Ripple Free Deadbeat Control for Nonlinear Systems with Time-Delays And Disturbances

Abstract

The design of controllers for the ripple-free deadbeat problem has long been investigated in the literature, but a need still exists to offer a better methodology for both performance and robustness for linear and nonlinear systems. This research proposes a new design methodology for ripple-free deadbeat control for nonlinear systems with time delays and disturbances. The proposed method combines two control laws, PID controller with Ripple-free Deadbeat controller. The new controller is applied to magnetic ball levitation CE 152 as a case study for nonlinear systems. The deadbeat tracking and rejection formulation combines both the polynomial approach and the time domain approach, the time domain approach (PID control) is used to ensure the local behavior of the nonlinear system, while the polynomial approach (Diophantine equation) is used to provide deadbeat control to the nonlinear system. The nonlinear system is firstly controlled with PID law which tuned using Simulink Design Optimization™ software, then a second order linear model for the resulting response is estimated to model the nonlinear system. After that, a ripple-free deadbeat reference tracking and disturbance rejection control method for the system with time delays and disturbances is proposed. The developed control is simulated using MATLAB software. Simulation results show that the output signal exactly tracks the input signal and rejects the disturbance in short settling time and at time-delay existence. The time domain specification for the output signal, control signal, and error signal are computed and satisfied the requirements and constraints.