Integral resonant negative derivative feedback suppression control strategy for nonlinear dynamic vibration behavior model

Abstract

One of the major problems in robotics research has been developing an actuator system for extremely dynamic-legged robots. High torque density and the capacity to control dynamic physical interactions are two design requirements for high-speed locomotion that are challenging for conventional actuators used in manufacturing applications to meet. To address this system and apply the desired control to reach the best stability position, the robot's foot was simulated with the Van der Pol equations, applied the required control, and studied that application. This work describes the actions of a new novel control mechanism known as the Integral Resonant Negative Derivative Feedback (IRNDF) controller, which reduces the vibration response of a double Van der Pol oscillator subjected to external excitations. This unique controller combines integral resonant control (IRC) and negative derivative feedback (NDF) controllers to provide a new controller effect for double Van der Pol oscillators. The multiple scale perturbation technique (MSPT) has been applied to solve the controlled system analytically. The MATLAB and MAPLE programs have been used to complete and clarify all of the numerical talks. The frequency response curves have been used to study the impact that altering the parameter values had on the amplitude. The controlled system vibration amplitude is governed by frequency-response equations (FREs), which have been constructed. In the vibration system, the IRC, NDF, and IRNDF controllers were compared to see which one was the best. Numerical results show that the unique IRNDF controller is the best at reducing oscillations and decreasing amplitude values. The effects of the effective parameters on the controlled system have been identified. The frequency-response equation that was derived has been used to plot the various response curves for the framework that show the stable and unstable zones when the controller is off and on. Lastly, excellent agreement between the derived numerical findings and the analytical ones was observed. Lastly, utilizing time histories and response curves to compare analytical and numerical solutions was fascinating and significant.