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.
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.