Publishers version - DTU Orbit

Magnitude (abs)
blade pitch
gen speed
10 5
10 0
10 −5
10 −10
10 0
10 −10
10 −4
feedback only
typical measurement
perfect measurement
10 −3
Bode Diagram
10 −2
Frequency (Hz)
Figure 151: Frequency responses of closed-loop transfer functions, with wind spectrum included,
showing generator speed error and blade pitch actuation with H2 optimal combined
feedforward/feedback control for the NREL 5-MW turbine at a 13 m/s wind speed operating
point with 9 seconds of available preview time.
lidar is removing high frequency content from the measurement, the remaining low frequency
errors due to evolution do not become significant until at least 7 s (126 m) of preview, when
even the low frequencies of turbulence have significantly evolved. Additional details regarding
this control study can be found in Laks et al. (2013).
10.8 Control Example 2: H2 Optimal Control with Model
of Measurement Coherence
In this section, an H2 optimal controller design is described where a model of wind measurement
coherence is included in the design process. This combined feedforward/feedback
controller is designed to minimize a weighted sum of RMS generator speed error and RMS
blade pitch (deviation from the operating point) using the NREL 5-MW model, assuming the
Kaimal wind spectrum, class B turbulence (medium turbulence) and the normal turbulence
model (NTM) (Jonkman, 2009).
Figure 151 shows the resulting closed-loop generator speed and pitch actuation responses
for three different cases: feedback only, typical measurements (measurement coherence is
modeled as the magnitude squared of a single-pole low-pass filter with bandwidth of 0.2 Hz),
and perfect measurements. We see that with lidar measurements, generator speed error is
improved at both lowand highfrequencies, and pitch actuationis reduced at highfrequencies.
Figure 152 shows the magnitudes of the optimal controllers. As the lidar measurement
improves, the feedforward controller action increases at low frequencies, and the feedback
controller action decreases at low frequencies, freeing it to act more at mid frequencies if
necessary. The decrease in low-frequency feedback action is helpful because feedback control
performance is fundamentally limited by the Bode sensitivity integral (Franklin et al., 2006),
which essentially says that a decrease in sensitivity to disturbance at one frequency must be
balanced by an increase in sensitivity to disturbance at another frequency. When feedforward
takes over at low frequencies, feedback can increase sensitivity to low-frequency disturbance,
and therefore can decrease sensitivity to mid-frequency disturbance. Thus low-frequency wind
measurements can lead to reductions in mid-frequency loads. This increase in mid-frequency
feedbackactionoccursfortypicallidarmeasurements,butforperfectmeasurements,feedback
is unnecessary because the feedforward controller takes over at all frequencies, assuming
DTU Wind Energy-E-Report-0029(EN) 215
10 −1
10 0