Frequency response analysis of a three capacity liquid level system

Includes bibliographical references (pages 67- 68)The dynamic response of a liquid level system consisting of three series connected tank was determined utilizing the technique of direct frequency response testing with a sinusoidal input disturbance. The response of the system was determined when operated in both a single capacity node, and a three capacity, interacting system. Mathematical models describing the single and three capacity systems were developed. Analog computer simulations of both linearized and non-linear versions of the mathematical models were made. Frequency response analyses were conducted on these simulations. The results of both the experimental runs, and analog simulations are presented in the form of Bode diagrams showing the gain and phase angle as a function of the frequency if the input disturbance. For the conditions under which the system was operated, the non-linear model provided the better representation of the gain and phase characteristics of the process. However, the difference in values predicted by the two models was small, and use of the simpler linearized model would appear justified for normal engineering calculations. For the three capacity mode of operation , the standard error in using the linearized model is 11.5 degrees in the phase angle, and 2.77 inches of level change per inch of valve stem motion. For the single capacity mode of operation, the standard error in phase angle and gain was 3.72 degrees and 3.46 inches of level change per inch of valve stem motion. The effect of amplitude of the input sine wave was investigated by subjecting the analog models to valve stem oscillations of 0.12, 0.22, and 0.32 inches. Essentially no effect of input amplitude was seen on the phase angle characteristics. While the deviation between the magnitude ratio calculated by the linear and non-linear models increased with amplitude, at the maximum studied, the standard error in gain using the linearized model was 7.8 % of the steady-state gain