Time-Delayed Feedback Control Applied in a Nonideal System with Chaotic Behavior

This chapter considers the application of time-delayed feedback control in a nonideal system. The system has as main characteristic the additional cubic nonlinearity. An electric DC motor with limited power supply that is driven by an unbalanced rotating mass provides a nonideal excitation to the system. To suppress the chaotic behavior presented by the nonideal system, the time-delayed feedback control is proposed, by considering the velocity of the rotating angle as a parameter to determine the time delay. In addition, it is considered a control for suppressing the chaotic behavior. Therefore, two control signals are considered in which one is the nonlinear feedforward controller to maintain the system in periodic orbit and the other one is the feedback controller obtained by the SDRE, which takes the system trajectory to the desired periodic orbit. Numerical simulations demonstrated the effectiveness of the control strategy in conducting the system from any initial condition to the desired orbit and the control of chaos by time-delayed feedback control.