Tuning of P I D D 2 controllers for oscillatory systems with time delays

Proportional–integral–derivative (PID) control is a durable control technology that has been widely applied in the process control industry. However, PID controllers cannot achieve satisfactory performance for oscillatory systems with long time delays; thus, high-order controllers like the proportional–integral–double derivative ( P I D D 2 ) can be adopted to enhance the control performance. In this paper, we propose a tuning formula for the P I D D 2 controller for oscillatory systems with time delays and its practical implementation via an observer bandwidth-based state-space P I D D 2 . Simulation results show that the state-space P I D D 2 controller tuned from the proposed formula trades-off among robustness, time domain performance, and measurement noise attenuation and can arrive at a better control effect than PID for oscillatory systems.