# ATI Courses: Attitude Determination & Control

Training Rocket Scientists Since 1984

(410) 956-8805
(888) 501-2100

## Attitude Determination & Control

### Summary

This four-day course provides a detailed introduction to spacecraft attitude estimation and control. This course emphasizes many practical aspects of attitude control system design but with a solid theoretical foundation. The principles of operation and characteristics of attitude sensors and actuators are discussed. Spacecraft kinematics and dynamics are developed for use in control design and system simulation. Attitude determination methods are discussed in detail, including TRIAD, QUEST, and Kalman filters. Sensor alignment and calibration are also covered, as well as various types of spacecraft pointing controllers, design and analysis methods. Students should have an engineering background including calculus and linear algebra. Sufficient background mathematics and control theory are presented in the course but is kept to the minimum necessary.

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Upon completion of this course you will be able to understand hardware specifications, kinematics and dynamics, and pointing error specifications. You will gain a good understanding of attitude determination and attitude sensor calibration. You will also understand environmental effects on spacecraft pointing, and you will know fundamental principles to design and analyze attitude control algorithms.

Who Should Attend?

This course will be most beneficial to attitude control systems engineers and systems engineers who want a more in-depth understanding of attitude determination and control. It is also useful to spacecraft engineers from other subsystems that need to know how the attitude control system affects their subsystem. Seasoned attitude control system engineers may find some topics in the course to be basic, but will find other parts of the course to be informative.

1. Kinematics. Vectors, direction-cosine matrices, Euler angles, quaternions, frame transformations, and rotating frames. Conversion between attitude representations.

2. Dynamics. Rigid-body rotational dynamics, Euler's equation. Slosh dynamics. Spinning spacecraft with long wire booms.

3. Sensors. Sun sensors, Earth Horizon sensors, Magnetometers, Gyros, Allan Variance & Green Charts, Angular Displacement sensors, Star Trackers. Principles of operation and error modeling.

4. Actuators. Reaction and momentum wheels, dynamic and static imbalance, wheel configurations, magnetic torque rods, reaction control jets. Principles of operation and modeling.

5. Environmental Disturbance Torques. Aerodynamic, solar pressure, gravity-gradient, magnetic dipole torque, dust impacts, and internal disturbances.

6. Pointing Error Metrics. Accuracy, Stability (Smear), and Jitter. Definitions and methods of design and analysis for specification and verification of requirements.

7. Attitude Control. B-dot and H X B rate damping laws. Gravity-gradient, spin stabilization, and momentum bias control. Three-axis zero-momentum control. Controller design and stability. Back-of-the envelope equations for actuator sizing and controller design. Flexible-body modeling, control-structure interaction, structural-mode (flex-mode) filters, and control of flexible structures. Verification and Validation, and Polarity and Phase testing.

8. Attitude Determination. TRIAD and QUEST algorithms. Introduction to Kalman filtering. Potential problems and reliable solutions in Kalman filtering. Attitude determination using the Kalman filter. Calibration of attitude sensors and gyros.

9. Coordinate Systems and Time. J2000 and ICRF inertial reference frames. Earth Orientation, WGS-84, geodetic, geographic coordinates. Time systems. Conversion between time scales. Standard epochs. Spacecraft time and timing.

• Kinematics and dynamics
• Characteristics and principles of operation of attitude sensors and actuators
• Pointing accuracy, stability/smear, jitter definitions and analysis methods
• Environmental effects on spacecraft pointing
• Various types of attitude control systems and controller design
• Attitude determination methods, algorithms, and attitude sensor and gyro calibration
• Inertial reference frames, Earth orientation, and time

Because there is more than enough material for a 3-day course, there is some latitude to adjust the content of the course to suite the needs of the students.

Students should have an engineering background including basic calculus and linear algebra.

Tuition for this four-day course is \$2090 per person at one of our scheduled public courses. Onsite pricing is available. Please call us at 410-956-8805 or send an email to ati@aticourses.com.

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### Instructor

Dr. Mark E. Pittelkau is an independent consultant. He was previously with the Applied Physics Laboratory, Orbital Sciences Corporation, CTA Space Systems (now Orbital), and Swales Aerospace. His early career at the Naval Surface Warfare Center involved target tracking, ship and ground vehicle gun pointing stabilization, gun fire control, and gun system calibration. His experience in satellite systems covers all phases of design and operation, including conceptual design, implementation, and testing of attitude control systems, attitude and orbit determination, and attitude sensor alignment and calibration, control-structure interaction analysis, stability and jitter analysis, and post-launch support. His current interests are precision attitude determination, attitude sensor calibration, orbit determination, and optimization of attitude maneuvers.

Dr. Pittelkau earned the B.S. and Ph. D. degrees in Electrical Engineering from Tennessee Technological University and the M.S. degree in EE from Virginia Polytechnic Institute and State University.

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