Page 202 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

176 Chapter Six

Anlwer Construct a simple RC circuit by shorting the inductor in Fig. 6-32. The
resulting circuit is described by

- - i
V = iR+~ j i(u)du V=iR+-
Cs
0

Alternatively, construct a simple RL circuit by shorting the capacitor in
Fig. 6-32. The resulting circuit is described by

'R Ldi
V =I+-
dt

6-8 Summary
This chapter has been devoted to just one process, the mass/spring/
dashpot process, because it has the unique characteristic of ringing
in response to an open-loop step input. In trying to control this pro-
cess the derivative component was added to the PI algorithm. After
showing that this modification could deal with the ringing but was
susceptible to sensor noise, a derivative filter was added and the
PIID algorithm was conceived.
In an alternative approach, the process was modified by state
feedback, after which it presented attractive nonringing dynamic
behavior. The compensation was developed using transfer functions
and state-space equations. To feed the state back, the mass's speed
had to be estimated. A filtered derivative was used to provide that
estimate. In general, the state may consist of other signals needing
something other than filtered differentiation. In this case Chap. 10
will show that the state-space approach along with the Kalman filter
will be needed.