![](bg7.png)
0 10 20 30 40 50 60 70 80 90 100
15
20
25
time (s)
Wind speed (m/s)
0 10 20 30 40 50 60 70 80 90 100
1.8
1.9
2
2.1
time (s)
Rotor speed (rad/s)
0 10 20 30 40 50 60 70 80 90 100
170
175
180
185
time (s)
Generator speed (rad/s)
0 10 20 30 40 50 60 70 80 90 100
1.9
2
2.1
2.2
x 10
6
time (s)
Generated power (W)
0 20 40 60 80 100
1
1.05
1.1
1.15
x 10
6
time (s)
Mechani cal t orque (Nm)
0 10 20 30 40 50 60 70 80 90 100
5
10
15
time (s)
Pitch angle (°)
0 10 20 30 40 50 60 70 80 90 100
1.1
1.15
1.2
x 10
4
time (s)
Electromagnetic torque (Nm)
0 10 20 30 40 50 60 70 80 90 100
0
20
40
time (s)
Control pitch angle (°)
Figure 7: Variation of the system variables.
6 CONCLUSIONS
This paper dealt with a technique of designing a
multimodel LQ regulator allowing to partially
control the process global dynamic, and with a study
of the global asymptotic stability of the controller by
means of a set of LMI. The proposed strategy
presented a compromise between different control
objectives: optimizing the performances of the
different system variables especially generating an
electrical power of a good quality, minimizing the
control efforts, alleviating the drive train dynamic
loads and controlling the global dynamic of the
studied process. The simulations results showed
good performances of the controller with acceptable
mechanical stress. But, satisfying such a trade-off
between all these objectives is indeed difficult and
the cost is however some high forces on the pitch
actuator. These effects brought more challenges in
the system analysis to improve the obtained results
in order to control actively the system dynamic and
to totally damp the oscillatory mode.
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(a)
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PERFORMANCES IMPROVEMENT AND STABILITY ANALYSIS OF MULTIMODEL LQ CONTROLLED
VARIABLE-SPEED WIND TURBINES
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