving voltage. However, the asymmetric rate-dependent hysteresis is a barrier for trajectory tracking control of DEAP actuators. To overcome the barrier, in this paper, a Hammerstein model is established for the asymmetric rate-dependent hysteresis of a DEAP actuator first, in which a modified Prandtl-Ishlinskii (MPI) model is used to represent the static hysteresis nonlinear part, and an autoregressive with exogenous inputs (ARX) model is used to represent the linear dynamic part. Applying Levenberg-Marquardt (LM) algorithm identifies the parameters of the Hammerstein model. Then, based on the MPI model, an inverse hysteresis compensator is obtained to compensate the hysteresis behavior. Finally, a compound controller consisting of the hysteresis compensator and a novel discrete-time terminal sliding mode controller (DTSMC) without state observer is proposed to achieve the high-precision trajectory tracking control. Stability analysis of the closed-loop system is verified by using Lyapunov stability theorem. Experimental results based on a DEAP actuator show that the proposed controller has better tracking control performance compared with a conventional discrete-time sliding mode controller (DSMC).

Precision Flux Control of Linear Reluctance Actuator Using the Integral Sliding Mode Method

“…To describe the characteristics of hysteresis, various model structures are proposed. The most representative methods include physical modeling, mathematical operator modeling, and intelligent modeling (Li M. et al, 2019;Al Janaideh et al, 2021;Zhang et al, 2021;Cheng et al, 2022;Flores et al, 2022;Otieno et al, 2022). Specifically, the Bouc-Wen model sorted by the physical method is the most popular one since its parameters have definite physical meaning and are easily obtained (Ismail et al, 2009;Hassani et al, 2014).…”

Advanced Trajectory Control for Piezoelectric Actuators Based on Robust Control Combined with Artificial Neural Networks

“…The first-mentioned group is a description of the ferromagnetic effect that produces the non-linearity, although the material dependency and complex numerical solutions are the downsides of these theories [20,21]. In regards to the phenomenological, the sub-classification is related to the ones based on differential equations (Dunhem [22], Backslash [23] and Bouc-Wen [24]), operator models (Preisach [5], Prandtl-Ishlinskii [25] and Krasnoselskii-Pokrovskii [26]) and polynomial models [27]. Nevertheless, the disadvantages of these approaches are linked with complicated solutions to gather the inverse model, incapability to deal with asymmetric hysteresis, rate dependency and complex implementation [20].…”

Single-Neuron Adaptive Hysteresis Compensation of Piezoelectric Actuator Based on Hebb Learning Rules

“…However, the inherent hysteresis nonlinearity of the PEA greatly degrades its positioning accuracy, thus affecting its applicability and performance in precise operation tasks. The most significant characteristics of the PEA's hysteresis are the rate-dependence and asymmetry [5][6][7], i.e., the hysteresis loop becomes thicker with the increment in the input rate (or frequency) and the hysteresis loop is not symmetric about the loop center. These characteristics increase the complexity of the system and cause great difficulties in hysteresis modeling and compensation.…”