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`· Satellite Attitude Control System Design Using Reaction WheelsBhanu Gouda Brian Fast Dan SimonAerospace Power &amp; Electronics Simulation Workshop 2004Outline1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. ConclusionAerospace Power &amp; Electronics Simulation Workshop 2004 2ADCS·ADCS: Attitude Determination and Control subsystem ·Attitude Determination Using sensors ·Attitude Control - Using actuatorsAerospace Power &amp; Electronics Simulation Workshop 20043Disturbance torques· Aerodynamic · Gravity gradient · Magnetic · Solar radiation · MicrometeoritesAerospace Power &amp; Electronics Simulation Workshop 20044Attitude control modes·Orbit insertion ·Acquisition ·Slew ·Contingency or SafeAerospace Power &amp; Electronics Simulation Workshop 20045Spacecraft control type· Passive control- Gravity gradient control- Spin controlAerospace Power &amp; Electronics Simulation Workshop 20046Spacecraft control type· Active control (Actuators) - Reaction wheels- Momentum wheels - Control - moment gyros - Magnetic torquers - Gas Jets or ThrustersAerospace Power &amp; Electronics Simulation Workshop 20047Tetrahedron configuration of Reaction wheelsAerospace Power &amp; Electronics Simulation Workshop 20048Outline1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. ConclusionAerospace Power &amp; Electronics Simulation Workshop 2004 9Problem formulationAerospace Power &amp; Electronics Simulation Workshop 200410Mathematical modelAngular momentum of each disk M = Mass of the space craft mi = mass of the reaction wheel wi= angular velocity of the wheel 1 H1 = I1w1 =  mr 2 + md 2 [- w1 ] 2 1  H 2 = I 2 w2 =  mr 2 + md 2 [w2 ] 2 Moment with respect to the space craft = Angular position of space craftr = radius of the wheel I= moment of inertiaI  = Mr + 2Md 2 2··()··Aerospace Power &amp; Electronics Simulation Workshop 200411Mathematical modelConservation of angular momentum·· d [H 1 + H 2 ] = I  dt··  d  1 2 1 2 2 2 2 2  2 mr + md (- w1 ) +  2 mr + md (w2 ) = Mr + 2 Md  dt     ()d M ·· (- w1 + w2 ) = 2. . dt m· (- w1 + w2 ) = M  + c2mAerospace Power &amp; Electronics Simulation Workshop 200412Outline1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. ConclusionAerospace Power &amp; Electronics Simulation Workshop 2004 13Control SchemeTwo types of controllers are investigated - Modified PI Controller - Active Disturbance Rejection ControllerAerospace Power &amp; Electronics Simulation Workshop 2004 14Simplorer· Simplorer· · · ·Circuit element models Electric machine models Data analysis tools Interfaces with Matlab / SimulinkAerospace Power &amp; Electronics Simulation Workshop 200415Outline1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. ConclusionAerospace Power &amp; Electronics Simulation Workshop 2004 16Modified PI Controller· This controller is used as the baseline controller · Only one tuning parameter · Generalized 2 DOF control structure is proposedReference: A Robust Two-Degree-of-Freedom Control Design Technique and its Practical Application -Robert Miklosovic, Zhiqiang GaoAerospace Power &amp; Electronics Simulation Workshop 200417deskis-1Plant transfer function actki c ( des -  act ). - k p . act = ( des -  act ). - 2.c . act S S2Aerospace Power &amp; Electronics Simulation Workshop 2004 18kpMotion profiling·The desired trajectories as the command input in the closed loop control ·In this case, a profile generator is used to produce desired angle to the system ·Motion profile is used instead of step.Aerospace Power &amp; Electronics Simulation Workshop 200419Simulation ResultsPlant Modelw1 acttheta_dew1w2theta theta_dotGAINMotion_profitY GAIN GAINerror in theta control signalTheta Actualw2GAINtheta_dot_det_des_dedeg_radMotion profileModified PI ControllerSUM5RANDOMDisturbancCONSTRandom_NoisRandom NoiseAerospace Power &amp; Electronics Simulation Workshop 200420Plant ModelGAIN310GAINw110theta_doGAIN10w2GAIN4 SUM4I10Modified PI Controller10 10I GAINthetaerror_in_theINTGGAINdisturbanceGAIN1010GAIN2theta_actu(- w1 + w 2 ) = · + c22( des k -  act ). i - k p . act = ( des -  act ). c - 2. c . act S SAerospace Power &amp; Electronics Simulation Workshop 200421Simulation ResultsTheta Actual &amp; desired0.1k 80 60 40 20 -10 0 2 4 6 8 10 t [s] t_des_ theta_d0.1k 80 60 40 20 -10 0 2 4 6 8 10 t [s] t_des_ theta_dNoise amplitude: 0.07 - 0.1Noise interval: 2 secAerospace Power &amp; Electronics Simulation Workshop 200422Simulation Resultscontrol inputs w1 and w278 7 6 5 4 3 2 1 0 2 4 6 8 10 t [s] w1.VAL w2.VALw1.VAL w2.VAL5 4 3 2 0 0 2 4 6 8 10 t [s]Noise amplitude: 0.07 - 0.1Noise interval: 2 secAerospace Power &amp; Electronics Simulation Workshop 200423Outline1. Overview of Attitude Determination and Control system 2. Problem formulation 3. Control schemes 3.1 Modified PI Controller 3.2 Active Disturbance Rejection Control 4. ConclusionAerospace Power &amp; Electronics Simulation Workshop 2004 24Active Disturbance Rejection Controller·New digital controller to motion control problems · Disturbances are estimated using extended state observer (ESO) and compensated in each sampling period. ·Dynamic compensation reduces motion system to a double integrator which can be controlled using a nonlinear PID controllerAerospace Power &amp; Electronics Simulation Workshop 200425Extended State Observer· It is a unique nonlinear observer · Proper Selection of the gains and functions are critical to the success of the observer · Once ESO is properly setup, the performance of the observer is quite insensitive to plant variations and disturbances ·  - 2 z o ·1  =  2  z 2   - o   1  z1  bo z  +  0 0  2   2o  u  o2   y   Aerospace Power &amp; Electronics Simulation Workshop 200426Simulation ResultsPlant ModelAerospace Power &amp; Electronics Simulation Workshop 200427Simplorer and MatlabDefine Simplorer inputs and outputs in the property dialog of the SiM2SiM componentAerospace Power &amp; Electronics Simulation Workshop 200428Matlab/Simulink ModelInputs to the simplorerOutputs from the SimplorerAerospace Power &amp; Electronics Simulation Workshop 200429Simulation ResultsTheta Actual and Theta desired0.1k 80 60 40 20-10 0.1k 80 60 40 20t_des_d GAIN1. theta_dt_des_ theta_-10 0 0.2 0.4 0.6 0.8 1.1 t [s]00.20.61 1.2 1.7 t [s]Noise amplitude: 0.05 Noise Interval: 0.5 sec30Aerospace Power &amp; Electronics Simulation Workshop 2004Simulation Resultsw1 and w212 8 6 4 2 -2 0 0.2 0.4 0.6 0.8 1.1 t [s] w1.VA w2.VA15 5 0 -5 -10 -20 0w1.VA w2.VA0.4 0.8 1 1.2 1.7 t [s]Noise amplitude: 0.05 Noise Interval: 0.5 secAerospace Power &amp; Electronics Simulation Workshop 2004 31Conclusion and Future work·· · ·The simulation of Modified PI and ADRC showed that ADRC worked well for the system 1 DOF problem will be extended to 3 degrees of freedom problem Implementation of the controller design in microcontroller/FPGA microchip. Comparisons with other controllersAerospace Power &amp; Electronics Simulation Workshop 200432`

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