Modeling and Performance Evaluation of P, PI, PD and PID Temperature Controller for Water Bath

Abstract

Water bath temperature control is one of the most widely used processes in academic laboratories and industries. It usually contains single or mixture of liquid substances whose temperature is the subject of control. In this paper, a performance evaluation of P, PI, PD, and PID algorithms for the system was investigated. A mathematical model of the first order system was derived using the lumped parameter model. The time constant of the water bath was obtained theoretically and found to be 356s and time lag of 5s. The gain of the heater of 1500 W was computed and found to be 0.047 ^oC/K. An open loop reaction curve of the system was then obtained by measuring the temperature response to step input against time and plotting same using MATLAB. The P, PI, PD and PID control strategies were subsequently designed to control the temperature of the water bath. The compensators were manually tuned to P = 3000; P = 21.5599, I = 0.0034539; P = 22.7179, D = 0.0067356; and P = 25.4904, I = 0.0034802, D = 10.5302 respectively. These gains were used to manipulate the temperature set points for the water bath. The performance of the MATLAB simulated results were evaluated and compared against each other. The results show that P control requires high step input (3000 W) though the offset could be reduced. The PI control on the other hand exhibits fast response and reduced steady state error. PD control for the plant was found to be highly unstable for all the tuned values of the gains which makes it unfit for the first order system. The PID compensator provided compromise between the P and PI. It exhibited a rise time of 541s, settling time of 794s and an overshoot 1.10%.