Applied Control in Astronautics
AAE59000
Credit Hours:
3Learning Objective:
By the end of the course, students will be able to:
- Acquire fundamental knowledge about control techniques for dynamical systems in astronautics
- Apply the learned theories to design controllers for a range of spaceflight problems
- Develop original computation software using a programming language to numerically simulate the spacecraft motion under control
- Assess the controller performance and resulting dynamical properties analytically and numerically
- Present and communicate their technical approaches to problems, their analysis/numerical results, and their interpretation in written and presentation formats
Description:
Dynamical systems considered in the context of spaceflight are largely different from those of ground-based systems. The objective of this course is to introduce students to the theoretical and practical foundations of control techniques with an emphasis on its application to dynamical systems in astronautics.
Topics Covered:
- Brief review of orbital mechanics and linear systems
- Optimal control via Pontryagin's minimum principle for space trajectory optimization
- Computational control via convex programming for space trajectory control & optimization
- Nonlinear feedback control via Lyapunov stability for spacecraft orbit control
- Stochastic process & performance evaluation for controlled space systems under uncertainty
Prerequisites:
Engineering or Science undergraduate degree in a field relevant to Aerospace Engineering, Mechanical Engineering, Electrical Engineering, Physics, or Applied Mathematics. Basic understanding of orbital mechanics, calculus, and linear algebra. Experience in programming and coding for numerical simulations of dynamic systems and numerical integration of ordinary differential equations.
Applied / Theory:
70/30
Web Address:
https://purdue.brightspace.com
Homework:
Double-problem sets (P-sets) will be posted roughly every two weeks, where the first P-set is due in 1 week and the other is due in 2 weeks from the posted date (i.e., on average on P-set per week, approximately). One of the two P-sets is typically about theory and the other is about its application to spaceflight problems. This structure is to encourage students to start working on the application part, which is often more time consuming due to extensive programming, after completing the theory part without waiting for the next P-set to be posted.
Projects:
There is an open-ended final project toward the end of the semester. Students may form groups of up to two persons. In the final project, students will explore spaceflight problems of their interest and apply the learned (or relevant) control techniques to the problems. Topics can be either new theoretical development of application of existing techniques to the problems. Topics can be either new theoretical development or application of existing techniques to your problems, but should involve some computational investigation either case.
Each group will first submit a short (1-3 page) project proposal that describes the topic you wish to do your project on, which will be due around mid-to-end March. At the end of the semester, each group will record and submit a video of a brief ~3-5 min presentation on their project result. Each group will also submit a professionally formatted technical report that summarizes the final project.
If you are interested in some previous project examples, you can find those at https://engineering. purdue.edu/OguriGroup/teaching
Exams:
One take-home midterm exam will take place during the semester, which will involve computational problems. The exam will not be proctored. The specific exam procedures will be discussed in class. It is anticipated that the exam takes place around min-to-end March.
Textbooks:
None required. However, the following textbooks are helpful for deeper understanding of the materials:
- Bryson, A.E., and Ho, Y.C., Applied Optimal Control, Taylor & Francis, 1975
- Battin, R.H., An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition, AIAA Education Series, 1999
- Longuski, J.M., Guzman, J.J., and Prussing, J.E., Optimal Control With Aerospace Applications, Springer, 2014
- Boyd, S., and Vandenberghe, L., Convex Optimization, Cambridge U. Press, 2004
- Schaub, H., and Junkins, J.L., Analytical Mechanics of Space Systems, AIAA Education Series, 2003
- Slotine, J.J.E., and Li, W., Applied Nonlinear Control, Prentice Hall, 1991
- Sastry, S., Nonlinear Systems: Analysis, Stability, and Control, SpringerVerlag, 1999
Computer Requirements:
P-set often involves extensive programming to solve problems. Students can use any computer language, O/S, or software to draw plots based on their preference.
Online office hours by the instructor and TAs will utilize MS Teams and/or Zoom. Laptop/tablet with pen will be helpful when communicating mathematical ideas and/or asking questions using equations in online office hours.