folienmaster eth zürich · 1. overview 2. aerodynamic basics 3. performance considerations 4....

||Autonomous Systems Lab

151-0851-00 V

:: Sebastian Verling, Philipp Oettershagen

Marco Hutter, Michael Blösch, Roland Siegwart, Konrad Rudin and Thomas Stastny

Autonomous Systems Lab

24.11.2015Robot Dynamics - Fixed Wing UAS: Stability and Dynamic Model 1

Robot DynamicsFixed Wing UAS: Control and Solar UAS


1. Overview

2. Aerodynamic Basics

3. Performance

Considerations

4. Stability

5. Simplified Dynamic

Model

6. UAV Control

Approaches

7. Case Studies

Lecture 3:

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

24.11.2015 2Robot Dynamics


Control of airplanes is not easy:

Inherently non-linear

Low control authority

Actuator saturation

„double integrator“ characteristics

MIMO: 4 inputs, 6 DoF, thus underactuated

Introduction



A popular concept: cascaded control loops

Control = low level part

Stabilize attitude and speed

Guidance = high level part

Follow pathes or trajectory

Effect: Reject constant low frequency

perturbation (constant wind)

Control & Guidance

Guidance

SKY-SAILORLLCHLC

Inner Loop

Outer Loop



Many control techniques :

Cascaded PID loops

Optimal Control

Robust Control

…

The chosen control techniques determined according to:

Computational Power

Type of flight (aerobatics - level flight)

Control Concepts



Some remarks about the conventions used in this lecture:

Input limits/units:

Aileron:

Down deflection / left = positive deflection

positive deflections will induce negative moments!!

The Plant

Velocities (Body Fr.): u,v,w

Turn rates (Body Fr.): p,q,r

Position (Earth Fr.): x,y,z

Tait-Bryan angles: ,,

Nonlinear

Aircraft

Dynamics

Forces

Moments

u,v,w

p,q,r

x,y,z

,,

Propulsion,

Mechanics,

Aerodynamics

Elevator

Aileron

Rudder

Throttle

Tzyxrqpwvu ,,,,,,,,,,,x

State

vector:

v

wuVT

22

y

Output

e.g.:

thr

rudd

ail

elev

u

Input

vector:

1,0;1,1;1,1;1,1 thrruddailelev

rightailleftailail ,,

24.11.2015 6Fixed Wing UAS: Control and Fuel Case Studies


The Plant: Separation of the Linearized System

Δu, Δw;

Δq;

Δthr

elev

Longitudinal

Plant

Δv;

Δp, Δr;

Δ Δrudd

ail

Lateral

Plant

im

re

2

-2

-2

Short Period

Mode:

ω = 5 rad/s

Phugoid

Mode:

ω = 0.6 rad/s

im

re

4

-4

-4

Roll Subsidence

Mode

Spiral Mode

Dutch Roll

Mode

ω = 5 rad/s

Corresponding Poles (Aerobatic Model Airplane)

Subsystem



The Plant: Separation of the Linearized System

Short Period Mode: oscillation of angle of attack

Phugoid mode: exchange between kinetic and potential energy

Spiral Divergence

Dutch Roll

Mode:

combined yaw-

roll oscillation

Grafics adapted from:

http://history.nasa.gov/SP-367/chapt9.htm and

http://www.fzt.haw-hamburg.de/pers/Scholz/Flugerprobung.html



Optimal Control: LQR (1)

I Linearize the system

around the operating point

xCy

uBxAx

uuxxx

uxfA

,

,

uuxxu

uxfB

,

),(

),(

,

uygy

uxfx

uuxxx

uxgC

,

),(

x,u

where Δx, Δy and Δu constitute differences to the linearization point24.11.2015 9Robot Dynamics



II Define the cost integral

Choose the Matrices Q and R:

Q punishes deviations of the states from the set-point

R punishes deviations of the control inputs from the set-point

0

)()()()( dtttttJ TTRuuQxx

Considerations for the choice of Q and R

• Diagonal Q and R

• Minimal lateral velocity v (coordinated turn, increased drag

otherwise)

• Small variation on airspeed

• Action on ailerons as small as possible (drag!)

• Fast control on roll and pitch




III )()( tt xKu Find the corresponding control law

By solving the (algebraic) Matrix-Riccatti Equation

(for P and K):

(use MATLAB…)

PBRK

0QPBPBRPAPA

T

TT

1

1



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 table

for discretized state space: Gain-Scheduling




Attitude

Controller

PI1: PI with anti-reset wind-up

PD2

: Gain scaled with 1/VT2

Body Rate

Controller

rd

qd

pdPD

2

PD2

PD2

Simple Cascaded Control Scheme

Airplane

Dynamics

rudd

elev

ail

x

PI1

PI1d

d

Constrain to

coordinated turn:

V

gd

tan

d

d

d

Jr

thr

• Bandwidths of inner Loops must

be sufficiently larger!

Trajectory

Generation

and

Guidance



L1 Guidance


Theroy 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, Aug

2004. AIAA-2004-4900

Following a Trajectory on Horizontal Plane

||Autonomous Systems Lab 24.11.2015Robot Dynamics 15

TECS (Total Energy Control System)

Control Altitude and Airspeed

||Autonomous Systems Lab 24.11.2015Robot Dynamics 16

TECS (Total Energy Control System)

folienmaster eth zürich · 1. overview 2. aerodynamic basics 3. performance considerations 4....

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