Dynamic Analysis and PID Control of a Double Pendulum Arm Excited by a Nonideal Source

In this paper the dynamics of a double pendulum arm coupled through a magnetic field to a nonlinear RLC based shaker circuit is presented and will be studied numerically. This kind of electromechanical system is often found in robotic systems and has important applications in Engineering Sciences. The double pendulum considered is coupled through a magnetic field to an RLC circuit based on nonlinear shaker. The nonlinear response analysis of the system is done by various techniques, including bifurcation diagrams, phase portraits, power spectral densities, and Lyapunov exponents. Numerical simulations show the existence of chaotic and hyperchaotic behavior for some regions of the parameter space. In order to suppress the chaotic motion, a PID control is proposed and analyzed. Numerical simulations show the effectiveness of the proposed control in suppressing the chaotic motion.