Regulation of flow through a T-Shaped open cavity by temperature dependent P, PI, and PID controllers

P (proportional), PI (proportional-integral), and PID (proportional-integral-derivative) controllers are popular means of controlling industrial processes. Due to superior response, accuracy, and stable performance, PID controllers are mostly used in control systems. This paper presents a mathematical model and subsequent response analysis regarding regulation of flow in mixed convection through a T-shaped open cavity by temperature dependent controllers. The T-shaped cavity has cold top and hot bottom walls, while air is flowing through the inlet at surrounding temperature. The inflow is regulated by a controlled gate which operates according to the signal received from the controller. Values of proportional gain (kp), integral gain (ki), and derivative gain (kd) are varied to obtain the desired system response and to ensure a stable system with fastest response. At first, only P controller is used and eventually PI and finally PID control scheme is applied for controller tuning. Tuning of different controllers (P, PI, and PID) are carried out systematically based on the reference temperature which is continuously monitored at a certain location inside the cavity. It is found that PID controller performs better than P or PI controller.