Enhanced Two-Degree-of-Freedom Control for Polynomial and Sinewave Reference Trajectories

Most of the control system design requires output signal to follow setpoint trajectories with zero steady state error. A discrete-time PID controller often struggles to track complex reference trajectories like sinusoidal and ramp signals, resulting in steady-state errors. However, real-time tuning of a PID controller can be quite challenging, and it also tends to lack the ability to reject disturbances effectively. A two-degree-of-freedom (2-DOF) controller structure offers a solution by enabling improved tracking performance of such reference trajectories. While recent approaches have successfully addressed steady-state error removal for polynomial trajectories, this paper extends these methods to sinusoidal reference signals. Additionally, it explores a combined approach for tracking both sinusoidal and polynomial references by leveraging the Auxiliary Aryabhatta’s Identity Equation. The control strategy has been validated on a thermal resistive plant utilizing both cyclic and ramping temperature setpoint profiles.