Folienmaster ETH Zürich
Robot DynamicsFixed Wing UAS: Control and Solar UAS151-0851-00 V:: Sebastian Verling, Philipp OettershagenMarco Hutter, Michael Blösch, Roland Siegwart, Konrad Rudin and Thomas StastnyAutonomous Systems LabAutonomous Systems LabRobot Dynamics - Fixed Wing UAS: Stability and Dynamic Model 24.11.2015 1
Contents:Fixed Wing UAS1. Overview2. Aerodynamic Basics3. PerformanceConsiderations4. Stability5. Simplified DynamicModel6. UAV ControlApproaches7. Case StudiesAutonomous Systems LabLecture 3:Control and Solar UAS1. Fixed Wing UAS Control Introduction Control Concepts Simple Control Scheme2. Solar (U)AS Case Studies History and Overview of SolarPowered Flight Scaling Laws Example for PowerConsumption Sky-Sailor senseSoarRobot Dynamics 24.11.2015 2
Introduction Control of airplanes is not easy: Inherently non-linearLow control authorityActuator saturation„double integrator“ characteristicsMIMO: 4 inputs, 6 DoF, thus underactuatedAutonomous Systems LabRobot Dynamics 24.11.2015 3
Control & GuidanceA popular concept: cascaded control loops Control low level part Stabilize attitude and speed Guidance high level part Follow pathes or trajectoryEffect: Reject constant low frequencyperturbation (constant wind)HLCLLCGuidanceSKY-SAILORInner LoopOuter LoopAutonomous Systems LabRobot Dynamics 24.11.2015 4
Control Concepts Many control techniques : Cascaded PID loopsOptimal ControlRobust Control The chosen control techniques determined according to: Computational Power Type of flight (aerobatics - level flight)Autonomous Systems LabRobot Dynamics 24.11.2015 5
The nics,Aerodynamics elev ail u rudd thr Inputvector:NonlinearForcesAircraftMoments DynamicsVelocities (Body Fr.): u,v,wTurn rates (Body Fr.): p,q,rPosition (Earth Fr.): x,y,zTait-Bryan angles: , , Statevector:x u, v, w, p, q, r, x, y, z, , , Tu,v,wp,q,rx,y,z , , VT u 2 w2 v y Outpute.g.: Some remarks about the conventions used in this lecture: Input limits/units: elev 1,1 ; ail 1,1 ; rudd 1,1 ; thr 0,1 Aileron: ail ail ,left ail ,right Down deflection / left positive deflection positive deflections will induce negative moments!!Autonomous Systems LabFixed Wing UAS: Control and Fuel Case Studies 24.11.2015 6
The Plant: Separation of the Linearized SystemSubsystem elev thrLongitudinalPlantΔu, Δw;Δq;Δ ail ruddΔv;Δp, Δr;Δ Δ LateralPlantCorresponding Poles (Aerobatic Model Airplane)im2-2reimω-2Autonomous Systems Lab4Short PeriodMode:ω 5 rad/sPhugoidMode: 0.6 rad/sRoll SubsidenceModeSpiral Mode-4reDutch RollModeω 5 rad/s-4Fixed Wing UAS: Control and Fuel Case Studies 24.11.2015 7
The Plant: Separation of the Linearized SystemPhugoid mode: exchange between kinetic and potential energyShort Period Mode: oscillation of angle of attackSpiral DivergenceDutch RollMode:combined yawroll oscillationGrafics adapted from:http://history.nasa.gov/SP-367/chapt9.htm rprobung.htmlAutonomous Systems LabFixed Wing UAS: Control and Fuel Case Studies 24.11.2015 8
Optimal Control: LQR (1)ILinearize the systemx f x, u y g ( y , u)x, uaround the operating pointA f x, u x x x ,u uB f ( x, u) u x x ,u u g( x, u)C x x x ,u u A x B u x y C xwhere Δx, Δy and Δu constitute differences to the linearization pointAutonomous Systems LabRobot Dynamics 24.11.2015 9
Optimal Control: LQR (2)II Define the cost integralJ x(t )T Qx(t ) u(t )T Ru(t ) dt0Choose the Matrices Q and R:Q punishes deviations of the states from the set-pointR punishes deviations of the control inputs from the set-pointConsiderations for the choice of Q and R Diagonal Q and R Minimal lateral velocity v (coordinated turn, increased dragotherwise) Small variation on airspeed Action on ailerons as small as possible (drag!) Fast control on roll and pitchAutonomous Systems LabRobot Dynamics 24.11.2015 10
Optimal Control: LQR (3)IIIFind the corresponding control lawu( t ) K x ( t )By solving the (algebraic) Matrix-Riccatti Equation(for P and K):A T P PA PBR 1BT P Q 0K R 1BT P(use MATLAB )Autonomous Systems LabRobot Dynamics 24.11.2015 11
Optimal Control: LQR (4) Problems: Non-linear effects when further away from operating point Computation Costs arising from: Linearization Solution to Riccatti Equation:Too expensive, cannot be done on-line Way out: compute gains off-line as a look-up tablefor discretized state space: Gain-SchedulingAutonomous Systems LabRobot Dynamics 24.11.2015 12
Simple Cascaded Control Scheme thrTrajectoryGenerationand d dGuidancePIPI1 d1 d dAttitudeControllerConstrain tocoordinated turn: d g tan VAutonomous Systems LabpdJrqdrd2 ail2 elevPDPD2PDBody RateControllerx ruddAirplaneDynamicsPI1: PI with anti-reset wind-up2PD : Gain scaled with 1/VT2 Bandwidths of inner Loops mustbe sufficiently larger!Robot Dynamics 24.11.2015 13
L1 GuidanceFollowing a Trajectory on Horizontal PlaneTheroy and Graphics from:S. Park, J. Deyst, and J. P. How, “A New Nonlinear Guidance Logic for Trajectory Tracking”, Proceedings of the AIAA Guidance, Navigation and Control Conference, Aug2004. AIAA-2004-4900Autonomous Systems LabRobot Dynamics 24.11.2015 14
TECS (Total Energy Control System)Control Altitude and AirspeedAutonomous Systems LabRobot Dynamics 24.11.2015 15
TECS (Total Energy Control System)Autonomous Systems LabRobot Dynamics 24.11.2015 16
Control and Solar UAS 1. Fixed Wing UAS Control Introduction Control Concepts Simple Control Scheme 2. Solar (U)AS Case Studies History and Overview of Solar Powered Flight Scaling Laws Example for Power Consumption Sky-Sailor senseSoar Contents: Fixed Wing UAS Robot Dynamics 24.11.2015 2
Introduction –History of Solar Flight Wingspan 9.76 m Sunrise II, 1975 Mass 12.25 kg 4480 solar cells 600 W; Max duration: 3 hours Solaris, 1976 MikroSol, PiciSol, NanoSol 1995-1998 Solar Excel, 1990 12.12.2016 7
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