Adaptive MPC controller

[icnosvbovwb]

Dear @jjonkman

Q1: Is the partial derivative of Tr and Fr derived from a formula? Or is it based on the linearization function?
Because based on this article "On the Design and Training of Linear Model Predictive Control for Wind Turbines", I am reproducing the MPC controller and currently encountering some code setting issues.

Q2: How to calculate KK_Tw, KK_Tθ and KK_TV, respectively? I guess it's based on the partial derivative of Tr over W in the picture 2，right?
For example : sensitivity of Torque to the rotor collective blade-pitch angle ∂T/∂w=(-0.5rhopiR^4^vCp)/λ^2 at the steady-state operating point of 18m/s wind speed, ∂T/∂v=(rhopiR^3^vCp)/λ, Right? If this is correct，I don't know how to calculate ∂T/∂θ.
KK_Tw = 10^6(-10.35) ;
KK_Tθ = 10^6*(-0.89);
KK_TV = 10^61.20 ;
Similarly，∂F/∂v=rhopiR^2^vCt, I don't know how to calculate ∂F/∂w and ∂F/∂θ.
Partial derivative of Ft at the steady-state operating point of 18m/s wind speed:
KK_Fw = 10^5*(-6.15 );
KK_Fbeta = 10^5*(-0.69);
KK_FV = 10^5*(0.77);

Q3: How to calculate the Damping ratio of tower first fore-aft bending?
ksi_t = 0.062;

Q4: What are the Ft_op and dt_op, respectively?
V_op = 18 ;
beta_op = 14.77 ;
lamda_op = 12.1pi./30R/18 ;
Ft_op = 10^5*4.347 ;
dt_op = 0.2117;

[jjonkman]

Dear @icnosvbovwb,

I'm not familiar with the paper you reference. Can you share the paper or a link?

Best regards,

[icnosvbovwb]

Dear @jjonkman
On the design and tuning of linear model predictive control for wind.pdf

[jjonkman]

I have not read this paper myself; perhaps someone more familiar with this paper can respond.

Best regards,