Modeling and control of antennas and telescopes

Mechanical engineering, and engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of productivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a series featuring graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of c- centrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of series editors, each an expert in one of the areas of concentration. The names of the series editors are listed on page vi of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. Preface This book is based on my experience with the control systems of antennas and radiotelescopes. Overwhelmingly, it is based on experience with the NASA Deep Space Network (DSN) antennas. It includes modeling the antennas, developing control algorithms, eld testing, system identi cation, performance evaluation, and 1 troubleshooting. My previous book emphasized the theoretical aspects of antenna control engineering, while this one describes the application part of the antenna control engineering.

1 Introduction	p. 1
1.1 Examples of Antennas and Telescopes	p. 1
1.1.1 NASA Deep Space Network	p. 1
1.1.2 Large Millimeter Telescope	p. 1
1.1.3 ESA Deep Space Antennas	p. 2
1.1.4 Atacama Large Millimeter Array	p. 2
1.1.5 Thirty Meter Telescope	p. 3
1.1.6 Green Bank Telescope	p. 4
1.1.7 Effelsberg Telescope	p. 4
1.2 Short Description of the Antenna Control System	p. 5
1.2.1 Velocity Loop	p. 6
1.2.2 Position-Loop	p. 7
1.3 Antenna and Telescope Literature	p. 7
References	p. 8
Part I Modeling
2 Analytical Models	p. 11
2.1 Rigid Antenna Model	p. 11
2.2 Structural Model	p. 12
2.2.1 Finite-Element Model	p. 12
2.2.2 Modal Model	p. 14
2.2.3 State-Space Model	p. 17
2.2.4 Models with Rigid Body Modes	p. 19
2.2.5 Discrete-Time Model	p. 21
2.3 Drive Model	p. 24
2.3.1 Motor Model	p. 24
2.3.2 Reducer Model	p. 25
2.3.3 Drive Model	p. 25
2.4 Velocity Loop Model	p. 26
2.5 Drive Parameter Study	p. 26
2.5.1 Drive Stiffness Factor	p. 27
2.5.2 Drive Inertia Factor	p. 28
References	p. 30
3 Models from Identification	p. 31
3.1 White Noise Testing of the Antenna	p. 31
3.1.1 Purpose and Conditions	p. 31
3.1.2 Test Input and Output	p. 32
3.1.3 Test Configuration	p. 32
3.1.4 Data Processing	p. 34
3.1.5 Basic Relationships for the Discrete-Time Data	p. 37
3.2 Identification of the Velocity Loop Model	p. 38
3.2.1 Description of the Velocity Loop Model	p. 39
3.2.2 Identification of the Velocity Loop Model	p. 39
3.2.3 A Comparison of the Analytical and Identified Models	p. 41
3.2.4 Azimuth Model Depends on the Antenna Elevation Position	p. 41
3.2.5 Fundamental Frequency Depends on Antenna Diameter	p. 43
References	p. 44
4 Model Reduction	p. 45
4.1 Why Reduction?	p. 45
4.2 Balanced Model Reduction	p. 45
4.3 Modal Model Reduction	p. 47
4.3.1 Norms of a Single Mode	p. 47
4.3.2 Norms of a Structure	p. 48
4.4 Antenna Model Reduction	p. 49
References	p. 50
5 Wind Disturbance Models	p. 51
5.1 Steady-State Wind Disturbance Model	p. 51
5.1.1 Dimensionless Wind Torques	p. 52
5.1.2 Obtaining Wind Torques from Field Data	p. 54
5.1.3 Comparing Wind Tunnel Results and the Field Data	p. 56
5.2 Wind Gusts Disturbance Models	p. 59
5.2.1 Model of Wind Forces Acting on the Dish	p. 60
5.2.2 Model of Wind Torque Acting at the Drives	p. 64
5.2.3 Algorithm to Generate a Time Profile of Wind Gusts Torque	p. 65
5.2.4 Model of Wind at the Velocity Input	p. 66
5.2.5 Algorithm to Generate Time Profile of Wind at the Velocity Input	p. 67
5.2.6 The Equivalence of Wind Torque and Wind Velocity Models	p. 67
5.2.7 Closed Loop Pointing Accuracy with Wind Gusts Disturbances	p. 68
References	p. 70
Part II Control
6 Preliminaries to Control	p. 73
6.1 Performance Criteria	p. 73
6.2 Transformations of the Velocity Loop Model	p. 77
6.2.1 Transformation into Modal Coordinates	p. 78
6.2.2 Antenna Position as the First State	p. 78
6.2.3 Augmentation with the Integral of the Position	p. 78
References	p. 79
7 PI and Feedforward Controllers	p. 81
7.1 Properties of the PI Controller	p. 81
7.1.1 Closed Loop Transfer Functions	p. 83
7.1.2 The Proportional Gain Analysis	p. 83
7.1.3 The Integral Gain Analysis	p. 85
7.2 PI Controller Tuning Steps	p. 86
7.3 Closed Loop Equations of a Flexible Antenna with a PI Controller	p. 87
7.4 Performance of the PI Controller	p. 87
7.4.1 Performance Characteristics	p. 87
7.4.2 Limits of Performance	p. 90
7.5 Feedforward Controller	p. 91
References	p. 93
8 LQG Controller	p. 95
8.1 Properties of the LQG Controller	p. 95
8.1.1 LQG Controller Description	p. 95
8.1.2 Tracking LQG Controller	p. 98
8.1.3 Closed Loop Equations of the Tracking LQG Control System	p. 101
8.1.4 LQG Weights	p. 101
8.1.5 Resemblance of the LQG and PI Controllers	p. 104
8.1.6 Properties of the LQG Weights	p. 105
8.1.7 Limits of the LQG Gains	p. 107
8.2 LQG Controller Tuning Steps	p. 108
8.3 Performance of the LQG Controller	p. 110
8.3.1 Summary of the Antenna Servo Performance Characteristics	p. 110
8.3.2 Performance of the DSN Antennas with LQG Controllers	p. 111
8.3.3 Disturbance Rejection Properties and the Position-Loop Bandwidth	p. 113
8.3.4 Performance Comparison of the PI and LQG Controllers	p. 115
8.3.5 Limits of Performance	p. 117
8.4 Tuning a LQG Controller Using GUI	p. 117
8.4.1 Selecting LQG Weights	p. 117
8.4.2 GUI for the LQG Controller Tuning	p. 119
8.4.3 Fine Tuning of the LQG Controller	p. 121
8.5 LQG Controller in the Velocity Loop	p. 124
8.5.1 Position Loop Bandwidth Depends on the Velocity Loop	p. 124
8.5.2 Four Control Configurations	p. 127
8.5.3 PP Control System	p. 127
8.5.4 PL Control System	p. 129
8.5.5 LP Control System	p. 132
8.5.6 LL Control System	p. 132
References	p. 133
9 H∞ Controller	p. 135
9.1 Definition and Gains	p. 135
9.2 Tracking H ∞ Controller	p. 138
9.3 Closed-Loop Equations of the Tracking H ∞ Controller	p. 138
9.4 34-M Antenna Example	p. 139
9.5 Limits of Performance	p. 141
References	p. 142
10 Single Loop Control	p. 145
10.1 Rigid Antenna	p. 145
10.1.1 Rigid Antenna with Velocity and Position Loops	p. 145
10.1.2 Rigid Antenna with Position Loop Only	p. 147
10.1.3 Simulation Results	p. 148
10.2 34-M Antenna	p. 149
References	p. 155
11 Non-Linear Control	p. 157
11.1 Velocity and Acceleration Limits	p. 157
11.1.1 Command Preprocessor	p. 157
11.1.2 Anti-Windup Technique	p. 162
11.2 Friction	p. 166
11.2.1 Dry Friction Model	p. 168
11.2.2 Low-Velocity Tracking Using Dither	p. 170
11.2.3 Non-linear Simulation Results	p. 173
11.3 Backlash	p. 174
11.3.1 Backlash and Its Prevention	p. 175
11.3.2 The Velocity Loop Model with Friction and Backlash	p. 177
References	p. 181
12 RF Beam Control	p. 183
12.1 Selecting the RF Beam Controller	p. 183
12.2 Monopulse	p. 187
12.2.1 Command following	p. 187
12.2.2 Disturbance Rejection Properties	p. 188
12.2.3 Stability Due to the Gain Variation	p. 190
12.2.4 Performance Simulations: Linear Model	p. 190
12.2.5 Performance Simulations: Nonlinear Model	p. 191
12.3 Scanning	p. 194
12.3.1 Conical Scan	p. 194
12.3.2 Sliding Window Conscan	p. 200
12.3.3 Lissajous Scan	p. 201
12.3.4 Rosette Scan	p. 204
12.3.5 Performance Evaluation	p. 206
References	p. 209
13 Track-Level Compensation	p. 211
13.1 Description of the Track-Level Problem	p. 211
13.2 Collection and Processing of the Inclinometer Data	p. 213
13.3 Estimating Azimuth Axis Tilt	p. 215
13.4 Creating the TLC Table	p. 217
13.5 Determining Pointing Errors from the TLC Table	p. 219
13.6 Antenna Pointing Improvement Using the TLC Table	p. 221
References	p. 222
Index	p. 223

Available:*

On Order

Summary

Summary

Table of Contents