Page 200 - Practical Control Engineering a Guide for Engineers, Managers, and Practitioners

174 Chapter Six

The following must also be true:

which yields (6-19)
K,gto! =ga>b

Equations (6-18) and (6-19) are similar to Eq. (6-14).
Depending on your comfort level with the different mathematical
tools, you might agree that the state-space approach is a little less
cluttered and more general than the transfer-function approach. Later
on, when methods of estimating the state are presented in Chap. 10,
the strength of the state-space approach will become even more
apparent.

6-7 An Electrical Analog to the Mass /Dashpot/Sprlng
Process
Consider the RLC circuit in Fig. 6-32 where R refers to resistance of
the resistor, L the inductance of the coil, and C the capacitance of the
capacitor. The applied voltage is V and it will also be the process
input U. The voltage over the resistor is iR where i is the process out-
put Y. The voltage over the capacitor is
1 t
C Ji(u)du
0
and the voltage over the inductor is

L di
dt

R

v--+......___
L
T

F1auaE 8-32 RLC circuit.