Linearization issue using Fast V7.02

Dear Forum Members,

First, I would like to thank the NREL team for their hard work in the development of these Software Tools.

Following, I will post the problem that I have with the linearisation.

I intend to linearise the NREL 5MW turbine model in region 3 of operation, in order to design control strategies. I set up the linearisation with all the changes as describe in NREL user manual pages 39-44.

For the liniarisation, I use a wind profile hitting the turbine from front with a wind velocity of 14 m/s.

The fst file for linearisation is as follows

--------------------------------------------------------------------------------
------- FAST INPUT FILE --------------------------------------------------------
NREL 5.0 MW Baseline Wind Turbine for Use in Offshore Analysis.
Properties from Dutch Offshore Wind Energy Converter (DOWEC) 6MW Pre-Design (10046_009.pdf) and REpower 5M 5MW (5m_uk.pdf); Compatible with FAST v7.02.
---------------------- SIMULATION CONTROL --------------------------------------
False       Echo        - Echo input data to "echo.out" (flag)
   1        ADAMSPrep   - ADAMS preprocessor mode {1: Run FAST, 2: use FAST as a preprocessor to create an ADAMS model, 3: do both} (switch)
   2        AnalMode    - Analysis mode {1: Run a time-marching simulation, 2: create a periodic linearized model} (switch)
   3        NumBl       - Number of blades (-)
999.0      TMax        - Total run time (s)
   0.0125   DT          - Integration time step (s)
---------------------- TURBINE CONTROL -----------------------------------------
   0        YCMode      - Yaw control mode {0: none, 1: user-defined from routine UserYawCont, 2: user-defined from Simulink/Labview} (switch)
9999.9      TYCOn       - Time to enable active yaw control (s) [unused when YCMode=0]
   0        PCMode      - Pitch control mode {0: none, 1: user-defined from routine PitchCntrl, 2: user-defined from Simulink/Labview} (switch)
   0.0      TPCOn       - Time to enable active pitch control (s) [unused when PCMode=0]
  1        VSContrl   - Variable-speed control mode {0: none, 1: simple VS, 2: user-defined from routine UserVSCont, 3: user-defined
9999.9E-9      VS_RtGnSp   - Rated generator speed for simple variable-speed generator control (HSS side) (rpm) [used only when VSContrl=1]
43093.6       VS_RtTq     - Rated generator torque/constant generator torque in Region 3 for simple variable-speed generator control (HSS side) (N-m) 
9999.9e-9      VS_Rgn2K    - Generator torque constant in Region 2 for simple variable-speed generator control (HSS side) (N-m/rpm^2) 
9999.9e-9      VS_SlPc     - Rated generator slip percentage in Region 2 1/2 for simple variable-speed generator control (%) 
   1        GenModel    - Generator model {1: simple, 2: Thevenin, 3: user-defined from routine UserGen} (switch) [used only when VSContrl=0]
True        GenTiStr    - Method to start the generator {T: timed using TimGenOn, F: generator speed using SpdGenOn} (flag)
True        GenTiStp    - Method to stop the generator {T: timed using TimGenOf, F: when generator power = 0} (flag)
9999.9      SpdGenOn    - Generator speed to turn on the generator for a startup (HSS speed) (rpm) [used only when GenTiStr=False]
   0.0      TimGenOn    - Time to turn on the generator for a startup (s) [used only when GenTiStr=True]
9999.9      TimGenOf    - Time to turn off the generator (s) [used only when GenTiStp=True]
   1        HSSBrMode   - HSS brake model {1: simple, 2: user-defined from routine UserHSSBr, 3: user-defined from Labview} (switch)
9999.9      THSSBrDp    - Time to initiate deployment of the HSS brake (s)
9999.9      TiDynBrk    - Time to initiate deployment of the dynamic generator brake [CURRENTLY IGNORED] (s)
9999.9      TTpBrDp(1)  - Time to initiate deployment of tip brake 1 (s)
9999.9      TTpBrDp(2)  - Time to initiate deployment of tip brake 2 (s)
9999.9      TTpBrDp(3)  - Time to initiate deployment of tip brake 3 (s) [unused for 2 blades]
9999.9      TBDepISp(1) - Deployment-initiation speed for the tip brake on blade 1 (rpm)
9999.9      TBDepISp(2) - Deployment-initiation speed for the tip brake on blade 2 (rpm)
9999.9      TBDepISp(3) - Deployment-initiation speed for the tip brake on blade 3 (rpm) [unused for 2 blades]
9999.9      TYawManS    - Time to start override yaw maneuver and end standard yaw control (s)
9999.9      TYawManE    - Time at which override yaw maneuver reaches final yaw angle (s)
   0.0      NacYawF     - Final yaw angle for yaw maneuvers (degrees)
9999.9      TPitManS(1) - Time to start override pitch maneuver for blade 1 and end standard pitch control (s)
9999.9      TPitManS(2) - Time to start override pitch maneuver for blade 2 and end standard pitch control (s)
9999.9      TPitManS(3) - Time to start override pitch maneuver for blade 3 and end standard pitch control (s) [unused for 2 blades]
9999.9      TPitManE(1) - Time at which override pitch maneuver for blade 1 reaches final pitch (s)
9999.9      TPitManE(2) - Time at which override pitch maneuver for blade 2 reaches final pitch (s)
9999.9      TPitManE(3) - Time at which override pitch maneuver for blade 3 reaches final pitch (s) [unused for 2 blades]
   8.70      BlPitch(1)  - Blade 1 initial pitch (degrees)
   8.70      BlPitch(2)  - Blade 2 initial pitch (degrees)
   8.70      BlPitch(3)  - Blade 3 initial pitch (degrees) [unused for 2 blades]
   8.70      BlPitchF(1) - Blade 1 final pitch for pitch maneuvers (degrees)
   8.70      BlPitchF(2) - Blade 2 final pitch for pitch maneuvers (degrees)
   8.70      BlPitchF(3) - Blade 3 final pitch for pitch maneuvers (degrees) [unused for 2 blades]
---------------------- ENVIRONMENTAL CONDITIONS --------------------------------
   9.80665  Gravity     - Gravitational acceleration (m/s^2)
---------------------- FEATURE FLAGS -------------------------------------------
True       FlapDOF1    - First flapwise blade mode DOF (flag)
False       FlapDOF2    - Second flapwise blade mode DOF (flag)
True       EdgeDOF     - First edgewise blade mode DOF (flag)
False       TeetDOF     - Rotor-teeter DOF (flag) [unused for 3 blades]
True        DrTrDOF     - Drivetrain rotational-flexibility DOF (flag)
True        GenDOF      - Generator DOF (flag)
False       YawDOF      - Yaw DOF (flag)
True         TwFADOF1    - First fore-aft tower bending-mode DOF (flag)
True         TwFADOF2    - Second fore-aft tower bending-mode DOF (flag)
True       TwSSDOF1    - First side-to-side tower bending-mode DOF (flag)
True         TwSSDOF2    - Second side-to-side tower bending-mode DOF (flag)
True       CompAero    - Compute aerodynamic forces (flag)
False       CompNoise   - Compute aerodynamic noise (flag)
---------------------- INITIAL CONDITIONS --------------------------------------
   0.0      OoPDefl     - Initial out-of-plane blade-tip displacement (meters)
   0.0      IPDefl      - Initial in-plane blade-tip deflection (meters)
   0.0      TeetDefl    - Initial or fixed teeter angle (degrees) [unused for 3 blades]
   0.0      Azimuth     - Initial azimuth angle for blade 1 (degrees)
  12.1      RotSpeed    - Initial or fixed rotor speed (rpm)
   0.0      NacYaw      - Initial or fixed nacelle-yaw angle (degrees)
   0.0      TTDspFA     - Initial fore-aft tower-top displacement (meters)
   0.0      TTDspSS     - Initial side-to-side tower-top displacement (meters)
---------------------- TURBINE CONFIGURATION -----------------------------------
  63.0      TipRad      - The distance from the rotor apex to the blade tip (meters)
   1.5      HubRad      - The distance from the rotor apex to the blade root (meters)
   1        PSpnElN     - Number of the innermost blade element which is still part of the pitchable portion of the blade for partial-span pitch control 
   0.0      UndSling    - Undersling length [distance from teeter pin to the rotor apex] (meters) [unused for 3 blades]
   0.0      HubCM       - Distance from rotor apex to hub mass [positive downwind] (meters)
  -5.01910  OverHang    - Distance from yaw axis to rotor apex [3 blades] or teeter pin [2 blades] (meters)
   1.9      NacCMxn     - Downwind distance from the tower-top to the nacelle CM (meters)
   0.0      NacCMyn     - Lateral  distance from the tower-top to the nacelle CM (meters)
   1.75     NacCMzn     - Vertical distance from the tower-top to the nacelle CM (meters)
  87.6      TowerHt     - Height of tower above ground level [onshore] or MSL [offshore] (meters)
   1.96256  Twr2Shft    - Vertical distance from the tower-top to the rotor shaft (meters)
   0.0      TwrRBHt     - Tower rigid base height (meters)
  -5.0      ShftTilt    - Rotor shaft tilt angle (degrees)
   0.0      Delta3      - Delta-3 angle for teetering rotors (degrees) [unused for 3 blades]
  -2.5      PreCone(1)  - Blade 1 cone angle (degrees)
  -2.5      PreCone(2)  - Blade 2 cone angle (degrees)
  -2.5      PreCone(3)  - Blade 3 cone angle (degrees) [unused for 2 blades]
   0.0      AzimB1Up    - Azimuth value to use for I/O when blade 1 points up (degrees)
---------------------- MASS AND INERTIA ----------------------------------------
   0.0      YawBrMass   - Yaw bearing mass (kg)
 240.00E3   NacMass     - Nacelle mass (kg)
  56.78E3   HubMass     - Hub mass (kg)
   0.0      TipMass(1)  - Tip-brake mass, blade 1 (kg)
   0.0      TipMass(2)  - Tip-brake mass, blade 2 (kg)
   0.0      TipMass(3)  - Tip-brake mass, blade 3 (kg) [unused for 2 blades]
2607.89E3   NacYIner    - Nacelle inertia about yaw axis (kg m^2)
 534.116    GenIner     - Generator inertia about HSS (kg m^2)
 115.926E3  HubIner     - Hub inertia about rotor axis [3 blades] or teeter axis [2 blades] (kg m^2)
---------------------- DRIVETRAIN ----------------------------------------------
 100.0      GBoxEff     - Gearbox efficiency (%)
  94.4      GenEff      - Generator efficiency [ignored by the Thevenin and user-defined generator models] (%)
  97.0      GBRatio     - Gearbox ratio (-)
False       GBRevers    - Gearbox reversal {T: if rotor and generator rotate in opposite directions} (flag)
  28.1162E3 HSSBrTqF    - Fully deployed HSS-brake torque (N-m)
   0.6      HSSBrDT     - Time for HSS-brake to reach full deployment once initiated (sec) [used only when HSSBrMode=1]
"Dummy"     DynBrkFi    - File containing a mech-gen-torque vs HSS-speed curve for a dynamic brake [CURRENTLY IGNORED] (quoted string)
 867.637E6  DTTorSpr    - Drivetrain torsional spring (N-m/rad)
   6.215E6  DTTorDmp    - Drivetrain torsional damper (N-m/(rad/s))
---------------------- SIMPLE INDUCTION GENERATOR ------------------------------
9999.9      SIG_SlPc    - Rated generator slip percentage (%) [used only when VSContrl=0 and GenModel=1]
9999.9      SIG_SySp    - Synchronous (zero-torque) generator speed (rpm) [used only when VSContrl=0 and GenModel=1]
9999.9      SIG_RtTq    - Rated torque (N-m) [used only when VSContrl=0 and GenModel=1]
9999.9      SIG_PORt    - Pull-out ratio (Tpullout/Trated) (-) [used only when VSContrl=0 and GenModel=1]
---------------------- THEVENIN-EQUIVALENT INDUCTION GENERATOR -----------------
9999.9      TEC_Freq    - Line frequency [50 or 60] (Hz) [used only when VSContrl=0 and GenModel=2]
9998        TEC_NPol    - Number of poles [even integer > 0] (-) [used only when VSContrl=0 and GenModel=2]
9999.9      TEC_SRes    - Stator resistance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9      TEC_RRes    - Rotor resistance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9      TEC_VLL     - Line-to-line RMS voltage (volts) [used only when VSContrl=0 and GenModel=2]
9999.9      TEC_SLR     - Stator leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9      TEC_RLR     - Rotor leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]
9999.9      TEC_MR      - Magnetizing reactance (ohms) [used only when VSContrl=0 and GenModel=2]
---------------------- PLATFORM ------------------------------------------------
   0        PtfmModel   - Platform model {0: none, 1: onshore, 2: fixed bottom offshore, 3: floating offshore} (switch)
"Dummy"     PtfmFile    - Name of file containing platform properties (quoted string) [unused when PtfmModel=0]
---------------------- TOWER ---------------------------------------------------
  20        TwrNodes    - Number of tower nodes used for analysis (-)
"NRELOffshrBsline5MW_Tower_Onshore.dat"          TwrFile     - Name of file containing tower properties (quoted string)
---------------------- NACELLE-YAW ---------------------------------------------
9028.32E6   YawSpr      - Nacelle-yaw spring constant (N-m/rad)
  19.16E6   YawDamp     - Nacelle-yaw damping constant (N-m/(rad/s))
   0.0      YawNeut     - Neutral yaw position--yaw spring force is zero at this yaw (degrees)
---------------------- FURLING -------------------------------------------------
False       Furling     - Read in additional model properties for furling turbine (flag)
"Dummy"     FurlFile    - Name of file containing furling properties (quoted string) [unused when Furling=False]
---------------------- ROTOR-TEETER --------------------------------------------
   0        TeetMod     - Rotor-teeter spring/damper model {0: none, 1: standard, 2: user-defined from routine UserTeet} (switch) [unused for 3 blades]
   0.0      TeetDmpP    - Rotor-teeter damper position (degrees) [used only for 2 blades and when TeetMod=1]
   0.0      TeetDmp     - Rotor-teeter damping constant (N-m/(rad/s)) [used only for 2 blades and when TeetMod=1]
   0.0      TeetCDmp    - Rotor-teeter rate-independent Coulomb-damping moment (N-m) [used only for 2 blades and when TeetMod=1]
   0.0      TeetSStP    - Rotor-teeter soft-stop position (degrees) [used only for 2 blades and when TeetMod=1]
   0.0      TeetHStP    - Rotor-teeter hard-stop position (degrees) [used only for 2 blades and when TeetMod=1]
   0.0      TeetSSSp    - Rotor-teeter soft-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]
   0.0      TeetHSSp    - Rotor-teeter hard-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]
---------------------- TIP-BRAKE -----------------------------------------------
   0.0      TBDrConN    - Tip-brake drag constant during normal operation, Cd*Area (m^2)
   0.0      TBDrConD    - Tip-brake drag constant during fully-deployed operation, Cd*Area (m^2)
   0.0      TpBrDT      - Time for tip-brake to reach full deployment once released (sec)
---------------------- BLADE ---------------------------------------------------
"NRELOffshrBsline5MW_Blade.dat"                  BldFile(1)  - Name of file containing properties for blade 1 (quoted string)
"NRELOffshrBsline5MW_Blade.dat"                  BldFile(2)  - Name of file containing properties for blade 2 (quoted string)
"NRELOffshrBsline5MW_Blade.dat"                  BldFile(3)  - Name of file containing properties for blade 3 (quoted string) [unused for 2 blades]
---------------------- AERODYN -------------------------------------------------
"NRELOffshrBsline5MW_AeroDyn.ipt"                ADFile      - Name of file containing AeroDyn input parameters (quoted string)
---------------------- NOISE ---------------------------------------------------
"Dummy"     NoiseFile   - Name of file containing aerodynamic noise input parameters (quoted string) [used only when CompNoise=True]
---------------------- ADAMS ---------------------------------------------------
"NRELOffshrBsline5MW_ADAMSSpecific.dat"          ADAMSFile   - Name of file containing ADAMS-specific input parameters (quoted string)
---------------------- LINEARIZATION CONTROL -----------------------------------
"NRELOffshrBsline5MW_Linear.dat"                 LinFile     - Name of file containing FAST linearization parameters (quoted string) 
---------------------- OUTPUT --------------------------------------------------
True        SumPrint    - Print summary data to "<RootName>.fsm" (flag)
3           OutFileFmt  - Format for tabular (time-marching) output file(s) (1: text file [<RootName>.out], 2: binary file [<RootName>.outb], 3: both) 
True        TabDelim    - Use tab delimiters in text tabular output file? (flag)
"ES10.3E2"  OutFmt      - Format used for text tabular output (except time).  Resulting field should be 10 characters. (quoted string)  
   0.0      TStart      - Time to begin tabular output (s)
   1        DecFact     - Decimation factor for tabular output {1: output every time step} (-)
   1.0      SttsTime    - Amount of time between screen status messages (sec)
  -3.09528  NcIMUxn     - Downwind distance from the tower-top to the nacelle IMU (meters)
   0.0      NcIMUyn     - Lateral  distance from the tower-top to the nacelle IMU (meters)
   2.23336  NcIMUzn     - Vertical distance from the tower-top to the nacelle IMU (meters)
   1.912    ShftGagL    - Distance from rotor apex [3 blades] or teeter pin [2 blades] to shaft strain gages [positive for upwind rotors] (meters)
   0        NTwGages    - Number of tower nodes that have strain gages for output [0 to 9] (-)
            TwrGagNd    - List of tower nodes that have strain gages [1 to TwrNodes] (-) [unused if NTwGages=0]
   3           NBlGages    - Number of blade nodes that have strain gages for output [0 to 9] (-)
 5,9,13     BldGagNd    - List of blade nodes that have strain gages [1 to BldNodes] (-) [unused if NBlGages=0]
               OutList     - The next line(s) contains a list of output parameters.  See OutList.txt for a listing of available output channels, (-)
"WindVxi"                              - Longitudinal, lateral, and vertical wind speeds
"GenPwr   , GenTq"                                           - Electrical generator power and torque
"BldPitch1"                                                  - Blade 1 pitch angle
"Azimuth"                                                    - Blade 1 azimuth angle
"RotSpeed , GenSpeed"                                        - Low-speed shaft and high-speed shaft speeds
"OoPDefl1 , IPDefl1  , TwstDefl1"                            - Blade 1 out-of-plane and in-plane deflections and tip twist
"TTDspFA  , TTDspSS  , TTDspTwst"                            - Tower fore-aft and side-to-side displacments and top twist
END of FAST input file (the word "END" must appear in the first 3 columns of this last line).
--------------------------------------------------------------------------------

Linearisation file .dat

--------------------------------------------------------------------------------
---------------------- FAST LINEARIZATION CONTROL FILE -------------------------
NREL 5.0 MW offshore baseline linearization input properties.
---------------------- PERIODIC STEADY STATE SOLUTION --------------------------
True        CalcStdy    - Calculate periodic steady state condition {False: linearize about initial conditions} (flag)
   3        TrimCase    - Trim case {1: find nacelle yaw, 2: find generator torque, 3: find collective blade pitch} (switch) 
   0.0001   DispTol     - Convergence tolerance for the 2-norm of displacements in the periodic steady state calculation (rad  ) 
   0.0001  VelTol      - Convergence tolerance for the 2-norm of velocities    in the periodic steady state calculation (rad/s) 
---------------------- MODEL LINEARIZATION -------------------------------------
  36        NAzimStep   - Number of equally-spaced azimuth steps in periodic linearized model (-)
   1        MdlOrder    - Order of output linearized model {1: 1st order A, B, Bd, C, D, Dd; 2: 2nd order M, C, K, F, Fd, VelC, DspC, D, Dd} (switch)
---------------------- INPUTS AND DISTURBANCES ---------------------------------
   2        NInputs     - Number of control inputs [0 (none) or 1 to 4+NumBl] (-)
   3,4        CntrlInpt   - List   of control inputs [1 to NInputs] { 3: generator torque, 4: collective blade pitch } 
   1        NDisturbs   - Number of wind disturbances [0 (none) or 1 to 7] (-)
   1        Disturbnc   - List   of input wind disturbances [1 to NDisturbs] {1: horizontal hub-height wind speed} (-) 

The linearisation goes well, it finds steady state solution in 50 steps. The result is as follows:

This linearized model file was generated by FAST (v7.02.00d-bjj, 20-Feb-2013) on 05-Feb-2015 at 08:53:18.
The aerodynamic calculations were made by AeroDyn (v13.00.02a-bjj, 20-Feb-2013).

 NREL 5.0 MW Baseline Wind Turbine for Use in Offshore Analysis.


Some Useful Information:

   Type of steady state solution found                Trimmed collective blade pitch (TrimCase = 3)
   Azimuth-average rotor speed, RotSpeed      (rad/s)    1.26711E+00
   Period of steady state solution              (sec)    4.95868E+00
   Iterations needed to find steady state solution      60
   Displacement 2-norm of steady state solution (rad)    6.29953E-05
   Velocity 2-norm of steady state solution   (rad/s)    4.66512E-05
   Number of equally-speced azimuth steps, NAzimStep    36
   Order of linearized model, MdlOrder                   1
   Number of active (enabled) DOFs                      12 (24 states)
   Number of control inputs, NInputs                     2
   Number of input wind disturbances, NDisturbs          1
   Number of output measurements                        13


Order of States in Linearized State Matrices:

   Row/column  1 = 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1)
   Row/column  2 = 1st tower side-to-side bending mode DOF (internal DOF index = DOF_TSS1)
   Row/column  3 = 2nd tower fore-aft bending mode DOF (internal DOF index = DOF_TFA2)
   Row/column  4 = 2nd tower side-to-side bending mode DOF (internal DOF index = DOF_TSS2)
   Row/column  5 = Variable speed generator DOF (internal DOF index = DOF_GeAz)
   Row/column  6 = Drivetrain rotational-flexibility DOF (internal DOF index = DOF_DrTr)
   Row/column  7 = 1st flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,1))
   Row/column  8 = 1st flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,1))
   Row/column  9 = 1st flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,1))
   Row/column 10 = 1st edgewise bending-mode DOF of blade 1 (internal DOF index = DOF_BE(1,1))
   Row/column 11 = 1st edgewise bending-mode DOF of blade 2 (internal DOF index = DOF_BE(2,1))
   Row/column 12 = 1st edgewise bending-mode DOF of blade 3 (internal DOF index = DOF_BE(3,1))
   Row/column 13 to 24 = First derivatives of row/column  1 to 12.


Order of Control Inputs in Linearized State Matrices:

   Column 1 = electrical generator torque       (N·m)    4.30936E+04 op
   Column 2 = rotor collective blade pitch      (rad)    1.51366E-01 op


Order of Input Wind Disturbances in Linearized State Matrices:

   Column 1 = horizontal hub-height wind speed  (m/s) : See selected wind file for op


Order of Output Measurements in Linearized State Matrices:

   Row   1 = WindVxi    (m/s)     
   Row   2 = GenPwr     (kW)      
   Row   3 = GenTq      (kN·m)    
   Row   4 = BldPitch1  (deg)     
   Row   5 = Azimuth    (deg)     
   Row   6 = RotSpeed   (rpm)     
   Row   7 = GenSpeed   (rpm)     
   Row   8 = OoPDefl1   (m)       
   Row   9 = IPDefl1    (m)       
   Row  10 = TwstDefl1  (deg)     
   Row  11 = TTDspFA    (m)       
   Row  12 = TTDspSS    (m)       
   Row  13 = TTDspTwst  (deg)     

In order to compare the results to the nonlinear model I have a second wind profile in which I set a step in the velocity from 14 m/s to 15m/s.

In Matlab, I simulate the averaged state space matrixes for the linearised model. In order to compare the results I use a wind step of one (corresponding to the 14m/s to 15m/s in the nonlinear case).

And I get the following result

In the figures, with black is represented nonlinear model output, and with blue the liniarised model output . Moreover, in the case of the liniarised model, the GenPwr and RotSpeed decrease, instead of getting to the same steady state as in the case of the nonlinear model. This effect is present when I set the FLAPDOF1 and EDGEDOF to be TRUE.

I cannot make any sense of this behavior, and I have tried several things, but ran out of ideas.
I hope that you can help me with a suggestion, on why is it happening, as maybe I am doing something wrong in the linearisation setup, or when I compare the nonlinear model to the liniarised model.

Thank you in advance!

Hi,

Could you also plot the controller outputs (pitch and torque) for both cases? It would be helpful to see these in order to understand,

Paul

Dear Paul,

The linearisation is done at the following operating points.

Column 1 = electrical generator torque (N·m) 4.30936E+04 op
Column 2 = rotor collective blade pitch (rad) 1.51377E-01 op

When I simulate it, I consider small signals, thus constant 0 through the simulation for both GenTq and Pitch.

Now for the nonlinear model I am simulationg with the inputs corresponding to the operating points of the linearization, the values from above, constant thorughout the simulation.

There is no other controller used except the Simple Variable-speed control mode.

I am changing only the value of the disturbance, the wind, with a step in from the operation point when simulation both linear and nonlinear models.

Best regards,
Attila Veress

Dear all,

It looks like, I have solved the problem, by applying the MBC transformation, and after averaging the matrixes. The results do look good now.

I still have one question left, and this is regarding the MBC tranformation code. I have noticed that this is possible in the case in which there are rotating DOF in the liniarised model, meaning that I need to have the DOF corresponding to the blade dynamics set as TRUE in the .fst file. This makes sense. However, now my question is if there is by any way, a chance to alter the MBC code such that it works also in the case when the DOF corresponding to the blade dynamics are set to FALSE? Meaning that I obtain the correct averaged matrixes for the linear state space also in this case. Or when the DOF corresponding to the blade dynamics are FALSE the liniarised averaged model is correct?

Thank you in advance for the time and answers!

Best regards,
Attila Veress

Dear Attila,

I’m glad you solved your problem.

The MBC transformation only needs to be applied to states, inputs, and outputs in the rotating frame. The linearized model can be used directly (perhaps after azimuth-averaging) when there are no states, inputs, or outputs in the rotating frame.

Best regards,

Dear Jason Jonkman,

Thank you for the fast answer.

Best regards,
Attila Veress

it’s great work
I start linearising AOC 15/50 with Test06. i follow instructions in Fast user guide,. the code was as following --------------------------------------------------------------------------------
------- FAST INPUT FILE --------------------------------------------------------
FAST certification Test #06: AOC 15/50 with many DOFs with gen start loss of grid and tip-brake shutdown.
Many parameters are pure fiction. Compatible with FAST v7.02.00.
---------------------- SIMULATION CONTROL --------------------------------------
False Echo - Echo input data to “echo.out” (flag)
1 ADAMSPrep - ADAMS preprocessor mode {1: Run FAST, 2: use FAST as a preprocessor to create an ADAMS model, 3: do both} (switch)
2 AnalMode - Analysis mode {1: Run a time-marching simulation, 2: create a periodic linearized model} (switch)
3 NumBl - Number of blades (-)
9999.0 TMax - Total run time (s)
0.0125 DT - Integration time step (s)
---------------------- TURBINE CONTROL -----------------------------------------
0 YCMode - Yaw control mode {0: none, 1: user-defined from routine UserYawCont, 2: user-defined from Simulink/Labview} (switch)
9999.9 TYCOn - Time to enable active yaw control (s) [unused when YCMode=0]
0 PCMode - Pitch control mode {0: none, 1: user-defined from routine PitchCntrl, 2: user-defined from Simulink/Labview} (switch)
9999.9 TPCOn - Time to enable active pitch control (s) [unused when PCMode=0]
0 VSContrl - Variable-speed control mode {0: none, 1: simple VS, 2: user-defined from routine UserVSCont, 3: user-defined from Simulink/Labview} (switch)
9999.9 VS_RtGnSp - Rated generator speed for simple variable-speed generator control (HSS side) (rpm) [used only when VSContrl=1]
9999.9 VS_RtTq - Rated generator torque/constant generator torque in Region 3 for simple variable-speed generator control (HSS side) (N-m) [used only when VSContrl=1]
9999.9 VS_Rgn2K - Generator torque constant in Region 2 for simple variable-speed generator control (HSS side) (N-m/rpm^2) [used only when VSContrl=1]
9999.9 VS_SlPc - Rated generator slip percentage in Region 2 1/2 for simple variable-speed generator control (%) [used only when VSContrl=1]
2 GenModel - Generator model {1: simple, 2: Thevenin, 3: user-defined from routine UserGen} (switch) [used only when VSContrl=0]
True GenTiStr - Method to start the generator {T: timed using TimGenOn, F: generator speed using SpdGenOn} (flag)
True GenTiStp - Method to stop the generator {T: timed using TimGenOf, F: when generator power = 0} (flag)
9999.9 SpdGenOn - Generator speed to turn on the generator for a startup (HSS speed) (rpm) [used only when GenTiStr=False]
0 TimGenOn - Time to turn on the generator for a startup (s) [used only when GenTiStr=True]
45.0 TimGenOf - Time to turn off the generator (s) [used only when GenTiStp=True]
1 HSSBrMode - HSS brake model {1: simple, 2: user-defined from routine UserHSSBr, 3: user-defined from Labview} (switch)
9999.9 THSSBrDp - Time to initiate deployment of the HSS brake (s)
9999.9 TiDynBrk - Time to initiate deployment of the dynamic generator brake [CURRENTLY IGNORED] (s)
9999.9 TTpBrDp(1) - Time to initiate deployment of tip brake 1 (s)
9999.9 TTpBrDp(2) - Time to initiate deployment of tip brake 2 (s)
9999.9 TTpBrDp(3) - Time to initiate deployment of tip brake 3 (s) [unused for 2 blades]
66.37 TBDepISp(1) - Deployment-initiation speed for the tip brake on blade 1 (rpm)
66.37 TBDepISp(2) - Deployment-initiation speed for the tip brake on blade 2 (rpm)
66.37 TBDepISp(3) - Deployment-initiation speed for the tip brake on blade 3 (rpm) [unused for 2 blades]
9999.9 TYawManS - Time to start override yaw maneuver and end standard yaw control (s)
9999.9 TYawManE - Time at which override yaw maneuver reaches final yaw angle (s)
0.0 NacYawF - Final yaw angle for yaw maneuvers (degrees)
9999.9 TPitManS(1) - Time to start override pitch maneuver for blade 1 and end standard pitch control (s)
9999.9 TPitManS(2) - Time to start override pitch maneuver for blade 2 and end standard pitch control (s)
9999.9 TPitManS(3) - Time to start override pitch maneuver for blade 3 and end standard pitch control (s) [unused for 2 blades]
9999.9 TPitManE(1) - Time at which override pitch maneuver for blade 1 reaches final pitch (s)
9999.9 TPitManE(2) - Time at which override pitch maneuver for blade 2 reaches final pitch (s)
9999.9 TPitManE(3) - Time at which override pitch maneuver for blade 3 reaches final pitch (s) [unused for 2 blades]
1.54 BlPitch(1) - Blade 1 initial pitch (degrees)
1.54 BlPitch(2) - Blade 2 initial pitch (degrees)
1.54 BlPitch(3) - Blade 3 initial pitch (degrees) [unused for 2 blades]
1.54 BlPitchF(1) - Blade 1 final pitch for pitch maneuvers (degrees)
1.54 BlPitchF(2) - Blade 2 final pitch for pitch maneuvers (degrees)
1.54 BlPitchF(3) - Blade 3 final pitch for pitch maneuvers (degrees) [unused for 2 blades]
---------------------- ENVIRONMENTAL CONDITIONS --------------------------------
9.80665 Gravity - Gravitational acceleration (m/s^2)
---------------------- FEATURE FLAGS -------------------------------------------
True FlapDOF1 - First flapwise blade mode DOF (flag)
True FlapDOF2 - Second flapwise blade mode DOF (flag)
True EdgeDOF - First edgewise blade mode DOF (flag)
False TeetDOF - Rotor-teeter DOF (flag) [unused for 3 blades]
True DrTrDOF - Drivetrain rotational-flexibility DOF (flag)
True GenDOF - Generator DOF (flag)
False YawDOF - Yaw DOF (flag)
False TwFADOF1 - First fore-aft tower bending-mode DOF (flag)
False TwFADOF2 - Second fore-aft tower bending-mode DOF (flag)
False TwSSDOF1 - First side-to-side tower bending-mode DOF (flag)
False TwSSDOF2 - Second side-to-side tower bending-mode DOF (flag)
True CompAero - Compute aerodynamic forces (flag)
False CompNoise - Compute aerodynamic noise (flag)
---------------------- INITIAL CONDITIONS --------------------------------------
0.0 OoPDefl - Initial out-of-plane blade-tip displacement (meters)
0.0 IPDefl - Initial in-plane blade-tip deflection (meters)
0.0 TeetDefl - Initial or fixed teeter angle (degrees) [unused for 3 blades]
0.0 Azimuth - Initial azimuth angle for blade 1 (degrees)
60 RotSpeed - Initial or fixed rotor speed (rpm)
0.0 NacYaw - Initial or fixed nacelle-yaw angle (degrees)
0.0 TTDspFA - Initial fore-aft tower-top displacement (meters)
0.0 TTDspSS - Initial side-to-side tower-top displacement (meters)
---------------------- TURBINE CONFIGURATION -----------------------------------
7.490 TipRad - The distance from the rotor apex to the blade tip (meters)
0.280 HubRad - The distance from the rotor apex to the blade root (meters)
1 PSpnElN - Number of the innermost blade element which is still part of the pitchable portion of the blade for partial-span pitch control [1 to BldNodes] [CURRENTLY IGNORED] (-)
0.0 UndSling - Undersling length [distance from teeter pin to the rotor apex] (meters) [unused for 3 blades]
0.0 HubCM - Distance from rotor apex to hub mass [positive downwind] (meters)
1.341 OverHang - Distance from yaw axis to rotor apex [3 blades] or teeter pin [2 blades] (meters)
0.0 NacCMxn - Downwind distance from the tower-top to the nacelle CM (meters)
0.0 NacCMyn - Lateral distance from the tower-top to the nacelle CM (meters)
0.6 NacCMzn - Vertical distance from the tower-top to the nacelle CM (meters)
24.4 TowerHt - Height of tower above ground level [onshore] or MSL [offshore] (meters)
0.6 Twr2Shft - Vertical distance from the tower-top to the rotor shaft (meters)
0.0 TwrRBHt - Tower rigid base height (meters)
0.0 ShftTilt - Rotor shaft tilt angle (degrees)
0.0 Delta3 - Delta-3 angle for teetering rotors (degrees) [unused for 3 blades]
6.0 PreCone(1) - Blade 1 cone angle (degrees)
6.0 PreCone(2) - Blade 2 cone angle (degrees)
6.0 PreCone(3) - Blade 3 cone angle (degrees) [unused for 2 blades]
0.0 AzimB1Up - Azimuth value to use for I/O when blade 1 points up (degrees)
---------------------- MASS AND INERTIA ----------------------------------------
0.0 YawBrMass - Yaw bearing mass (kg)
1747.0 NacMass - Nacelle mass (kg)
247.3 HubMass - Hub mass (kg)
5.9 TipMass(1) - Tip-brake mass, blade 1 (kg)
5.9 TipMass(2) - Tip-brake mass, blade 2 (kg)
5.9 TipMass(3) - Tip-brake mass, blade 3 (kg) [unused for 2 blades]
976.3 NacYIner - Nacelle inertia about yaw axis (kg m^2)
10.0 GenIner - Generator inertia about HSS (kg m^2)
9.0 HubIner - Hub inertia about rotor axis [3 blades] or teeter axis [2 blades] (kg m^2)
---------------------- DRIVETRAIN ----------------------------------------------
100.0 GBoxEff - Gearbox efficiency (%)
89.4 GenEff - Generator efficiency [ignored by the Thevenin and user-defined generator models] (%)
28.25 GBRatio - Gearbox ratio (-)
False GBRevers - Gearbox reversal {T: if rotor and generator rotate in opposite directions} (flag)
9999.9 HSSBrTqF - Fully deployed HSS-brake torque (N-m)
9999.9 HSSBrDt - Time for HSS-brake to reach full deployment once initiated (sec) [used only when HSSBrMode=1]
“unused” DynBrkFi - File containing a mech-gen-torque vs HSS-speed curve for a dynamic brake [CURRENTLY IGNORED] (quoted string)
6.0E5 DTTorSpr - Drivetrain torsional spring (N-m/rad)
1.0E5 DTTorDmp - Drivetrain torsional damper (N-m/(rad/s))
---------------------- SIMPLE INDUCTION GENERATOR ------------------------------ Crude approximation of torque/speed curve.
2.222 SIG_SlPc - Rated generator slip percentage (%) [used only when VSContrl=0 and GenModel=1]
1800.0 SIG_SySp - Synchronous (zero-torque) generator speed (rpm) [used only when VSContrl=0 and GenModel=1]
314.3 SIG_RtTq - Rated torque (N-m) [used only when VSContrl=0 and GenModel=1]
1.75 SIG_PORt - Pull-out ratio (Tpullout/Trated) (-) [used only when VSContrl=0 and GenModel=1]
---------------------- THEVENIN-EQUIVALENT INDUCTION GENERATOR -----------------
60.0 TEC_Freq - Line frequency [50 or 60] (Hz) [used only when VSContrl=0 and GenModel=2]
4 TEC_NPol - Number of poles [even integer > 0] (-) [used only when VSContrl=0 and GenModel=2]
4.92E-02 TEC_SRes - Stator resistance (ohms) [used only when VSContrl=0 and GenModel=2]
5.34E-04 TEC_RRes - Rotor resistance (ohms) [used only when VSContrl=0 and GenModel=2]
480.0 TEC_VLL - Line-to-line RMS voltage (volts) [used only when VSContrl=0 and GenModel=2]
1.00E-04 TEC_SLR - Stator leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]
1.00E-04 TEC_RLR - Rotor leakage reactance (ohms) [used only when VSContrl=0 and GenModel=2]
4.49E-03 TEC_MR - Magnetizing reactance (ohms) [used only when VSContrl=0 and GenModel=2]
---------------------- PLATFORM ------------------------------------------------
0 PtfmModel - Platform model {0: none, 1: onshore, 2: fixed bottom offshore, 3: floating offshore} (switch)
“unused” PtfmFile - Name of file containing platform properties (quoted string) [unused when PtfmModel=0]
---------------------- TOWER ---------------------------------------------------
11 TwrNodes - Number of tower nodes used for analysis (-)
“AOC_Tower.dat” TwrFile - Name of file containing tower properties (quoted string)
---------------------- NACELLE-YAW ---------------------------------------------
0.0 YawSpr - Nacelle-yaw spring constant (N-m/rad)
0.0 YawDamp - Nacelle-yaw damping constant (N-m/(rad/s))
0.0 YawNeut - Neutral yaw position–yaw spring force is zero at this yaw (degrees)
---------------------- FURLING -------------------------------------------------
False Furling - Read in additional model properties for furling turbine (flag)
“unused” FurlFile - Name of file containing furling properties (quoted string) [unused when Furling=False]
---------------------- ROTOR-TEETER --------------------------------------------
0 TeetMod - Rotor-teeter spring/damper model {0: none, 1: standard, 2: user-defined from routine UserTeet} (switch) [unused for 3 blades]
0.0 TeetDmpP - Rotor-teeter damper position (degrees) [used only for 2 blades and when TeetMod=1]
0.0 TeetDmp - Rotor-teeter damping constant (N-m/(rad/s)) [used only for 2 blades and when TeetMod=1]
0.0 TeetCDmp - Rotor-teeter rate-independent Coulomb-damping moment (N-m) [used only for 2 blades and when TeetMod=1]
0.0 TeetSStP - Rotor-teeter soft-stop position (degrees) [used only for 2 blades and when TeetMod=1]
0.0 TeetHStP - Rotor-teeter hard-stop position (degrees) [used only for 2 blades and when TeetMod=1]
0.0 TeetSSSp - Rotor-teeter soft-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]
0.0 TeetHSSp - Rotor-teeter hard-stop linear-spring constant (N-m/rad) [used only for 2 blades and when TeetMod=1]
---------------------- TIP-BRAKE -----------------------------------------------
0.0 TBDrConN - Tip-brake drag constant during normal operation, CdArea (m^2)
10.0 TBDrConD - Tip-brake drag constant during fully-deployed operation, Cd
Area (m^2)
0.5 TpBrDT - Time for tip-brake to reach full deployment once released (sec)
---------------------- BLADE ---------------------------------------------------
“AOC_Blade.dat” BldFile(1) - Name of file containing properties for blade 1 (quoted string)
“AOC_Blade.dat” BldFile(2) - Name of file containing properties for blade 2 (quoted string)
“AOC_Blade.dat” BldFile(3) - Name of file containing properties for blade 3 (quoted string) [unused for 2 blades]
---------------------- AERODYN -------------------------------------------------
“Test06_AD.ipt” ADFile - Name of file containing AeroDyn input parameters (quoted string)
---------------------- NOISE ---------------------------------------------------
“unused” NoiseFile - Name of file containing aerodynamic noise input parameters (quoted string) [used only when CompNoise=True]
---------------------- ADAMS ---------------------------------------------------
“AOC_ADAMS.dat” ADAMSFile - Name of file containing ADAMS-specific input parameters (quoted string) [unused when ADAMSPrep=1]
---------------------- LINEARIZATION CONTROL -----------------------------------
“AOC_Linear.dat” LinFile - Name of file containing FAST linearization parameters (quoted string) [unused when AnalMode=1]
---------------------- OUTPUT --------------------------------------------------
True SumPrint - Print summary data to “.fsm” (flag)
1 OutFileFmt - Format for tabular (time-marching) output file(s) (1: text file [.out], 2: binary file [.outb], 3: both) (switch)
True TabDelim - Use tab delimiters in text tabular output file? (flag)
“ES10.3E2” OutFmt - Format used for text tabular output (except time). Resulting field should be 10 characters. (quoted string) [not checked for validity!]
5.0 TStart - Time to begin tabular output (s)
10 DecFact - Decimation factor for tabular output {1: output every time step} (-)
5.0 SttsTime - Amount of time between screen status messages (sec)
0.0 NcIMUxn - Downwind distance from the tower-top to the nacelle IMU (meters)
0.0 NcIMUyn - Lateral distance from the tower-top to the nacelle IMU (meters)
0.0 NcIMUzn - Vertical distance from the tower-top to the nacelle IMU (meters)
0.5 ShftGagL - Distance from rotor apex [3 blades] or teeter pin [2 blades] to shaft strain gages [positive for upwind rotors] (meters)
0 NTwGages - Number of tower nodes that have strain gages for output [0 to 9] (-)
0 TwrGagNd - List of tower nodes that have strain gages [1 to TwrNodes] (-) [unused if NTwGages=0]
5 NBlGages - Number of blade nodes that have strain gages for output [0 to 9] (-)
2,4,6,8,9 BldGagNd - List of blade nodes that have strain gages [1 to BldNodes] (-) [unused if NBlGages=0]
OutList - The next line(s) contains a list of output parameters. See OutList.xlsx for a listing of available output channels, (-)
“TipDxb3,TipDyb3” - Blade 3 flapwise and edgewise tip deflections
“TipRDxb3,TipRDyb3” - Blade 3 roll and pitch tip deflections
“Spn5ALxb1,Spn5ALyb1” - Blade 1 Gage #5 (Node 9) local flapwise and edgewise accelerations
“RotSpeed,LSSGagV,HSShftV” - Rotor, LSS (GBox side), and HSS speed
“RootFxb3,RootFyb3” - Blade 3 root flapwise and edgewise shear forces
“RootMEdg3,RootMFlp3” - Blade 3 root edgewise and flapwise bending moments
“Spn4MLxb1,Spn4MLyb1” - Blade 1 Gage #4 (Node 8) local edgewise and flapwise bending moments
“LSSGagFxs,LSSGagFys,LSSGagFzs” - Non-rotating LSS thrust and shear forces
“LSShftTq,HSShftTq,GenTq” - LSS, HSS, and generator torque
“LSShftPwr,HSShftPwr,GenPwr” - LSS, HSS, and generator power
END of FAST input file (the word “END” must appear in the first 3 columns of this last line).

I execute Simsetup.m file after that i run Openloop.dml model… this leads an error “Matlab stop working” what is wrong ?

Dear Rana,

Normally, the FAST error messages are written to the MATLAB workspace. In your case, I would guess the problem is that you are not permitted to perform a FAST v7 linearization analysis when running FAST v7 interfaced to Simulink.

Best regards,

thanks for quick reply but why i am not permitted. i follow all instructions in Fast user guide as "change AnalMode from 1 to 2 " how i can have permission

Dear Rana,

The Simulink interface to FAST v7 was not designed to support linearization analysis. You must set AnalMod = 1 when running FAST v7 interfaced to Simulink.

I’m not sure why you are using FAST v7 in place of FAST v8, but FAST v8 does permit linearization when running FAST v8 interfaced to Simulink.

Best regards,

Dear Jason
At first great thanks for you quick reply,
you mean that i can linearize using Fast v7 ?
I try to use Fast v8 for linearising the same WT and system output was "many .lin files " i did not know which file i can use to GetMats. Can you tell which file ?

Dear Rana,

You can linearize a FAST v7 model when running the FAST v7 executable, but not when running FAST v7 interfaced to Simulink.

The linearization process is a bit different in FAST v8, but the GetMats_f8.m script added to the MATLAB MBC post-processor will allow you to process different linearization output files collectively (e.g. for different azimuth angles around a rotor revolution); variable FileNames specified at the top of GetMats_f8.m should be used to set the name (or names) of the linearization output file(s) that you wish to process.

Best regards,

Dear Jason
thanks for reply, I am a beginner in FAST
I use Fast v8 in linearising test 11 and the mission has been done. the output .lin file is “test11a.SFunc.1.lin”
i start run GetMat_f8 file to gain system matrices, you tell me to use Filenames variable and i follow as
FileNames = ‘Test11a.SFunc.1.lin’ ; when running Matlab gives an error
Cell contents reference from a non-cell array object.

Error in GetMats_f8 (line 26)
data(NAzimStep) = ReadFASTLinear(FileNames{1}); %ReadFASTLinear(FileNames{1});

i try to running Test14.m which is basic file in Fast v8 and matlab gives the same error
My regards

Dear Rana,

FileNames should store a cell array, so, you must be brackets around the file names e.g. FileNames = {‘Test11a.SFunc.1.lin’}.

Best regards,

Dear Jason
Really i am thankful for replying, now i decide to run mbc3.m at first there was matlab error asking me for size of (RotTripletIndicesOutput )
i return to GetMats-F8 and knows it 3x3 matrix and define it in mbc3.m… it gives another error

Index exceeds matrix dimensions.

Error in mbc3 (line 130)
new_seq_dof = get_new_seq(RotTripletIndicesStates,ndof);

i want to ask about the difference between GetMats_f8 and GetMats ? … the comments say that one provide a solution and the another provide all solutions Can you explain ? :unamused:

Dear Rana,

GetMats_f8.m is a replacement for GetMats.m; GetMats_f8.m processes the linearization output files from FAST v8 whereas GetMats.m processes the linearization output files from FAST v7.

The Matlab variables RotTripleIndicesOutput and RotTripletIndicesStates should be generated by GetMats_f8; you shouldn’t need to define these yourself. I’d have to see your linearization output file to comment more.

Best regards,

Dear Jason
Really, I am thanks for your caring, this is the output file :
Linearized model: Predictions were generated on 05-Mar-2017 at 01:45:50 using FAST (v8.16.00a-bjj, 27-Jul-2016), compiled as a DLL S-Function for Simulink as a 64-bit application using single precision
linked with NWTC Subroutine Library (v2.09.00, 23-Jul-2016); ElastoDyn (v1.04.00a-bjj, 26-Jul-2016); InflowWind (v3.03.00, 26-Jul-2016); ServoDyn (v1.06.00a-bjj, 26-Jul-2016)

Description from the FAST input file: FAST Certification Test #11: WindPACT 1.5 MW Baseline with many DOFs undergoing a pitch failure.

Simulation information:
Simulation time: 0.0000 s
Rotor Speed: 2.0944 rad/s
Azimuth: 0.0000 rad
Number of continuous states: 30
Number of discrete states: 0
Number of constraint states: 0
Number of inputs: 0
Number of outputs: 0
Jacobians included in this file? No

Order of continuous states:
Row/Column Operating Point Rotating Frame? Description


      1    0.000E+00                                 F        ED 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1), m
      2    0.000E+00                                 F        ED 1st tower side-to-side bending mode DOF (internal DOF index = DOF_TSS1), m
      3    0.000E+00                                 F        ED 2nd tower fore-aft bending mode DOF (internal DOF index = DOF_TFA2), m
      4    0.000E+00                                 F        ED 2nd tower side-to-side bending mode DOF (internal DOF index = DOF_TSS2), m
      5    4.712E+00                                 F        ED Variable speed generator DOF (internal DOF index = DOF_GeAz), rad
      6    0.000E+00                                 F        ED Drivetrain rotational-flexibility DOF (internal DOF index = DOF_DrTr), rad
      7    0.000E+00                                 T        ED 1st flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,1)), m
      8    0.000E+00                                 T        ED 1st flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,1)), m
      9    0.000E+00                                 T        ED 1st flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,1)), m
     10    0.000E+00                                 T        ED 1st edgewise bending-mode DOF of blade 1 (internal DOF index = DOF_BE(1,1)), m
     11    0.000E+00                                 T        ED 1st edgewise bending-mode DOF of blade 2 (internal DOF index = DOF_BE(2,1)), m
     12    0.000E+00                                 T        ED 1st edgewise bending-mode DOF of blade 3 (internal DOF index = DOF_BE(3,1)), m
     13    0.000E+00                                 T        ED 2nd flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,2)), m
     14    0.000E+00                                 T        ED 2nd flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,2)), m
     15    0.000E+00                                 T        ED 2nd flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,2)), m
     16    0.000E+00                                 F        ED First time derivative of 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1), m/s
     17    0.000E+00                                 F        ED First time derivative of 1st tower side-to-side bending mode DOF (internal DOF index = DOF_TSS1), m/s
     18    0.000E+00                                 F        ED First time derivative of 2nd tower fore-aft bending mode DOF (internal DOF index = DOF_TFA2), m/s
     19    0.000E+00                                 F        ED First time derivative of 2nd tower side-to-side bending mode DOF (internal DOF index = DOF_TSS2), m/s
     20    2.094E+00                                 F        ED First time derivative of Variable speed generator DOF (internal DOF index = DOF_GeAz), rad/s
     21    0.000E+00                                 F        ED First time derivative of Drivetrain rotational-flexibility DOF (internal DOF index = DOF_DrTr), rad/s
     22    0.000E+00                                 T        ED First time derivative of 1st flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,1)), m/s
     23    0.000E+00                                 T        ED First time derivative of 1st flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,1)), m/s
     24    0.000E+00                                 T        ED First time derivative of 1st flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,1)), m/s
     25    0.000E+00                                 T        ED First time derivative of 1st edgewise bending-mode DOF of blade 1 (internal DOF index = DOF_BE(1,1)), m/s
     26    0.000E+00                                 T        ED First time derivative of 1st edgewise bending-mode DOF of blade 2 (internal DOF index = DOF_BE(2,1)), m/s
     27    0.000E+00                                 T        ED First time derivative of 1st edgewise bending-mode DOF of blade 3 (internal DOF index = DOF_BE(3,1)), m/s
     28    0.000E+00                                 T        ED First time derivative of 2nd flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,2)), m/s
     29    0.000E+00                                 T        ED First time derivative of 2nd flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,2)), m/s
     30    0.000E+00                                 T        ED First time derivative of 2nd flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,2)), m/s

Order of continuous state derivatives:
Row/Column Operating Point Rotating Frame? Description


      1    0.000E+00                                 F        First time derivative of ED 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1), m/s
      2    0.000E+00                                 F        First time derivative of ED 1st tower side-to-side bending mode DOF (internal DOF index = DOF_TSS1), m/s
      3    0.000E+00                                 F        First time derivative of ED 2nd tower fore-aft bending mode DOF (internal DOF index = DOF_TFA2), m/s
      4    0.000E+00                                 F        First time derivative of ED 2nd tower side-to-side bending mode DOF (internal DOF index = DOF_TSS2), m/s
      5    2.094E+00                                 F        First time derivative of ED Variable speed generator DOF (internal DOF index = DOF_GeAz), rad/s
      6    0.000E+00                                 F        First time derivative of ED Drivetrain rotational-flexibility DOF (internal DOF index = DOF_DrTr), rad/s
      7    0.000E+00                                 T        First time derivative of ED 1st flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,1)), m/s
      8    0.000E+00                                 T        First time derivative of ED 1st flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,1)), m/s
      9    0.000E+00                                 T        First time derivative of ED 1st flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,1)), m/s
     10    0.000E+00                                 T        First time derivative of ED 1st edgewise bending-mode DOF of blade 1 (internal DOF index = DOF_BE(1,1)), m/s
     11    0.000E+00                                 T        First time derivative of ED 1st edgewise bending-mode DOF of blade 2 (internal DOF index = DOF_BE(2,1)), m/s
     12    0.000E+00                                 T        First time derivative of ED 1st edgewise bending-mode DOF of blade 3 (internal DOF index = DOF_BE(3,1)), m/s
     13    0.000E+00                                 T        First time derivative of ED 2nd flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,2)), m/s
     14    0.000E+00                                 T        First time derivative of ED 2nd flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,2)), m/s
     15    0.000E+00                                 T        First time derivative of ED 2nd flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,2)), m/s
     16   -1.558E-01                                 F        First time derivative of ED First time derivative of 1st tower fore-aft bending mode DOF (internal DOF index = DOF_TFA1), m/s/s
     17   -1.061E-03                                 F        First time derivative of ED First time derivative of 1st tower side-to-side bending mode DOF (internal DOF index = DOF_TSS1), m/s/s
     18   -2.587E-01                                 F        First time derivative of ED First time derivative of 2nd tower fore-aft bending mode DOF (internal DOF index = DOF_TFA2), m/s/s
     19    1.767E-03                                 F        First time derivative of ED First time derivative of 2nd tower side-to-side bending mode DOF (internal DOF index = DOF_TSS2), m/s/s
     20   -1.715E+00                                 F        First time derivative of ED First time derivative of Variable speed generator DOF (internal DOF index = DOF_GeAz), rad/s/s
     21    1.705E+00                                 F        First time derivative of ED First time derivative of Drivetrain rotational-flexibility DOF (internal DOF index = DOF_DrTr), rad/s/s
     22    8.513E+00                                 T        First time derivative of ED First time derivative of 1st flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,1)), m/s/s
     23    6.722E+00                                 T        First time derivative of ED First time derivative of 1st flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,1)), m/s/s
     24   -4.785E+00                                 T        First time derivative of ED First time derivative of 1st flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,1)), m/s/s
     25    2.310E+00                                 T        First time derivative of ED First time derivative of 1st edgewise bending-mode DOF of blade 1 (internal DOF index = DOF_BE(1,1)), m/s/s
     26   -1.766E+01                                 T        First time derivative of ED First time derivative of 1st edgewise bending-mode DOF of blade 2 (internal DOF index = DOF_BE(2,1)), m/s/s
     27    1.765E+01                                 T        First time derivative of ED First time derivative of 1st edgewise bending-mode DOF of blade 3 (internal DOF index = DOF_BE(3,1)), m/s/s
     28   -6.910E+00                                 T        First time derivative of ED First time derivative of 2nd flapwise bending-mode DOF of blade 1 (internal DOF index = DOF_BF(1,2)), m/s/s
     29   -7.271E+00                                 T        First time derivative of ED First time derivative of 2nd flapwise bending-mode DOF of blade 2 (internal DOF index = DOF_BF(2,2)), m/s/s
     30    2.897E+00                                 T        First time derivative of ED First time derivative of 2nd flapwise bending-mode DOF of blade 3 (internal DOF index = DOF_BF(3,2)), m/s/s

Linearized state matrices:

A: 30 x 30
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00 0.000E+00
0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 0.000E+00 1.000E+00
-7.154E+00 -1.796E-03 1.330E+02 -8.441E-02 -3.686E-07 -4.112E+02 5.198E-01 3.437E-01 3.701E-01 3.620E-01 3.302E-01 9.416E-02 -2.126E+00 -1.632E+00 -1.730E+00 -7.274E-02 -1.931E-04 4.569E-01 -2.775E-03 1.721E-06 -7.343E-01 5.827E-03 2.758E-03 3.001E-03 -5.329E-04 5.132E-03 2.907E-03 -7.661E-03 -4.838E-03 -5.146E-03
-1.982E-03 -6.867E+00 -2.190E+00 1.431E+02 -6.825E-06 6.615E+02 1.140E-01 -4.888E-02 -6.380E-02 -1.001E+00 5.085E-01 4.938E-01 -4.239E-01 1.891E-01 2.287E-01 1.288E-04 -6.996E-02 -5.323E-03 4.897E-01 9.158E-04 1.181E+00 1.081E-03 5.158E-03 -6.225E-03 -9.609E-03 -2.104E-02 3.065E-02 -1.353E-03 -4.501E-03 5.827E-03
2.151E-01 -3.850E-03 -3.333E+02 -2.166E-01 -2.128E-07 -3.659E+01 2.752E-01 -9.043E-02 -7.045E-02 2.396E-01 5.990E-03 -1.724E-01 -8.134E-01 1.877E-01 1.136E-01 1.849E-03 -4.120E-04 -1.137E+00 -6.047E-03 3.334E-06 -6.535E-02 3.347E-03 -1.222E-03 -1.043E-03 -6.885E-04 1.524E-03 -1.349E-04 -3.249E-03 9.145E-04 6.878E-04
-3.022E-04 2.331E-01 -2.186E-01 -3.448E+02 -8.646E-07 1.694E+03 1.227E-02 1.249E-02 -2.462E-02 -1.079E-01 7.095E-02 3.707E-02 -4.562E-02 -2.776E-02 7.280E-02 3.826E-04 1.817E-03 4.748E-03 -1.179E+00 2.337E-03 3.024E+00 1.162E-04 7.296E-04 -8.445E-04 -1.036E-03 -2.108E-03 3.144E-03 -1.455E-04 -6.420E-04 7.849E-04
1.704E-06 9.462E-04 1.418E-03 1.276E+00 1.088E-06 1.364E+04 -7.691E-05 -3.442E-05 1.108E-04 6.782E-04 -4.062E-04 -2.732E-04 2.880E-04 5.613E-05 -3.436E-04 -2.842E-06 1.043E-05 -1.892E-05 4.376E-03 -1.638E+00 2.436E+01 -7.315E-07 -4.156E-06 5.210E-06 6.512E-06 1.365E-05 -2.017E-05 9.159E-07 3.633E-06 -4.550E-06
-4.903E-02 8.235E-02 -2.422E+00 1.110E+02 -5.402E-07 -2.652E+04 5.076E-01 5.077E-01 5.210E-01 -4.582E+00 -4.687E+00 -4.679E+00 -1.260E+00 -1.270E+00 -1.305E+00 -6.160E-04 1.021E-03 -9.968E-03 3.793E-01 1.637E+00 -4.735E+01 4.996E-03 4.629E-03 5.418E-03 -4.522E-02 -4.454E-02 -4.751E-02 -4.100E-03 -3.798E-03 -4.511E-03
2.334E+01 5.043E+00 6.979E+03 3.006E+02 6.642E+00 1.983E+05 -8.280E+01 -7.492E+00 -7.991E+00 7.053E+01 7.323E+01 7.819E+01 5.649E+01 2.239E+01 2.427E+01 2.385E-01 -4.179E-01 2.376E+01 -5.665E+00 -3.461E-03 3.541E+02 -7.766E-01 -6.828E-02 -6.301E-02 7.923E-01 7.027E-01 7.043E-01 2.098E-01 6.820E-02 6.514E-02
1.475E+01 -2.249E+00 -2.332E+03 3.212E+02 -7.676E+00 1.976E+05 -7.371E+00 -7.668E+01 -9.325E+00 7.565E+01 7.618E+01 7.394E+01 1.897E+01 3.374E+01 2.422E+01 4.885E+00 2.160E-01 5.970E+01 4.485E+00 -1.703E-03 3.528E+02 -6.957E-02 -6.899E-01 -9.336E-02 7.336E-01 7.630E-01 7.383E-01 5.904E-02 1.198E-01 8.042E-02
1.590E+01 -2.737E+00 -1.854E+03 -6.187E+02 1.034E+00 2.026E+05 -7.839E+00 -9.335E+00 -7.663E+01 7.471E+01 7.484E+01 7.577E+01 2.043E+01 2.461E+01 3.378E+01 -4.588E+00 2.080E-01 -7.404E+01 1.269E+00 5.069E-03 3.618E+02 -7.532E-02 -8.791E-02 -6.936E-01 7.299E-01 7.217E-01 7.806E-01 6.488E-02 7.667E-02 1.238E-01
5.587E+00 -1.515E+01 2.050E+03 -9.044E+02 -2.038E+01 -5.984E+05 2.321E+01 2.533E+01 2.502E+01 -3.772E+02 -2.286E+02 -2.274E+02 1.142E+00 -6.178E+01 -6.071E+01 5.946E-02 -2.948E-01 7.013E+00 -5.116E+00 1.037E-02 -1.069E+03 2.255E-01 2.655E-01 2.328E-01 -3.694E+00 -2.329E+00 -2.181E+00 5.505E-03 -2.157E-01 -1.853E-01
4.905E+00 7.668E+00 1.748E+01 5.970E+02 8.852E+00 -6.107E+05 2.447E+01 2.508E+01 2.504E+01 -2.282E+02 -3.748E+02 -2.303E+02 -6.001E+01 -4.155E+00 -6.169E+01 1.500E+00 1.506E-01 2.077E+01 3.077E+00 -6.177E-03 -1.091E+03 2.395E-01 2.411E-01 2.533E-01 -2.245E+00 -3.648E+00 -2.304E+00 -1.939E-01 -9.813E-03 -2.069E-01
1.380E+00 7.497E+00 -1.453E+03 3.080E+02 1.153E+01 -6.097E+05 2.610E+01 2.476E+01 2.518E+01 -2.270E+02 -2.303E+02 -3.752E+02 -6.521E+01 -6.173E+01 -4.778E+00 -1.442E+00 1.460E-01 -2.570E+01 2.061E+00 -4.084E-03 -1.089E+03 2.590E-01 2.338E-01 2.535E-01 -2.250E+00 -2.227E+00 -3.712E+00 -2.141E-01 -1.919E-01 -2.348E-02
-2.277E+01 -4.440E+00 -4.792E+03 -2.647E+02 -5.869E+00 -1.123E+05 1.190E+01 4.440E+00 4.804E+00 6.292E-01 -4.089E+01 -4.459E+01 -6.047E+02 -1.435E+01 -1.573E+01 -2.301E-01 2.480E-01 -1.630E+01 3.275E+00 3.066E-03 -2.005E+02 1.908E-01 4.027E-02 3.493E-02 -5.447E-02 -3.922E-01 -3.873E-01 -1.943E+00 -4.386E-02 -4.031E-02
-1.725E+01 2.037E+00 1.100E+03 -1.635E+02 5.661E+00 -1.128E+05 5.122E+00 6.212E+00 5.672E+00 -4.204E+01 -3.101E+00 -4.205E+01 -1.426E+01 -5.911E+02 -1.577E+01 -3.138E+00 -1.298E-01 -3.859E+01 -2.691E+00 6.230E-04 -2.014E+02 5.035E-02 1.245E-01 5.620E-02 -4.161E-01 -2.176E-02 -4.188E-01 -4.650E-02 -1.875E+00 -5.188E-02
-1.826E+01 2.341E+00 6.766E+02 4.248E+02 2.083E-01 -1.160E+05 5.551E+00 5.594E+00 6.240E+00 -4.133E+01 -4.206E+01 -3.520E+00 -1.561E+01 -1.578E+01 -5.914E+02 2.790E+00 -1.248E-01 4.472E+01 -6.807E-01 -3.616E-03 -2.071E+02 5.557E-02 5.060E-02 1.284E-01 -4.141E-01 -3.968E-01 -4.341E-02 -5.184E-02 -4.754E-02 -1.880E+00

Dear Rana,

From your FAST v8 linearization output file, it looks like you have should have NRotTripletStates = 3 and NRotTripletOutput = 0. Is this what GetMats_f8.m is returning?

Best regards,

Dear Jason
i run it now and it gives this error
mbc3

Running mbc3 (v1.00.00a-gbir, 15-Oct-2008)

Undefined function or variable ‘get_new_seq’.

Error in mbc3 (line 129)
new_seq_dof = get_new_seq(RotTripletIndicesStates,ndof);

What shell i do ?

Dear Rana,

get_new_seq is a function distributed with MBC3 (written in get_new_seq.m). Do you have that file and is it in your MATLAB search path?

Best regards,