Dear All
I have a question regarding the azimuth of the linear model.
I am trying to find it using the integration of the rotor speed of the linear model. However, it gives me an endless ramp (As the rotor speed is a constant ) which exceeds the 360 deg of the rotation.
Can you guide me towards finding this angle correctly from the linear model?
I tried to make the same comparison but using the azimuth that was calculated from the nonlinear model with the same DOFs as mentioned above
But the results were frustrating. Additionally, the azimuth calculated from the linear model is always zero. The connection diagram of the linear model is shown below.
This linear model is calculated by azimuth averaging after applying the MBC transformation.
The operating point is added to the states after the application of MBC transformation from the rotating frame to the non-rotating frame as follows:
function T_inv = fcn_T_inv_OP(azmth)
T = 2/3*[0.5 0.5 0.5;
cosd(azmth) cosd(azmth+120) cosd(azmth+240);
sind(azmth) sind(azmth+120) sind(azmth+240)];
T_inv =[eye(1) zeros(1,8);
zeros(3,1) T zeros(3,5);
zeros(2,4) eye(2) zeros(2,3);
zeros(3,6) T];
end
The input pitch angles are transformed to the non-rotating frame using the following transformation:
function T_inv = fcn_T_inv(azmth)
T_inv = 2/3*[0.5 0.5 0.5;
cosd(azmth) cosd(azmth+120) cosd(azmth+240);
sind(azmth) sind(azmth+120) sind(azmth+240)];
end
The output of the blade RootMFlps are transformed to the rotating frame using the following transformation:
function T = fcn_T(azmth)
T=[1 cosd(azmth) sind(azmth);
1 cosd(azmth+120) sind(azmth+120);
1 cosd(azmth+240) sind(azmth+240)];
end
Again, all the used azimuth angles are calculated from the nonlinear model.
The lookup table is used to reflect the azimuth dependant operating points.
The order of the states are:
ED 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1), m
ED 1st flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,1)), m
ED 1st flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,1)), m
ED 1st flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,1)), m
ED First time derivative of 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1), m/s
ED First time derivative of Variable speed generator DOF (internal DOF index = DOF_GeAz), rad/s
ED First time derivative of 1st flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,1)), m/s
ED First time derivative of 1st flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,1)), m/s
ED First time derivative of 1st flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,1)), m/s
The comparison results are shown below: the blue line represents the linear model and the yellow line represents the non-linear model
The Generator speed VS Simulation time ( rpm VS seconds)
The Tower fore-aft VS Simulation time ( m VS seconds)
Regards
M.Fekry