Gain Scheduled H Control of Wind Turbines for the Entire Operating Range - Wind Turbine Control and Monitoring - page 80

4.5.1 H ' Optimal Pitch Control

As described in the previous section, the first step in the design of an H ? optimal
control is to state the augmented plant. This implies stating the specifications in
terms of the norm-minimization of the mapping between the performance output
z and the disturbance w. Model uncertainty can be covered by properly choosing
these signals, thus ensuring robust stability. Therefore, before describing the
augmented plant, we find the model uncertainty representation to cover the vari-
ation of the parameter B r and other errors caused by the approximation of the wind
turbine behavior with a low-order model. The use of the scheduling gain k 1

gs ð b Þ
allows canceling the variation of the linearized aerodynamic torque with respect to
the operating conditions. However, the variations in B r are not so simple to
compensate for, since they affect the eigenvalues of the linear model.
For control design purposes, the wind turbine can be modeled, after applying
the scheduling gain in the control input, by the following parameter dependent
transfer function

Figure 4.10 shows the frequency response of this transfer function for several
operating points in region 3. These results correspond to the 5 MW wind turbine
previously mentioned. It can be seen that these variations can be covered by
additive uncertainty of the form in Eq. 4.10 with the weighting function W D ð s Þ
shown in the right plot of Fig. 4.10 . In the uncertainty set, the scheduling gain
errors caused by the polynomial approximation and the high-frequency unmodeled
oscillation modes can also be covered.
In high wind speeds, the control objectives are the regulation of the rotational
speed close to the rated value X N and the reduction of the pitch activity to avoid
high mechanical stresses. In the H ? optimal control framework, these objectives
lead to the augmented plant of Fig. 4.11 . In this case, the control input u is the
pitch command and the controlled signal y is the rotational speed error
e ¼ X N X g . Then, the performance signal is z ¼½ e ; b r T and the disturbance is
the rotational set-point w ¼ X N . Notice that the wind speed could also be con-
sidered as a disturbance. However, this would not improve the performance, but
only increase the controller complexity.