Line of Sight Stabilization Primer Table of Contents

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3 Line of Sight Stabilization Primer Table of Contents Preface 1 Chapter 1.0 Introduction 3 Chapter 2.0 LOS Control Architecture and Design Direct LOS Stabilization Indirect LOS Stabilization Pointing Performance Error Budgets Design Criteria and Methodology LOS Control Operating Modes LOS Control with Multi-Axis Gimbals 31 Chapter 3.0 The LOS Stabilization Servo Problem Gimbal Motor Drive Basic LOS Stabilization Servo Design Direct LOS Stabilization Indirect LOS Stabilization Track Loop Impact on Stabilization 51 Chapter 4.0 Two-Axis Rigid Body Dynamics and Controls Two-Axis Gimbaled Dynamics and Control Elevation Axis Dynamics Elevation Axis Direct Stabilization Control Elevation Axis Indirect Stabilization Control Cross Elevation Dynamics Cross Elevation Direct Stabilization Control Cross Elevation Axis Indirect Stabilization Control Stabilization Control Loop Servo Stability Alternative LOS Stabilization Control Techniques 82 Chapter 5.0 LOS Stabilization with a Steering Mirror Mirror Elevation Axis LOS Dynamics Direct Stabilization Control Using a Stable Body 93 i

4 5.3 Mirror Cross Elevation Axis LOS Dynamics Direct Stabilization Control Using a Stable Body Mirror Stabilization Control Loop Stability 103 Chapter 6.0 LOS Disturbances Track Following Error Sensor Accuracy and Noise Atmospheric Induced Sensor Noise Alignment Jitter from Residual Stabilization Imbalance Residual Motion from Platform Acceleration Air stream Turbulence Torques Structural Vibration Friction Static Friction Dynamic Friction Cable Restraint Torques Reaction Torques Cross Product Torques Gyro Noise Servo/Processor Noise Motor Ripple/Cogging 121 Chapter 7.0 LOS Control Component Specifications Inertial Stabilization Sensors Rate Sensors Magnetic Hydrodynamic Spinning Mass Gyro Ring Laser Gyro Fiber Optic Gyro Inertial Measurement Units Inertial Navigation Systems 134 ii

5 7.1.8 Gyro and INS Specifications Gyro Drift/Bias Gyro Scale Factor Error Gyro Excitation Noise Misalignment Gyro Random Walk INS Related Errors Long-time Unaided INS Accuracy Short-time Unaided INS Accuracy Position and Velocity Aiding Rotary Position Sensors Resolvers Encoders Potentiometers Other Rotary Position Sensor Types Rotary Position Sensor Performance Component Resolution Limitations Mechanical and Electrical Component Error Total Rotary Position Error Motors 147 Chapter 8.0 LOS Stabilization Preliminary Design Example Pointing Requirement Elevation LOS Control Design Disturbance Related Accelerations Stabilization Servo Loop Bandwidth Estimation Slew Related Accelerations Total Acceleration and Torque Elevation Error Budget Elevation Positioning Requirements Cross Elevation LOS Control Design Disturbance Related Accelerations 163 iii

6 8.3.2 Stabilization Servo Loop Bandwidth Estimation Slew Related Accelerations Total Acceleration Cross Elevation Error Budget Azimuth Positioning Requirements 173 List of Appendices Appendix A Parameterization of Mass Imbalance Torque 175 Appendix B 2-Axis Gimbal Kinematics 176 Appendix C Simple Cross Elevation Dynamics and Direct Control Model 178 Appendix D 2-Axis Gimbal Stability Analysis 183 Appendix E 2-Axis Mirror Kinematics 187 Appendix F 2-Axis Mirror Stability Analysis Bound 190 References 192 iv

7 List of Figures Figure 1.1 LOS Pointing Geometry 5 Figure 1.2 LOS Stabilization Design Angle Relationships 6 Figure 1.3 Track Sensor 7 Figure 1.4 LOS pointing Control Architecture 8 Figure 1.5 Conceptual Performance of Stabilization and Vibration Isolation 9 Figure 2.1 Two Axis Tracker Configuration 12 Figure 2.2 Typical Control Configuration for Direct LOS Stabilization 16 Figure 2.3 Typical Control Configuration for Indirect LOS Stabilization 17 Figure 2.4 Performance Level Pointing Error Allocation 19 Figure 2.5 Component Level Error Allocation 21 Figure 2.6 Jitter vs Bias Error Normalized to E max for P point = Figure 2.7 Gimbal Design Criteria Flowchart 24 Figure 2.8 Design Methodology 27 Figure 2.9 Multi-Axis Gimbal Inner to Outer Control Architecture 31 Figure 3.1 Geared Motor Drive Block Diagram 34 Figure 3.2 Acceleration Versus Slew Time for 180 Slew 35 Figure 3.3 Motor Drive with Current Feedback 36 Figure 3.4 Reduced Motor Drive with Current Feedback 37 Figure 3.5 Simple Model Direct LOS Rate Servo Stabilization Loop 39 Figure 3.6 Normalized Open Loop, Closed Loop, Compliance Functions 46 Figure 3.7 Normalized Open Loop Phase 47 Figure 3.8 Simple Model Indirect rate Servo Stabilization Loop 49 Figure 3.9 Track Loop Closed about Direct Stabilization Loop 51 Figure Axis Elevation over Azimuth Steering Mirror LOS Geometries 86 Figure 5.2 Steering Mirror Stabilization Design with 2:1 Optical Gain 87 Figure 5.3 Functional Control Loop of Stabilized Mirror using a Stable Body 89 v

8 Figure 5.4 Block Diagram of Mirror Elevation Axis LOS Servo with Stable Body and Non-Mechanical 2:1 Drive 96 Figure 5.5 Cross Elevation LOS Servo Loop for Stabilized Mirror 102 Figure 6.1 Typical Vehicle Disturbance Spectrum 115 Figure 7.1 Ring Laser Gyro 131 Figure 8.1 Linear Acceleration Disturbance Spectrum for Example 153 Figure 8.2 Example Angular Acceleration Disturbance Spectrum 154 Figure Hz Rate Loop Gain and Phase Frequency Response 159 Figure 8.4 Compliance for a Typical 60 Hz Rate Loop 159 Figure Hz Rate Loop Gain and Phase Frequency Response 169 Figure 8.6 Compliance (rad/rps 2 ) for a Typical 50 Hz Rate Loop 170 Figure C1 Cross Elevation Control and Dynamics via Azimuth Drive 178 Figure C2 Cross Elevation Control and Dynamics 180 List of Tables Table 4.1 Term Definitions for Elevation LOS Response: Equation: Table 4.2 Term Definitions for Cross Elevation LOS Response: Equation: Table 5.1 Term Definitions for Elevation LOS Response: Equation: Table 5.2 Term Definitions for Stable Body Response: Equation: Table 5.3 Term Definitions for Cross Elevation LOS Response: Equation: Table 6.1 Ball Bearing Manufacturers 117 Table 7.1 Typical Performance Levels for Different Gyro Grades 125 Table 7.2 Brief List of Gyros, Manufacturers, and Typical Performance Parameters 126 vi

9 Table 7.3 Websites for Some Rate Sensor, Gyros, and IMU Manufacturers 127 Table 7.4 Resolver Manufacturers 139 Table 7.5 Encoder Manufacturers 140 Table 7.6 Potentiometer Manufacturers 142 Table 7.7 Counts per Revolution for each Rotary Position Sensor Type 144 Table 7.8 Mechanical and Electrical Error for each Rotary Position Sensor Type 144 Table 7.9 Accuracy Comparison for Example 146 Table 7.10 Manufacturers of BDD and BLDD Motors 147 Table 8.1 El LOS RMS Disturbance Errors 162 Table 8.2 CEl LOS RMS Disturbance Errors 172 vii