This course is part of the Spacecraft Dynamics and Control Specialization

4.7
stars
61 ratings

Hanspeter Schaub

8,504 already enrolled

Offered By

Spacecraft Dynamics and Control SpecializationUniversity of Colorado Boulder

About this Course

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This course trains you in the skills needed to program specific orientation and achieve precise aiming goals for spacecraft moving through three dimensional space. First, we cover stability definitions of nonlinear dynamical systems, covering the difference between local and global stability. We then analyze and apply Lyapunov's Direct Method to prove these stability properties, and develop a nonlinear 3-axis attitude pointing control law using Lyapunov theory. Finally, we look at alternate feedback control laws and closed loop dynamics. 
After this course, you will be able to...

* Differentiate between a range of nonlinear stability concepts
* Apply Lyapunov’s direct method to argue stability and convergence on a range of dynamical systems
* Develop rate and attitude error measures for a 3-axis attitude control using Lyapunov theory
* Analyze rigid body control convergence with unmodeled torque

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Course 3 of 4 in the

Spacecraft Dynamics and Control Specialization

Advanced Level

Approx. 31 hours to complete

English

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Flexible deadlines

Reset deadlines in accordance to your schedule.

Shareable Certificate

Earn a Certificate upon completion

100% online

Start instantly and learn at your own schedule.

Coursera Labs

Includes hands on learning projects.

Learn more about Coursera Labs

Course 3 of 4 in the

Spacecraft Dynamics and Control Specialization

Advanced Level

Approx. 31 hours to complete

English

Could your company benefit from training employees on in-demand skills?

Try Coursera for Business

Instructor

Instructor rating

4.83/5 (12 Ratings)

Hanspeter Schaub

Glenn L. Murphy Chair in Engineering, Professor

Department of Aerospace Engineering Sciences

28,841 Learners

7 Courses

Offered by

University of Colorado Boulder

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Syllabus - What you will learn from this course

Week1

Week 1

4 hours to complete

Nonlinear Stability Definitions

4 hours to complete

12 videos (Total 67 min)

12 videos

Course Introduction1mModule 1 Introduction1m1: Overview of Nonlinear Control6m1.1: Overview Stability Definition Discussion5m1.2: Nonlinear Equations Representation8m2: Definition: Neighborhood3m3: Definitions: Lagrange Stability3m4: Definitions: Lyapunov Stability5m5: Definitions: Asymptotic Stability6m6: Definitions: Global Stability2m7: Linearizing a Dynamical System6mOptional Review: Stability Definitions16m

7 practice exercises

Concept Check 1 - State Vector Representation30mConcept Check 2 - State Neighborhood30mConcept Check 3 - Lagrange Stability30mConcept Check 4 - Lyapunov Stability30mConcept Check 5 - Asymptotic Stability30mConcept Check 6 - Global Stability Definitions30mConcept Check 7 - Linearization20m

Week2

Week 2

5 hours to complete

Overview of Lyapunov Stability Theory

5 hours to complete

14 videos (Total 129 min)

14 videos

Module 2 Introduction1m1: Overview of Definite Function15m2: Lyapunov Function Definition10m2.1: Lyapunov Asymptotic Stability17m3: Lyapunov Stability of Linear System4m4: Global Stability Applications2mOptional Review: Definiteness7mOptional Review: Stability Definitions3mOptional Review: Lyapunov's Direct Method9m5: General Elemental Velocity Lyapunov Function12m5.1 Example: Multi-Link System3m6: Rigid Body Detumble Control20m7: State-Based Lyapunov Functions14mOptional Review: Elemental Lyapunov Functions2m

7 practice exercises

Concept Check 1 - Definite Function20mConcept Check 2 - Lyapunov Functions45mConcept Check 3 - Asymptotic Stability40mConcept Check 4 - Global Stability Applications30mConcept Check 5 - General Elemental Rate5mConcept Check 6 - Rigid Body Elemental Rate Lyapunov Function30mConcept Check 7 - General Elemental State Lyapunov Function20m

Week3

Week 3

11 hours to complete

Attitude Control of States and Rates

11 hours to complete

8 videos (Total 82 min)

8 videos

Module 3 Introduction1m1: Nonlinear Rigid Body State and Rate Control14m2: Global Stability of Nonlinear Attitude Control8m2.1 Example: Nonlinear Regulation Control11m2.2: Asymptotic Stability for Nonlinear Attitude Control5m3: Unmodeled Disturbance Torque15m4: Nonlinear Integral Control11m5: Feedback Gain Selection13m

5 practice exercises

Concept Check 1 - General 3-Axis Attitude Control1h 30mConcept Check 2 - Asymptotic Stability1h 30mConcept Check 3 - Unknown External Torques2h 8mConcept Check 4 - Integral Feedback2h 30mConcept Check 5 - Feedback Gain Selection2h 30m

Week4

Week 4

10 hours to complete

Alternate Attitude Control Formulations

10 hours to complete

6 videos (Total 97 min)

Reviews

4.7

16 reviews

5 stars
81.96%
4 stars
9.83%
3 stars
4.91%
2 stars
3.27%

TOP REVIEWS FROM CONTROL OF NONLINEAR SPACECRAFT ATTITUDE MOTION

by JPSep 26, 2020

Course is amazing and well detailed with different live perspectives.

by SHSep 11, 2020

Thanks Prof Schaub, that was a wonder of a course! Learned so much and still want to proceed :)

by SDFeb 3, 2018

Excellent teaching from Professor Schaub ! Course has been very well organised and touches on the important aspects of nonlinear control. Looking forward to more courses from you.

Thank you !

by PPNov 26, 2020

The whole course is really good. The instructor is awesome at teaching concepts. I got to learn a lot of new things.

View all reviews

About the Spacecraft Dynamics and Control Specialization

Spacecraft Dynamics and Control covers three core topic areas: the description of the motion and rates of motion of rigid bodies (Kinematics), developing the equations of motion that prediction the movement of rigid bodies taking into account mass, torque, and inertia (Kinetics), and finally non-linear controls to program specific orientations and achieve precise aiming goals in three-dimensional space (Control). The specialization invites learners to develop competency in these three areas through targeted content delivery, continuous concept reinforcement, and project applications.

Frequently Asked Questions

When will I have access to the lectures and assignments?
Access to lectures and assignments depends on your type of enrollment. If you take a course in audit mode, you will be able to see most course materials for free. To access graded assignments and to earn a Certificate, you will need to purchase the Certificate experience, during or after your audit. If you don't see the audit option:
The course may not offer an audit option. You can try a Free Trial instead, or apply for Financial Aid.
The course may offer 'Full Course, No Certificate' instead. This option lets you see all course materials, submit required assessments, and get a final grade. This also means that you will not be able to purchase a Certificate experience.
What will I get if I subscribe to this Specialization?
When you enroll in the course, you get access to all of the courses in the Specialization, and you earn a certificate when you complete the work. Your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.
Is financial aid available?
Yes. In select learning programs, you can apply for financial aid or a scholarship if you can’t afford the enrollment fee. If fin aid or scholarship is available for your learning program selection, you’ll find a link to apply on the description page.

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Control of Nonlinear Spacecraft Attitude Motion

About this Course