42 HANDBOOK OF ELECTRICAL ENGINEERING
Figure 2.12 Open-loop speed regulation of a gas turbine.where
Pe=F(ωo−ω) ( 2. 54 )
andωois the nominal shaft speed, andF is the feedback gain.
Hence the closed-loop control system for steady state conditions may be described by the
forward transfer function of (2.52), using the positive root, and the feedback transfer function of
(2.54). In order to establish suitable relationships betweenkandF it is necessary to consider small
changes in the variables and by so doing linearise the equations using a two-term Taylor’s series.
Transpose and square the positive root of (2.52).
(
ω−1 +k
2) 2
=
1
4
(
( 1 +k)^2 − 4 kP)
( 2. 55 )
Letωbe increased byωas the powerP is increased byP.
Equation (2.55) becomes,2 ωω−ω( 1 +k)+ω^2 −ω( 1 +k)+(
1 +k
4) 2
=
(
1 +k
4) 2
−kP−kP (2.56)Subtract the predisturbance state,
ω
P
=
−k
4 ( 2 ω− 1 −k)