Data-Driven Tuning Method for LQR Based Optimal PID Controller

Data-driven control methods for modern controller design are becoming popular recently. However, the traditional Proportional–Integral–Derivative (PID) controller is still the most widely used controller to the industrial preference. To tune the parameters of the PID controller, optimal PID tuning approaches such as solving the Riccati equation of the Linear Quadratic Regulator (LQR) provide the optimal solution. The disadvantages of the LQR are that an accurate model of the system is required, and the high-order system must be reduced to the second-order system so that the Riccati equation can be solved. In this paper, a novel data-driven method is proposed to cope with these problems. For the system which is difficult to be identified accurately, the proposed data-driven method can skip the procedure of system identification and tune the parameters of the PID controller directly with the experimental data instead of solving the Riccati equation. This data-driven tuning method also ensures that the parameters of the PID controller for the high-order system are optimized without using the reduced-order model of the system. Simulations are conducted on a tray indexing system with the second-order model and the full-order model demonstrating high applicability and accuracy of the proposed method.