# Tuning the PID controller used to control pitch.

Hello everyone,
In the PI control used to control pitch:

Δθ(t)=Kp*Δω(t)+Ki*∫Δω(t)dt where ω is the RPM of the rotor and Δω is the RPM error

Why can’t Kp and Ki be made as large as possible, (just so large that the (1) resulting RPM curve does not have spikes, (2) the pitch change rate is within the actuator limit)

What we usually do instead, is use the above expression along with the drivetrain dynamic equations to eventually get
{J+(-∂P/ ∂θ)* KdN/ω}φ2 + {(-∂P/ ∂θ) NKp1/ω - Po/ωω}φ1 + {(-∂P/∂θ)N Ki1/ω}φ=0 ≅ Mφ2 ̈+Cφ1 ̇+Kφ=0

where φ2,φ1 are the second, first order partial derivative of φ w.r.t time. φ is such that ∂φ/∂t=ΔΩ.

And then we impose the conditions, that natural frequency of the above system should be 0.6 rad/s and that damping ratio should be 0.6-0.7.Why do we aim for these response characteristics? The reference given in the 5MW FAST turbine report simply states that these are because of experience. Why is this response characteristic desirable, for instance why can’t say the natural frequency be higher?

Dear Harimanjunathan Sankaranarayanan,

Increasing the response natural frequency will lead to increased control gains. You could, of course, do this, but it may not always be beneficial. Controls design almost always involves balancing a set of competing objectives, including meeting the design goals, staying within actuator limits, and avoiding undesireable unintended consequences. For example, increasing the gains on a rotor-speed controller may result in improved rotor-speed regulation at the expense of excessive actuator usage or increased turbine loads.

Best regards,

Just seconding what Jason wrote, increasing the gains as high as possible is not desirable. As an example, imagine what a cruise control system would do to a car if it attempted to exactly maintain a given speed with no deviation though large application of acceleration and brakes. For wind turbines, higher gains will improve the speed tracking, but they also increase actuator usage, cause more loading throughout the turbine and possibly feedback more noise which is typically in higher frequencies. Additionally, a higher bandwidth might include certain resonant modes. A final issue is stability, margins of stability will tend to decrease with higher feedback gains.

A good paper on this topic I can recommend can be found here:
onlinelibrary.wiley.com/doi/10.1002/we.34/pdf

Good luck!
Paul

@Paul : Thanks a lot. Your information along with Mr. Jason’s post was very useful in itself. I can’t access the paper that you’ve mentioned without paying though .