2D and 3D Visualizations of the Mass-Damper-Spring Model Dynamics Controlled by a Servo-Controlled Linear Actuator

Abstract

This paper focuses on controlling the dynamics of a mass-damper-spring model via a servo-controlled linear actuator (SCLA). The displacements of the mass are sensed and measured by a linear variable differential transformer (LVDT) whose output electrical signal is proportional with the position of the mass. Furthermore, a positive position feedback (PPF) controller is then provided with this signal to be processed and to generate the suitable control signal. The control signal itself is applied to the actuator which in turn controls the mass position. The whole system dynamical equations for the amplitudes and phases are derived with the aid of Krylov-Bogoliubov averaging perturbation method. 2D and 3D visualizations are included to give the reader a wider aspect of the system behavior before and after control.