Modeling and Controller Tuning of a Humidifying Process
A humidifying process with time delay was studied experimentally. The model was identified for different airflow rates and fixed water level in the humidity chamber. The exit air relative humidity was measured using Honeywell make HIH – 3610 series humidity sensor. The data was fitted to a first order plus dead time model. Based on the model, three different PI controllers based on Z-N, IMC and direct synthesis were analyzed using MATLAB. The results based on performance (Rise time, Peak time, Settling time, and Overshoot) showed that IMC and Direct synthesis were equally superior than Z-N.
Online humidity analysis is vital for control and maintenance of material and human comfort in air-conditioned rooms and cold storage. Humidity control is important in industries such as textile, food processing, tobacco and pharmaceuticals. For proper control of humidity, choice of good control device is essential. A controller designed for a process has to provide fast, accurate tracking of set point changes and also should perform for external disturbance. Sundaram et al.[1 - 4] have identified model and designed various controllers for linear and non linear processes. Ziegler and Nichols developed a simple traditional method for PI controller for a stable first order plus time delay process. Hagglund and Astrom have presented new rules for Z – N tuning from step test data. Foley Michael. W et al. have compared Direct synthesis and IMC controller for both servo and regulatory problems. Chen and Seborg proposed formulae for designing PI/PID controller using direct synthesis method. Fruehauf et al. discussed IMC based PID tuning rules.
Experimental set up and process identification:
The experimental set up consists of a humidity chamber (HC) wherein primary air is bubbled into the HC by manipulating the valve V1 and is metered using rotameter R. The exit humidified air flows through a coil 3 m long and 1.25 cm diameter. The exit air humidity is measured using HIH – 3610 series Honeywell relative humidity sensor.
The air rate was varied from 0.35 to 0.6 LPM in steps of 0.05 LPM. After steady state was reached at the flow rate of 0.35 LPM, a step input of 0.05 LPM was introduced by adjusting the valve V1. The relative humidity with respect to time was recorded. This was repeated for six different flow rates. The recorded data were plotted with respect to time to obtain process reaction curve. The process parameters were found as suggested by Bequette13]. The data fitted a first order plus dead time model with an accuracy of ±4%. The model parameters are shown in table 1.
Table : 1 Process parameters
Design of PI controller using ZN method (ZNPI)
Ziegler and Nichols closed loop technique for tuning of the controller. In this method the ultimate gain and ultimate period were found by making the process to sustained oscillation. Ziegler and Nichols also proposed tuning parameters for the first order process with time delay by direct substitution in the formulae. The ultimate gain (Ku) and ultimate period (Pu) can also be found using cross over frequency from Bode plot. According to the rules the Z – N settings can be directly determined. The Z –N PI rules are given as follows.
Kc = 0.45 Ku
KI = Pu / 1.2
Design of Direct Synthesis method (DSPI)
Based on process model and desired closed loop transfer function the controller is designed in this method. This approach provides valuable insight into the relationship between the process model and the resulting controller. The controller gain in inversely proportional to the model gain K, which is reasonable based on stability analysis. In this approach the product of controller gain and model gain remains constant. The characteristic equation and the stability characteristics of the closed loop system do not change. The PI controller settings are as follows.
tI = t
The key decision in this approach is the choice of design parameter tc. Rivera et al have proposed choice for this design parameter.
Design of Internal Model Control (IMC) based PI controller (IMCPI)
The pure IMC procedure is suitable for first order plus dead time process. But for the IMC based PI procedure, the process with time delay will not give same performance as IMC. The time delay is approximated and the controller is designed. The controller settings are as follows.
tI = t+
Selecting the filter coefficient l is the prime factor in this design.
Table 2: Controller settings
Results and discussions
The model parameters for the humidifying pilot plant were identified. For the model, three different tuning methods like Ziegler Nichols, Direct Synthesis and IMC based PI procedures were simulated using MATLAB. The response curves for step and load changes were obtained. From the graph the time domain specifications rise time, peak time, peak overshoot and settling time were found. It is clear that direct synthesis and IMC based PI procedures are giveing faster settling time and lesser overshoot compared with traditional Ziegler Nichols tuning in all the cases.
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