Environmental Engineering Reference
In-Depth Information
14.5.1.4 Controller Design
A robust controller G
p
(s) for the system X
rs
(s)/b
di
(s)—Eq. (
14.39
) and the above
performance specifications—Eqs. (
14.40
) and (
14.41
)—is calculated by using the
loop-shaping window of the QFT Control Toolbox [
2
,
3
], as shown in Fig.
14.18
.
The controller G
p
(s) has a Proportional-Integral (PI) structure with a first order filter,
as shown in Eq. (
14.42
). It meets all the performance specifications, which are the
QFT bounds requirements at every frequency of interest, as is seen in Fig.
14.18
.
s
e
ð
s
Þ
¼
4
:
5
2
þ
1
G
p
ð
s
Þ
c
2
c
1
¼
b
di
ð
s
Þ
analog
00
s
00
ð
expression
Þ
ð
14
:
42a
Þ
s
s
4
þ
1
7
:
8722 z
1
þ
1
:
1389 z
2
1
1
:
0025 z
1
þ
0
:
0025 z
2
G
p
ð
z
Þ
c
2
c
1
¼
b
di
ð
z
Þ
digital
00
z
00
e
ð
z
Þ
¼
ð
expression
Þ
ð
14
:
42b
Þ
The controller algorithm is:
• Rotor speed data received from the sensor (Glide-Wheel AS): X
rs
(n) in rpm.
• Error calculation: e(n) = X
rs_ref
(n)-X
rs
(n), with X
rs_ref
(n) and X
rs
(n) in rpm.
• Control law, based on Eqs. (
14.42a
) and (
14.42b
):
b
di
ð
n
Þ¼
1
:
0025 b
di
ð
n
1
Þ
0
:
0025 b
di
ð
n
2
Þ
7
:
8722 e
ð
n
1
Þþ
1
:
1389 e
ð
n
2
Þ
ð
14
:
42c
Þ
being b
di
(n) the demanded pitch angle at the input of the NxT motor in degrees,
e(n) = X
rs_ref
(n)-X
rs
(n) the control error in rpm, and T
sampling
= 1.5 s the sam-
pling time (see also Fig.
14.14
). An anti-wind-up function is also implemented in
the algorithm to help the controller when the actuator is saturated at the upper or
lower limits.
Equation (
14.42a
) shows the controller in continuous-time G
p
(s)c
2
c
1
.
Equation (
14.42b
) shows the controller in discrete-time G
p
(z)c
2
c
1
after a discret-
ization with a zero-order hold approach and for a sampling time T
sampling
= 1.5 s.
And Eq. (
14.42c
) shows the control algorithm in terms of the actuator inputs
b
di
(n - k) (in degrees) and the control errors e(n - k) (in rpm), implemented in
the microcontroller with a sampling time of 1.5 s.
14.5.2 Power/Torque Control System
Power maximization is typically achieved by optimizing in real-time the power
coefficient C
p
for each tip speed ratio k = X
r
r
b
/v
1
—see Fig.
14.11
a. As wind
speed v
1
changes, the rotor speed X
r
is automatically modified in order to keep the
