Disturbance accounting control

Wind & Water Controls
1

Hello,

I’m trying to design the DAC control described in A.D. Wright, Chapter 7, Section 7.2.

As suggested, with my estimated state feedback controller, I only move the rotor speed pole, moving more left in the complex plane. My problems, however, comes from the DAC control design. I have following questions:

  1. the dimension of the state space model for the disturbances: if I model the system with three states, as suggested, I get a “constant” wind component and an “oscillating” one. I don’t understand how to chose the disturbance input matrix (Bd), since it needs to have two columns (which disturbance input do I need to chose?)

  2. The wind estimate is EXTREMELY sensitive to the placement of the estimator poles: if I use the values suggested by Wright, the wind estimate results in having “wild” oscillations, therefore giving unrealistic high pitch rate commands. I’ve tried many different values, but the wind estimation still is not accurate at all. Does this depend from the disturbance state space model?

If my questions are not clear enough, or if you need more data, please feel free to ask!

Thanks in advance,
Mario

2

Ok, I probably need to reformulate my question:

It seems to me that in order to obtain a good control in turbulent wind conditions it is necessary to adopt independent pitch control with DAC with hub-height wind speed and sinusoidal vertical shear disturbance model.
To do this, the wind acting on two blades has to be estimated. The wind is modeled with a three states dynamic system with a pole in the origin (constant wind speed) and a pair of complex poles (sinusoidal vertical shear, with frequency related to the rotor speed).
By feeding the system outputs into the wind disturbance estimator, and by making the system asymptotically stable (using a feedback matrix) the amplitude should be determined, and the wind disturbance estimate should converge to the actual wind speed. This means that we could focus only on the first of the two estimator outputs, right? (the other one should “just” be the oscillating part we use to take the vertical shear into account).
Now, what happens to me, is that the control action is particularly sensitive to the choice of the closed loop poles of the wind disturbance estimator, and that the estimate really is not accurate.

My question is therefore quite simple: how do I have to choose the closed loop poles?