Small Decrease in Jacket Flowrate

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Small Decrease in Jacket Flowrate

Consider a step change of -0.1 (from 1.5 to 1.4 ) in jacket flowrate. The responses of the linear and nonlinear models are shown in Figure 5. Since the the change in input is small, the linear model provides a good approximation to the nonlinear model.

Remarks on Step Response Behavior

For the nonlinear model the gain (change in output/change in input) varied as a function of both the input magnitude and direction. If small input changes were made, the gain did not change much from the linear model case. For large input changes, the gain of the nonlinear system was less than the linear system for increases in jacket flowrate, but more than the linear system for decreases in jacket flowrate.

The response of the jacket temperature is faster than than of the tank temperature. This makes sense from a physical point of view, because the jacket volume is one-tenth of the heater volume. Also, the jacket flowrate has a direct effect of jacket temperature and an indirect effect on tank temperature. Notice that the numerator time constant partially ``cancels'' the slow denominator time constant for the transfer function relating jacket flowrate to jacket temperature.

B. Wayne Bequette,