786 Chapter 10 / Control Systems Design in State SpaceComments
1.In designing regulator systems, note that if the dominant controller poles are placed
far to the left of the jvaxis, the elements of the state feedback gain matrix Kwill
become large. Large gain values will make the actuator output become large, so
that saturation may take place. Then the designed system will not behave as
designed.
2.Also, by placing the observer poles far to the left of the jvaxis, the observer
controller becomes unstable, although the closed-loop system is stable. An unstable
observer controller is not acceptable.
3.If the observer controller becomes unstable, move the observer poles to the right
in the left-half splane until the observer controller becomes stable. Also, the desired
closed-loop pole locations may need to be modified.
4.Note that if the observer poles are placed far to the left of the jvaxis, the band-
width of the observer will increase and will cause noise problems. If there is a
serious noise problem, the observer poles should not be placed too far to the left
of the jvaxis. The general requirement is that the bandwidth should be sufficiently
low so that the sensor noise will not become a problem.
5.The bandwidth of the system with the minimum-order observer is higher than that
of the system with the full-order observer, provided that the multiple observer
poles are placed at the same place for both observers. If the sensor noise is a seri-
ous problem, use of a full-order observer is recomnended.
10–7 Design of Control Systems with Observers
In Section 10–6 we discussed the design of regulator systems with observers. (The systems
did not have reference or command inputs.) In this section we consider the design of
control systems with observers when the systems have reference inputs or command
inputs. The output of the control system must follow the input that is time varying. In
following the command input, the system must exhibit satisfactory performance (a
reasonable rise time, overshoot, settling time, and so on).
In this section we consider control systems that are designed by use of the pole-
placement-with-observer approach. Specifically, we consider control systems using
observer controllers. In Section 10–6 we discussed regulator systems, whose block
diagram is shown in Figure 10–25. This system has no reference input, or r=0.When
the system has a reference input, several different block diagram configurations are
conceivable, each having an observer controller. Two of these configurations are shown
in Figures 10–26 (a) and (b); we shall consider them in this section.
r= 0 u y
Plant- y Observer
+– controller
Figure 10–25
Regulator system.Openmirrors.com