A time-delayed proportional-derivative controller for a dielectric elastomer circular membrane

Abstract

• In this paper, an internal resonance of a circular DE membrane is investigated within mechanical and electrical excitations in order to find internal resonances for improving its performance for future applications. • This work proposes a time-delayed proportional-derivative (TDPD) controller for decreasing the oscillations of a DE system with quadratic and cubic nonlinearities. • Averaging method is used to solve the controlled system to obtain the first-order approximation solutions and response equations for the DE system. • The TDPD controller is the best control strategy that can reduce the framework vibrations regardless of the excitation frequency. Due to the substantial deformation generated by voltage excitation, the dielectric elastomer (DE) is a new type of functional polymer that can be employed as a smart actuator. In this paper, an internal resonance of a circular DE membrane is investigated within mechanical and electrical excitations in order to find internal resonances for improving its performance for future applications. All programs that contain DE will perform flawlessly if DE is managed. This work proposes a time-delayed proportional-derivative (TDPD) controller for decreasing the oscillations of a DE system with quadratic and cubic nonlinearities. The system is researched and investigated when using a Proportional–derivative (PD) controller to apply time-delayed control on displacement and velocity. Stability is improved, maximum peak overshoot is reduced, settling time is reduced, and the framework transient response is recovered using this control method. The first-order approximation solutions for the DE system are calculated using the averaging method. Simultaneous resonance is regarded as the worst type of resonance. To obtain the dynamic solution of the device with TDPD controllers, analytical and numerical approaches are used. The Routh-Huriwitz approach is used to review and analyze the consistency of the steady state solution in the near-resonance case. The effects of various factors on the steady-state solution are identified and discussed. The effects of time delay are investigated in order to determine the most stable range of time delays for the best performance. The MATLAB software package is used to generate simulation effects. When the results are compared to the numerical simulations, they show that the approximate solution and the control algorithm used in this paper are well validated. At the end, there is a comparison with previously published work. The focus of this paper is on using a TDPD controller to manage the nonlinear dynamic response and probable internal resonances of a circular DE membrane under mechanical and electrical excitations. The approximate solution of a nonlinear system of differential equations is investigated using the averaging technique in the cases of primary and 1:2 internal resonance, which are the worst-case scenarios that should be avoided. To display and compare controller effects at various system settings, several response curves are used. The TDPD controller is used to research nonlinear dynamics control of the DE system with harmonic force. The stability analysis and the effects of parameter behavior are tested using MATLAB program. To examine the controller effect, several response curves are used. The collected findings demonstrated that the TDPD control efficiency in reducing the system's nonlinear oscillations. The frequency response curves of the system were studied at various uncontrolled and regulated coefficients. Before and after control, response curve diagrams employing frequency response equations are created. Finally, validation curves are shown to measure the degree of similarity between analytical and numerical simulation predictions. At the end, there is a comparison with previously published works.