Biomedical Engineering Reference
In-Depth Information
FIGURE 4-46
Classic
configuration of an
integral controller.
In general, a gearbox is incorporated at the output of the motor to better match the
motor torque to the load. This can be represented by a gain that is representative of the
gear ratio.
4.8.1.1 Disadvantages of Proportional Controllers
The main disadvantage of this form of controller is that the transfer function of the plant
with the controller is still the same order, so if the plant exhibits a steady-state error the
controller does not eliminate it completely.
4.8.2 Integral Controller
With integral control, the output of the controller is equal to the integral of the error. This
is shown in a unity gain configuration in Figure 4-46.
The forward path transfer function for this control system is
K
i
s
G
o
(
s
)
=
G
p
(
s
)
(4.91)
It can be seen that the controller introduces an additional
s
into the denominator, with the
result that the order of the system increases. A system that exhibited a steady-state error
for a step input will now converge with no error. The main disadvantage of the system is
that it introduces a pole at the origin (
s
−
0) and that can result in a less stable system.
If an integral controller is used to control the motor position, the system becomes
unstable for any gain, as is shown in the step response in Figure 4-47.
4.8.3 Proportional Plus Integral Controller
The reduction of the relative controllability of a plant as a result of using integral control can
sometimes be overcome by introducing a proportional term to make the control function
K
i
s
G
c
(
s
)
=
K
p
+
(4.92)
Implementation of this controller results in a system block diagram, with unity gain feed-
back, as shown in Figure 4-48.
The forward path transfer function for this control system is
K
p
+
G
p
(
s
)
K
i
s
G
o
(
s
)
=
(4.93)
