Robot Dynamics Fixed Wing UAS: Control and Solar UAS
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1 Fied Wing UAS: Control and Solar UAS V :: Sebastian Verling, Philipp Oettershagen Marco Htter, Michael Blösch, Roland Siegwart, Konrad Rdin and Thomas Stastny - Fied Wing UAS: Stability and Dynamic Model
2 Contents: Fied Wing UAS 1. Overview 2. Aerodynamic Basics 3. Performance Considerations 4. Stability 5. Simplified Dynamic Model 6. UAV Control Approaches 7. Case Stdies Lectre 3: Control and Solar UAS 1. Fied Wing UAS Control Introdction Control Concepts Simple Control Scheme 2. Solar (U)AS Case Stdies History and Overview of Solar Powered Flight Scaling Laws Eample for Power Consmption Sky-Sailor sensesoar
3 Introdction Control of airplanes is not easy: Inherently non-linear Low control athority Actator satration doble integrator characteristics MIMO: 4 inpts, 6 DoF, ths nderactated
4 Control & Gidance A poplar concept: cascaded control loops Control = low level part Stabilize attitde and speed Gidance = high level part Follow pathes or trajectory Effect: Reject constant low freqency pertrbation (constant wind) Gidance HLC LLC SKY-SAILOR Inner Loop Oter Loop
5 Control Concepts Many control techniqes : Cascaded PID loops Optimal Control Robst Control The chosen control techniqes determined according to: Comptational Power Type of flight (aerobatics - level flight)
6 The Plant Elevator Aileron Rdder Throttle Proplsion, Mechanics, Aerodynamics Forces Moments Nonlinear Aircraft Dynamics Velocities (Body Fr.):,v,w Trn rates (Body Fr.): p,q,r Position (Earth Fr.):,y,z Tait-Bryan angles:,,,v,w p,q,r,y,z,, Inpt vector: elev ail rdd thr State vector:, v, w, p, q, r,, y, z,,, Some remarks abot the conventions sed in this lectre: Inpt limits/nits: elev 1,1 ; ail 1,1 ; rdd 1,1 ; thr Aileron: ail ail, left ail, right Down deflection / left = positive deflection positive deflections will indce negative moments!! T Otpt e.g.: y 2 2 V T v w 0,1 Fied Wing UAS: Control and Fel Case Stdies
7 The Plant: Separation of the Linearized System Sbsystem elev thr Longitdinal Plant Δ, Δw; Δq; Δ ail rdd Lateral Plant Δv; Δp, Δr; Δ Δ Corresponding Poles (Aerobatic Model Airplane) -2 im 2 re -2 Short Period Mode: ω = 5 rad/s Phgoid Mode: ω = 0.6 rad/s -4 im 4 re -4 Roll Sbsidence Mode Spiral Mode Dtch Roll Mode ω = 5 rad/s Fied Wing UAS: Control and Fel Case Stdies
8 The Plant: Separation of the Linearized System Phgoid mode: echange between kinetic and potential energy Short Period Mode: oscillation of angle of attack Spiral Divergence Dtch Roll Mode: combined yawroll oscillation Grafics adapted from: and Fied Wing UAS: Control and Fel Case Stdies
9 Optimal Control: LQR (1) I Linearize the system arond the operating point C y B A f A,, f B, ), ( ), (, y g y f g C, ), (, where Δ, Δy and Δ constitte differences to the linearization point
10 Optimal Control: LQR (2) II Define the cost integral J T T t) Q( t) ( t) R( t) Choose the Matrices Q and R: Q pnishes deviations of the states from the set-point R pnishes deviations of the control inpts from the set-point 0 ( dt Considerations for the choice of Q and R Diagonal Q and R Minimal lateral velocity v (coordinated trn, increased drag otherwise) Small variation on airspeed Action on ailerons as small as possible (drag!) Fast control on roll and pitch
11 Optimal Control: LQR (3) III Find the corresponding control law ( t) K ( t) By solving the (algebraic) Matri-Riccatti Eqation (for P and K): A T K P PA PBR R 1 B T P (se MATLAB ) 1 B T P Q
12 Optimal Control: LQR (4) Problems: Non-linear effects when frther away from operating point Comptation Costs arising from: Linearization Soltion to Riccatti Eqation: Too epensive, cannot be done on-line Way ot: compte gains off-line as a look-p table for discretized state space: Gain-Schedling
13 Simple Cascaded Control Scheme thr Trajectory Generation and Gidance d d PI 1 PI 1 d d d J r p d PD 2 q d r d PD 2 PD 2 ail elev rdd Attitde Controller Body Rate Controller Airplane Dynamics Constrain to coordinated trn: d g tan V PI 1 : PI with anti-reset wind-p PD 2 : Gain scaled with 1/V T 2 Bandwidths of inner Loops mst be sfficiently larger!
14 L1 Gidance Following a Trajectory on Horizontal Plane Theroy and Graphics from: S. Park, J. Deyst, and J. P. How, A New Nonlinear Gidance Logic for Trajectory Tracking, Proceedings of the AIAA Gidance, Navigation and Control Conference, Ag AIAA
15 TECS (Total Energy Control System) Control Altitde and Airspeed
16 TECS (Total Energy Control System)
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