Determination of optimal PID control parameters by response surface methodology

Abstract

Proportional–Integral–Derivative (PID) controllers are the most widely used systems in industrial applications and in academic research regarding control engineering. In this study, the optimal PID control parameters of a liquid level control system were determined with Response Surface Methodology. Dynamic analysis was carried out on the liquid level control system to prepare the reaction curve. Accordingly, dead time, time constant and process gain values were determined as 16s, 261s and 0.842, respectively. Based on the dynamic analysis, PID parameters were calculated in accordance with the Cohen-Coon, Ziegler-Nichols, Yuwana-Seborg methods, which are the commonly used tuning methods. The Kp, τI, τD parameters were calculated as 30.77, 29.15 and 5.4 with the Cohen-Coon method, as 0.453, 30.0 and 7.5 with the Ziegler-Nichols method and as 1.63, 686.3 and 117.7 with the Yuwana-Seborg method, respectively. The PID control parameters applied for the 40cm, 50cm and 60cm set points and ISE and IAE control performance values after experiments were calculated. The Kp, τI and τD values were selected as the independent parameters, while the ISE and IAE values were chosen as the dependent variables. The numerical values of the responses for the runs in the design matrices were determined with a closed-loop PID controller with the liquid level system block diagram that was designed in MATLAB/Simulink. The simulations proposed by the trial version of Design Expert 7.0 program were performed in order and the IAE and ISE values were calculated after the simulations were processed. In this study, minimum ISE and IAE values were selected to determine the best PID parameters of a liquid level control system. The optimal PID control parameters of the liquid level system required to obtain the lowest ISE and IAE values were determined as 23.14, 28.31 and 11.50 for Kp, τI and τD, respectively.