Specifications

4 Designing Controllers Using the Command Line
4-12
figure(2)
plot(tsave,usave(:,3));
title('Coolant Temperature')
CSTR Results and Discussion
The plotted results appear below. Note the following points:
• The setpoint is being ramped from the initial concentration to the desired final value
(see the step-wise changes in the reactor concentration plot below). The reactor
concentration tracks this ramp smoothly with some delay (see the smooth curve), and
settles at the final state with negligible overshoot. The controller works equally well
(and achieves the final concentration more rapidly) for a step-wise setpoint change,
but it makes unrealistically rapid changes in coolant temperature (not shown).
• The final steady state requires a coolant temperature of 305.20 K (see the coolant
temperature plot below). An interesting feature of this nonlinear plant is that if
one starts at the initial steady state (coolant temperature = 298.15 K), stepping
the coolant temperature to 305.20 and holding will not achieve the desired final
concentration of 2. In fact, under this simple strategy the reactor concentration
stabilizes at a final value of 7.88, far from the desired value. A successful controller
must increase the reactor temperature until the reaction “takes off,” after which
it must reduce the coolant temperature to handle the increased heat load. The
relinearization approach provides such a controller (see following plots).