| Summary: | Successful control of a dielectric elastomer actuator (DEA) can be a challenging task, especially if no overshoot is desired. The work presents the first use of the <inline-formula><math display="inline"><semantics><mrow><mi>P</mi><msup><mi>I</mi><mi>λ</mi></msup><msup><mi>D</mi><mi>μ</mi></msup></mrow></semantics></math></inline-formula> control for a dielectric elastomer actuator to eliminate the overshoot. The mathematical model of the dielectric elastomer was established using the fractional Kelvin-Voigt model. Step responses are first tested in the Laplace domain, which gave the most satisfactory results. However, they did not represent the real model. It cannot have negative force acting on the dielectric elastomer actuator. Simulations in Matlab/Simulink were performed to obtain more realistic responses, where output of the <inline-formula><math display="inline"><semantics><mrow><mi>P</mi><msup><mi>I</mi><mi>λ</mi></msup><msup><mi>D</mi><mi>μ</mi></msup></mrow></semantics></math></inline-formula> controller was limited. Initial parameters for a PID control were obtained by the Wang–Juang–Chan algorithm for the first order plus death time function approximation to the step response of the model, and reused as the basis for the <inline-formula><math display="inline"><semantics><mrow><mi>P</mi><msup><mi>I</mi><mi>λ</mi></msup><msup><mi>D</mi><mi>μ</mi></msup></mrow></semantics></math></inline-formula> actuator control. A quasi-anti-windup method was introduced to the final control algorithm. Step responses of the PID and the <inline-formula><math display="inline"><semantics><mrow><mi>P</mi><msup><mi>I</mi><mi>λ</mi></msup><msup><mi>D</mi><mi>μ</mi></msup></mrow></semantics></math></inline-formula> in different domains were verified by simulation and validated by experiments. Experiments proved that the fractional calculus <inline-formula><math display="inline"><semantics><mrow><mi>P</mi><msup><mi>I</mi><mi>λ</mi></msup><msup><mi>D</mi><mi>μ</mi></msup></mrow></semantics></math></inline-formula> step responses exceeded performance of the basic PID controller for DEA in terms of response time, settling time, and overshoot elimination.
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