Introduction .........................................................................................................1 1. Control laws design techniques ................................................................... 1.1 Classical control............

i

Index

Introduction...1

1. Control laws design techniques... 1.1 Classical control...4

1.1.1 Introduction...4

1.1.2 Compensator design...5

ii

1.3 Modern control theory...7

1.3.1 Introduction...7

1.3.2 Optimal control...8

1.3.3 LQ theory...8

1.3.3.1 Performance index...8

1.3.3.2 Weight selection...11

1.3.3.3 Guaranteed stability margins...12

1.3.3.4 Frequency shaping...13

1.4 Gain scheduling...16

1.4.1 Introduction...16

1.4.2 D-Method...17

2. Stability and Handling Criteria... 2.1 Introduction...19

2.2 Lateral Stability...20

2.2.1 Stability margins...20

2.2.2 Controlled modes...21

2.3 Lateral Handling...22

2.3.1 Long period response...22

2.3.2 Short period response...22

2.3.2.1 Linear roll time response...22

2.3.2.2 Linear pedal time response...24

2.3.2.3 Dihedral effect...25

iii

3. Control Laws Synthesis...

3.1 Problem Definition...26

3.1.1 Introduction...26

3.1.2 Flight Envelope...27

3.1.3 Mass Properties Variations...28

3.1.4 Aerodynamic Tolerances...29

3.2 Linear Design...30

3.2.1 Lateral-Directional AC model...30

3.2.2 Reduced-Order Design model...32

3.2.3 FCS model...34

3.2.4 Linear quadratic regulator...36

3.2.4.1 Frequency shaping...36

3.2.4.2 Construction of the 'Performance Criteria' systems...37

3.2.4.3 LQR with Output weighting...39

3.2.4.4 Choice of matrix weight...40

3.2.4.5 Results...41

3.2.5 Feed-forward gains...41

3.2.6 Closed loop design model...42

3.2.7 Choice of gains set...43

3.3 Surfaces use strategy...44

3.4 Non-Linear Design...45

3.4.1 Complete Non linear controller...46

3.4.2 Signal preprocessing...47

3.4.3 Command path...47

3.4.3.1 Roll Authority...47

iv 3.4.3.3 Rate limiter...48 3.4.4 Gain scheduling...50 3.4.4.1 D-method implementation...50 3.4.4.2 Scheduler implementation...51 4. Design Validation ... 4.1 Linear Analysis...54 4.1.1 First iteration...55 4.1.1.1 Introduction...55 4.1.1.2 Stability margins...56

4.1.1.3 Controlled modes and Handling requirements...57

4.1.2 Second iteration...60

4.1.2.1 Introduction...60

4.1.1.1 Stability margins...60

4.1.1.2 Controlled modes and Handling requirements...61

4.1.3 Third iteration... ..64

4.1.2.1 Introduction...64

4.1.1.1 Stability margins...64

4.1.1.2 Controlled modes and Handling requirements...65

4.2 Non linear model validation...68

5. Results... 5.1 Lateral controller evaluation...72

v

5.1.2 Yaw response...77

5.1.3 Gust response...80

Conclusions...83