Image Processing Reference
In-Depth Information
K p
~
~
~
~ max
TC
system
z
τ
e s
K i
z- 1
~
t c ( z )
~ min
L
FIGURE 9.41
PI controller with antiwindup compensation for a TC system.
systems use a trial and error-based approach for compensation. Figure 9.41 shows a
typical antiwindup scheme used in printers for a SISO TC system.
In the absence of actuator limits, the actuator signal
v will be same as
u. When
v
u max during the course of the loop operation, which may happen
when the development voltage is changing rapidly, for example, the error signal e s
will be nonzero. The integration of the error signal will lead to a larger
saturates to
v which will
have no effect on the TC output since the actuator is limited to
u max . If the
integrating effect continues further in the same direction, the integrator output
may become excessively large. To compensate for these effects, we need to create
a situation where the sign of the error is inverted (i.e., opposite to what was
happening when
u max ). This is achieved by inserting a high gain
dead zone feedback using another error signal obtained by subtracting
v saturates to
v.
In this scheme, when the integrator saturates, the antiwindup feedback obtained
through the high gain, L, at the integrator becomes active to force the integrator
windup error to zero. During this time, the integrator acts like a fast
u max from
first-order lag
with a transfer function that has a single pole created by the antiwindup compen-
sator gain L. The value of the compensator gain determines how fast the integral
action is pulled back from actuator saturation. When
v is within the actuator limits
u max ), a dead zone is created by disabling the high gain
feedback automatically. The output of the integrator
(i.e., between
u min and
v is the input to the high gain
feedback. The implementation of the actuator limits would involve the use of a
saturation function to generate the control signal
u, which is the input to the high
gain antiwindup compensator loop. The high gain antiwindup compensator can also
be applied in Figure 9.41 before the integrator constant, Ki, i , as an alternate feedback
structure.
Example 9.12
Consider the design of a TC feedback system with a transport delay using a state
feedback estimator and controller. Design the observer gain matrix and
the controller gain matrix using pole-placement techniques. Apply the area cov-
erage disturbance shown in Figure 9.42. Use actuator saturation. Compare the TC
response using the conventional approach with a PI controller, a Smith predictor,
and an antiwindup compensator. Construct a
figure of merit
to compare
the results.
 
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