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Technische Universität München

Lehrstuhl für

Flugsystemdynamik

Modellbasierte Entwicklung und Test

von Regelungssytemen Prof. Dr.-Ing. Florian Holzapfel

Rx2 active

[Rx1 healthy] [Rx1 fail]

RSw second lane active

CSw first input active CSw second input active

RSw second lane active

Rx2 active

[CSw fail]

Rx2 active

[Rx2 healthy]

[Rx2 fail]

CSw first input active

[RSw fail] [RSw healthy]

Manual

Control

Loss of

aircraftLoss of

servo

[CSw healthy]

[RSw fail] [RSw healthy]

[CSw healthy]

[CSw fail]

[CSw healthy]

[Rx2 healthy]

[Rx2 fail]

[CSw fail]

[CSw healthy]

[CSw fail] CSw second input active

[Rx2 healthy]

[Rx2 fail]

Loss of

servoAutopilot

Control

Manual

Control

Loss of

servoLoss of

aircraft

Loss of

aircraftAutopilot

Control

[Rx2 healthy]

RSw first lane active

[Rx2 fail]

Rx1 active

CSw first input active [CSw fail]

[CSw healthy]

Loss of

servo

Autopilot

ControlLoss of

servo

Rx2 active

Assisted and Auto Mode

Loss of Aircraft

Bat1 fail Bat2 fail RSw failPSw1 fail Rx1 fail Rx2 failCSw 1-N failPSw2 fail

0

0.5

1

1.5

2

2.5

3

-2

-1.5

-1

-0.5

0

0.5

1

1.5

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0

0.2

0.4

Institute of

Flight System Dynamics Modellbasierte Entwicklung und Test von Regelungssystemen

Prof. Dr.-Ing. Florian Holzapfel

What will this presentation be about?

• Introducing TUM Institute of Flight System Dynamics

• Model Based Development in Aerospace Applications

• Model Based Requirements Assessment

• Model Based Control Design

• Embedded System Design

• Model Based Testing

2

Institute of



Introducing TUM Institute of Flight System Dynamics

Research 4

Modeling, Simulation &

Parameter Estimation

Flight Control &

Flight Guidance

Sensors,

Data Fusion & Navigation Trajectory Optimization

Main

Research

Areas

Avionics &

Safety Critical Systems

Institute of




DA42M-NG – Flying test bed for the Free State of Bavaria 5

Institute of




Industry Partners involved in Projects 6

Institute of



Model Based Development in Aerospace Applications

Development in Accordance with Aerospace Standards

• Requirements based, process driven

development

• All development done in accordance to

safety process

• Extensive testing in real as well as

simulated environments

7

DO-

178B/C

ARP 4754

DO-254

ARP 4761

DO-160E

Quality

Assurance

Process

Project Management Process

Prerequisites &

Infrastructure

Project Planning &

Organization

Configuration

Management

Process

Certification

Liaison

Process

Verification

Process

EASA Cert Memos

SWCEH-001 / -002

Institute of



9 Model Based Requirement Assessment

Requirements for Flight Controllers of manned aircraft

• Manned aircraft:

Many requirement catalogs – MIL-F-8785C, MIL-STD-1797, AS94900…

• Unmanned Aircraft:

Top Level Requirements given by mission

• Many people take the same requirements as for manned a/c

But what about requirements to inner control loops for

unmanned systems?

Institute of



10

Zn

Zn

0q

0q

Model Based Requirement Assessment

Example: CAP Control Anticipation Parameter

Institute of




How to get Requirements that make Sense?

• Propagate them from outer loop / mission to inner loops

• Example of top level requirement:

The probability that the deviation from the commanded altitude is more than

xx [m] must be smaller than 10^-yy

• Fulfillment depends on:

sensor quality, disturbance probabilities & amplitudes, control error

SO WHAT ARE SPECIFICATIONS THAT MAKE SENSE?!?

Institute of




Motivation

System requirements

Sensor requirements • Accuracy

• Latency

• etc.

System dynamic requirements • overshoot

• damping

• etc.

Top level

Requirements Specify

Stakeholders

Customer

Project proposal

…

Functional model

Usage model

…

• Top level requirements are inherited

from different sources (Stakeholders,

Customer, Project proposal)

• They are formulated very general

e.g.: „The aircraft must land

automatically on RWY …“

• How can more specific requirements

for the system be derived?

• How can the knowledge of the

system’s physical properties be

utilized?

Deriva

tion

?

L0

L1

…

L(n-1)

Ln

Ph

ysic

s

Eq

ua

tio

n o

f m

otio

n

Institute of



14 Model Based Requirements Assessment

General Procedure for Stochastic Variables

• In case of stochastic variables “Monte Carlo” Methods (can) be utilized for

evaluating the probability of an event 𝐹

• One can then apply the same methods as in deterministic case to find the

system Parameter configuration that barely satisfies a certain probability level

𝑃(𝐹)

• Desired / minimum Probability level 𝑃𝑑𝑒𝑠 𝐹 can be inherited from certification documents (CS-AWO, STANAG, …)

“Monte Carlo” Methods with sample size 𝑁 and 𝑛 = 1…𝑁

Suitable model

𝑓 𝚯, 𝒚

Requirements Derivation

𝒚𝑛 Constraints for event 𝐹

𝑔𝐹 𝒚𝑛 = 1, 𝑖𝑓 𝑠𝑎𝑡𝑖𝑠𝑓𝑖𝑒𝑑0, 𝑖𝑓 𝑣𝑖𝑜𝑙𝑎𝑡𝑒𝑑

System parameters to

be constrained

𝚯

𝚯𝑛

Physics

Probability

for event 𝐹 𝑃 𝐹

Institute of




ATOL Example: L1 Requirements

Position requirements Attitude requirements Aerodynamic & Structure

• In a first step simple geometric models are applied for L1-level

requirements

Geometric inequality constraint

Δ𝑦 <𝑏𝑅𝑊𝑌

2

Δ𝑥 <𝑙𝑅𝑊𝑌 − 𝑙𝑑𝑒𝑐𝑒𝑙𝑒𝑟𝑎𝑡𝑖𝑜𝑛

2

2 ⋅ Δ𝑥

2⋅Δ

y

Geometric inequality constraint

0 < Θ < Θ𝑚𝑎𝑥

ΔΨ < ΔΨ𝑚𝑎𝑥

ΔΦ < ΔΦ𝑚𝑎𝑥

Aerodyn. Const.

𝛼𝐴 < 𝛼𝑆𝑡𝑎𝑙

𝑉𝐴 > 𝑉𝐴𝑚𝑖𝑛

Structural inequality

constraints

VK < 𝑉𝐾𝑚𝑎𝑥

𝑛𝑧 < 𝑛𝑧𝑆𝑡𝑟𝑢𝑐𝑡

• Quantitative constraints for system outputs have been found applying

simple (geometric) models

• These constraints are now utilized for deriving subordinate system

Requirements

Aircraft wing strike1

Institute of




ATOL L1 Example: Probabilistic Methodology

• Aircraft states (position/velocity)

afflicted with total error

o 5 control errors:

constant

o 7 navigation errors:

normal (Gaussian) distribution

• Integration into Simulink model as additional inputs Control_error, Navigation_error

• Application of statistical methods:

“Reliability methods“

o Generation of n samples

of navigation errors

according to statistical distributions

o n Simulink model executions

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

n times ( n samples)

0 0.5 1 1.5 2 2.5 3 3.5 40

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

0 0.5 1 1.5 2 2.5 3 3.5 40

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Institute of




ATOL L1 Example: Failure Probabilities

• n simulated landing maneuvers with different touchdown parameters

• Criteria for successful landings o Multiple touchdown parameters are limited upwards and downwards:

o Violation of at least 1 parameter limit damage or loss of the aircraft

• Computation of failure probability o Probability that a landing maneuver results in a missed approach

o Touchdown parameters of n simulations evaluated by statistical methods

xTD,min

Institute of




ATOL L1 Example: Subset Simulation

• Adaptive simulation method

o Iterative and strategic placement of samples for computation of Pr(F)

significant reduction of number of samples nS required for a good level of accuracy

o Particularly useful to small probabilities

• Original failure domain

o Generation of samples (e.g. 200)

according to their probability distribution (e.g. Gaussian)

o Too few samples within failure domain

inaccurate computation of corresponding failure probability

• Solution: Creation of sub-events

o Enlargement of failure domain by creating intermediate failure events Ei

o Principle:

The higher the failure probability, the more accurate its calculation

with a given/unchanged number of samples.

decrease of probability: 1% 0,01%

number of samples: x 100 with Monte Carlo Simulation, x 2 with Subset Simulation

Failure domain F

-5 0 5-5

0

5Step #0

u1

u2

Non-failure

domain

Institute of




ATOL L1 Example: Subset Simulation Example

-5 0 5-5

0

5Step #1

u1

u2

-5 0 5-5

0

5Step #1

u1

u2

Placement of samples:

Monte Carlo Simulation

Definition of sub-event E0

so that probability Pr(E0) 0,1

Samples (200 per step) Samples within failure domain Samples for next step

Placement of samples: Special technique (“Markov Chain Monte Carlo“)

All samples for step 1 within failure domain E0!

Definition of sub-event E1

so that conditional probability Pr(E1|E0) 0,1

E0 E0 E1

Institute of




ATOL L1 Example: Subset Simulation Step

-5 0 5-5

0

5Step #4

u1

u2

-5 0 5-5

0

5Step #4

u1

u2

-5 0 5-5

0

5Step #3

u1

u2

-5 0 5-5

0

5Step #3

u1

u2

-5 0 5-5

0

5Step #2

u1

u2

-5 0 5-5

0

5Step #2

u1

u2

Institute of




ATOL L1 Example: Subset Simulation Final

-5 0 5-5

0

5Final

u1

u2

Step #0

Step #1

Step #2

Step #3

Step #4

Step #5

-5 0 5-5

0

5Step #5

u1

u2

-5 0 5-5

0

5Step #5

u1

u2

Sub-event E5 = original failure domain F

Estimation of conditional probability

Pr(E5|E4) = Pr(F|E4) (e.g. by counting the samples)

Pr(F) = Pr(F|E4) · Pr(E4|E3) · Pr(E3|E2) · Pr(E2|E1) · Pr(E1|E0) · Pr(E0)

Institute of




Requirements Definition: Example 1

• Derivation of requirements o Definition of a targeted level of safety (e.g. Pr(F) = 1%)

o Variation of:

– Performance of controllers control errors

– Performance of sensors /measurement accuracy probability distributions (standard deviation)

– Wind conditions etc.

• Example: Impact of sensory equipment on failure probability o Different sensors different measurement errors (computation of Pr(F) for each of them)

o E.g. measurement errors in vertical speed and horizontal position (x, y)

Institute of




Requirements Definition: Example 2

• Derivation of requirements o Definition of a targeted level of safety (e.g. Pr(F) = 1%)

o Variation of:

o Performance of controllers control errors

o Performance of sensors /measurement accuracy probability distributions (standard deviation)

o Wind conditions etc.

• Example: Impact aircraft mass and wind on failure probability o 3 different landing masses: 92,25 kg / 106,5 kg / 125 kg (computation of Pr(F) for each of them)

o Wind conditions: no wind / maximum wind (15 kts tail, 10 kts cross)

Institute of



26 Model Based Control Design

Introduction

• Flight Control Design is not a

single point issue but spans a

large operation envelope /

domain

– Plant analysis

– Controller Design

– Gain Design

• Controller assessment needs

to be automated

– Non-compliance needs to be

detected automatically

– Reports ands evaluations need to

be organized automatically

0

0.5

1

1.5

2

2.5

3

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0

0.2

0.4

Institute of




Process Steps

High Fidelity Model

Reduced Control Design Model

System Analysis

Control Structure Design

Validation

Gain Design

Automated Assessment on reduced Model

(clsassical: Linear)

Automated Assessment on High Fidelity Model

Configuration & Target Integration

Virtual Flight Test: HIL C/L clearance

Flight Test

Failure ModelsUncertainty

Models

Systems: Sensors/Actuation

Disturbance Models

Validation & Verification

• MathWorks tools are used during the

whole Controller Design and Verification

Process

• The usage of an integrated toolchain

throughout the process generates

benefits at the interfaces between the

particular process steps.

Institute of




Trim and Linearize

Trim applications:

Computation of performance data:

= p(1)

= x S (1)

= x S (2)

= Haddad

= Haddad

= Haddad

= Haddad

= Haddad

egal

egal

egal

= p(2)

= x S (3)

= x S (4)

= x S (5)

= x S (6)

x

u

V a

b

p

q

r

F

Q

Y l m

h

x h

z

T d

pxfr ,S

r

V

a b

p q r

S x a

b x h

z

T d

p

V

h g

Y

Haddad Constraint

[ ]

Y Q F

, , , ,

, , , ,

K K K HD V f

r q p

g b a

a b

g Y V

0pxfr!

, S

Nonlinear Equation solver

Numerical Linearization

= r(1)

= r(2)

= r(3)

= r(4)

= r(5)

= r(6)

= 0 ( auto )

= 0 ( auto )

= p(4) ( auto )

egal

egal

x

V

a b

p q r

F

Q

Y

l m

g sin × V h

0 B Y F

yuxh

xuxf

),(

),(

yyuuxxh

xuuxxf

ddd

ddd

000

00

),(

),(

u

x

u

x

d

d

0

0

y

x

d

d

Numerical Linearization:

linsyslinsyslinsys uAxx

linsyslinsyslinsys DuCxy

- Flight envelope parameter configurable

(Altitude, Velocity, Center of gravity, flap

configuration,…).

- Automated trim point calculation for

each flight condition.

- Output of all important trim result data

(trim success, used trim strategy,

number of iterations, …) for evaluation

of the trim results.

- Free configuration of the desired model

parameters (States, Inputs, outputs),

which shall be extracted from the

nonlinear model.

- For each trim point, a linearized model

of the nonlinear equation system is

generated

Institute of




Example: DA42 Longitudinal Controller Design with MATLAB

10-1

100

101

102

-30

-20

-10

0

10

Mag

nitude (d

B)

Frequency (rad/s)

Config 1 Flaps = 0 Gear = 0

10-1

100

101

102

-30

-20

-10

0

10

Phase (deg)

Frequency (rad/s)


10-1

100

101

102

-30

-20

-10

0

10

Mag

nitude (d

B)

Frequency (rad/s)


10-1

100

101

102

-30

-20

-10

0

10

Phase (deg)

Frequency (rad/s)


10-1

100

101

102

-30

-20

-10

0

10

Mag

nitude (d

B)

Frequency (rad/s)


10-1

100

101

102

-30

-20

-10

0

10

Phase (deg)

Frequency (rad/s)

Config 6 Flaps = 42 Gear =1

10-1

100

101

102

-30

-20

-10

0

10

Frequency (rad/s)

Ma

gn

itu

de

(d

B)

Bode - All borders combined







Trim Linearization

„qcom-CSAS“

Controller

G (s)dS

Stick-to-Command

Shape

V0/g cosg sinF tanFqturn,c

Aircraft qhcmd, el

FP

GA(s)-

H

FKds,q

qcmd Eq

qMEAS

hcmd hmecqcmd,s

Prefilter Delayafter FCC

Delayto FCC

Sensor

Turn compensation

Actuator

Plant

Extended Plant Dynamics

Controller Design

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.450

0.2

0.4

0.6

0.8

1

1.2

1.4

Time (seconds)

Am

plitu

de

Pe

ak re

sp

on

se

Ris

etim

e

Pla

nt

an

aly

sis

H

Q

req

uir

em

en

ts

10-1

100

101

102

-50

-40

-30

-20

-10

0

10

Actuator

assumption

Delay

assumption

CAP C* BW etc.

HQ Requirements

Automatic trim and

linearization for the whole

flight envelope (h – Ma)

as well as all configur-

ations (gear, flaps)

Automatic HQ analysis

(Dropback, CAP, C*,

Neal Smith, Band-

width, ...) based on w0 and T (z = 0.71) for desired short period

dynamics

Institute of





„qcom-CSAS“

Controller

G (s)dS

Stick-to-Command

Shape

V0/g cosg sinF tanFqturn,c

Aircraft qhcmd, el

FP

GA(s)-

H

FKds,q

qcmd Eq

qMEAS

hcmd hmecqcmd,s

Prefilter Delayafter FCC

Delayto FCC

Sensor

Turn compensation

Actuator

Plant

Extended Plant Dynamics

Controller implementation

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80

0.5

1

1.5

2

2.5

3

3.5

4

db/qss

qm

ax/q

ss

Level 1

Level 2/3

Level 1/2

0 0.5 1 1.5 2 2.50

0.5

1

1.5

2

2.5

3

3.5

4Gibson´s dropback criterion

peak

/qss

qpeak/

qss

Excessive (PIO possible)Acceptable

-350 -300 -250 -200 -150 -100 -50 0-30

-25

-20

-15

-10

-5

0

5

10

15

20

25

-20dB

-14dB

-10dB

-8dB

-6dB

-4dB

-3dB

-2dB

-1dB0dB1dB

2dB

3dB

6dB

-10°

-20°

-30°

-40°

-50°

-60°

-70°

-80°

-90°

-100°

-110°

-120°

-130°

-140°

-150°

-160°

-170°

-180°

-190°

-200°

-210°

-220°

-230°

-240°

-250°

-260°

-270°

-280°

-290°

-300°

-310°

-320°

-330°

-340°

-350°

Phase des ORK [°]

Fre

quenzgangbetr

ag d

es O

RK

[dB

]

-40 -20 0 20 40 60 80-2

0

2

4

6

8

10

12

14

16

Level 1

Level 2

Level 3

Lag Lead

Pilot Phase Compensation [deg] at Omega = 3.5 rad/s

Clo

sed L

oop R

esonance [

dB

]

100

101

102

10-1

100

101

102

LEVEL 2

LEVEL 1

LEVEL 1

LEVEL 2

LEVEL 3

Cla

s. I,II-C

,IV

Cla

s. II-L

,III

LE

VE

L 2

. C

las. I,II-C

,IV

LE

VE

L 2

. C

las. II-L

,III

0.0960.15

3.610.0

Category C flight phases CAP boundaries

CAPNote: The boundaries for values n/a

outside the range show n are defined

by straight-line extensions

n/a (g/rad)

wn

SP

(rad/sec)

10-1

100

10-2

10-1

100

101

Category A & C flight phases (CAP - damping ratio boundaries)

zSP

CAP

LEVEL 1

LEVEL 2

LEVEL 3

-2

-1

0

1

2

3

q [

°/s

]

Closed loop pull & release Open loop pull & release

0 2 4 6 8 10-4

-2

0

2

4

Time [s]

q [

°/s

]

Closed loop doublet

0 2 4 6 8 10

Time [s]

Open loop doublet

-20

-10

0

10

20

Magnitude [

dB

]

Mismatch - Amplitude

10-1

100

101

102

-150

-100

-50

0

50

100

150

Frequency [rad/s]

Phase [

°]

Mismatch - Phase

• Automatic controller

stability and Handling

Qualities analysis

featuring LOES (low

order system generation)

for all trim conditions and

configurations (~12000

points)

• Automatic Gain design

for the controller to

comply the requirements

for all 12000 points.

Institute of





0 20 40 60 80 100 120 140 160 180-10

-5

0

5

10

Time (s)

g-T

rackin

g / g (

°)

Tracking - Josef-Niederl-Run-09-2013-05-22-19-19-Con-act-1-K-stick-11.74-MC-grad-1200.mat

Error-RMS: 1.5042 Error-rate-RMS: 164.8987 Finetracking-RMS: 0.29065

10-1

100

-30

-20

-10

0

10

20

Frequency (rad/s)

Magnitu

de (

dB

)

YC / Y

CL / w

co,AC = 0.89 rad/s

YC

YCL

10-1

100

0.2

0.4

0.6

0.8

1

Frequency (rad/s)

Kohäre

nz

Kohärenz

10-1

100

-20

-10

0

10

20

Frequency (rad/s)

Magnitu

de (

dB

)

YP x Y

C

wCO

= 0.69193 wCO-A

= 0.70578

Comp.

Pursuit

10-1

100

0

0.2

0.4

0.6

0.8

1

Frequency (rad/s)

Kohäre

nz

Kohärenz

10-1

100

-10

0

10

20

30

Frequency (rad/s)

Magnitu

de (

dB

)

YP - Pilotgain@co: 0.79

YP

YP-pursuit

10-1

100

0

0.2

0.4

0.6

0.8

1

Frequency (rad/s)

Kohäre

nz

Kohärenz

0 20 40 60 80 100 120 140 160 180-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Deflection [

-]

Time (s)

Stick - : 0.097974 RMS: 0.097972 Mittelw.: -4.7533e-005 Force-RMS: 8.9456 Speed-RMS: 0.30615

0 20 40 60 80 100 120 140 160 180-50

-25

0

25

50

Forc

e [

N]

dS

dKraft

-Stick

• Simulator flight testing with 10 pilots

• Automatic data analysis of the simulation results with MATLAB

• Export of the analysis results to Excel

Microsoft

Excel

Automatic simulation

result analysis

Export:

• Analysis results.

• Automatic report

generator.

• Automatic

compliance matrix.

Institute of



Flight Control Computer & FCC Algorithms

Controller

Algorithms

Simulink Coder

Embedded

Coder

Navigation &

Data Fusion

MATLAB

Embedded

Simulink Coder

Embedded

Coder

Startup, Runtime, Robustness and Interface Framework

ANSI C

Real Time Operating System

COTS

Electronic Hardware

COTS and Special Built

Sensors Actuators

Embedded System Design

Architecture of a Flight Control System 32

Institute of



Embedded System Design

Tool Chain Structure and Workflow for Power PC 33

Model Development and Verification

• Embedded MATLAB, Simulink, Stateflow

• Simulink Model Advisor, Report Generator and Model Coverage

Source Code Development and Verification

• Simulink Embedded Coder

• Simulink Code Inspector

• PolySpace

• VerOCode and VeroSource (structural code coverage)

Debugging and Target Testing

• Lauterbach TRACE 32 Debugger (debugging and PIL)

• Bernecker + Rainer (B&R) (hardware in the loop test bed)

Startup, Runtime, Robustness and

Interface Framework

ANSI C

Embedded Coder

Source Code

Object Code

Target Deployment

In-Circuit

Debugging

Integrated

Debugging

Hardware &

Processor In the Loop

(HIL / PIL)

Model Link

Integrated

Build

Code

Reference

+

Structural Coverage

on Target

Simulink

Code

Inspector

• Generation and deployment of

source and object code to target

environment

• Strategy on qualifiable

verification tools

• All tools in use in aerospace

applications

Institute of



Model Based Testing

Testing in Final Target Environment

34

DA42 Total System Simulation HIL

Flight Control

Computers (FCCs)

© B&R Automation

Actuator Test Bench Diamond DSIM

Flight Training Device

Aircraft Flight Test

Installation

High Fidelity

Aircraft Model

on Automation PC

Processor In The Loop Test Bench

Traceability between

Simulink and Trace32

Debugger Integration

in Simulink

• Target testing is required for generated and handwritten code (make it efficient!)

• PIL is a proven method for testing equivalence to Simulink (reuse of test cases)

• HIL testing is important to develop good and robust control algorithms (e.g. latencies)

• Requirements based testing of the final product is a fundamental idea of DO-178 B/C

Institute of



• MBD helps engineers to keep focus on technical task

• Simulation / analysis based derivation of requirements:

basis for consistent requirements and

powerful method for early validation through simulation

• Continuity of development process

from requirements capturing to verification on target system

• Main challenge:

Improvement of automated design und analyses of algorithms over large

envelope

• Continuity and automation opens opportunities for SMEs to enter avionics

market

35

Summary

Institute of



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