MAE280a - Linear Systems & Control

Policies: Please read the Course & Homework Policy for this class.

Instructor: Thomas Bewley (Office hours: usually, 8:00-9:00am M-F in 1805 ebu1 and for 30 min after each lecture; any possible changes will be posted on his online schedule.)

Time and place: Fall 2012 (Class Section ID: 752753).

Administrative details: Midterm: TBA. Final: TBA.

Text: This class is taught from selected sections of Numerical Renaissance, with supplemental texts held on reserve at the library as announced in class.

Course description: A brief review of Laplace/Z transform methods for analysis of SISO systems. A brief review of essential concepts in linear algebra, including the solution of the Lyapunov and Riccati equations. A thorough description and analysis of continuous-time and discrete-time MIMO linear systems in transfer function and state-space form. Canonical forms. Controllability and observability matrices and grammians. Stabilizability, detectability, reachability, constructability. A brief introduction to modern control design (optimal control and Kalman filtering).

Prerequisites: Undergraduate-level classical control theory (root-locus, Bode, Nyquist) and graduate-level linear algebra (SVD, Shur and Jordan decompositions, pseudoinverses). To cover the latter, concurrent enrollment in a graduate-level linear algebra class (e.g., MAE290a or Math270a) is strongly encouraged.

Previous exams: All of our old exams for MAE280a are posted below. Note that the notes have evolved significantly since 2007, so some of this material is just a repeat of what is now in the notes (and some of it is in a slightly different notation). I post these exams here mostly so you can get an idea of what my exams look like before taking one. By going through these exams, you will see that I occasionally (but not frequently) reuse some of the questions.

Previous Midterms    Previous Finals    Previous Final Solutions    
  2011 Midterm   2011 Final   2011 Final Solutions
  2010 Midterm   2010 Final   
  2009 Midterm   2009 Final   2009 Final Solutions
  2007 Midterm   2007 Final   2007 Final Solutions

Thought for the day:
   ... und ich möchte Sie, so gut ich es kann, bitten,
   Geduld
   zu haben
   gegen alles Ungelöste in Ihrem Herzen
   und zu versuchen,
   die Fragen selbst lieb zu haben
   wie verschlossene Stuben und wie Bücher,
   die in einer fremden Sprache geschrieben sind.
   Forschen Sie jetzt nicht nach den Antworten,
   die Ihnen nicht gegeben werden können,
   weil Sie sie nicht leben könnten.
   Und es handelt sich darum, alles zu leben.
   Leben Sie jetzt die Fragen.
   Vielleicht leben Sie dann allmählich,
   ohne es zu merken,
   eines Tages in die Antwort hinein.
   (Rainer Maria Rilke, "Briefe an einen jungen Dichter")
English Translation:
   ... and I would like to ask you, as best I could,
   to have patience towards everything that's unsolved in your heart
   and to try to love the questions themselves
   as locked rooms and as books that are written in a foreign language.
   Do not study for the answers right now
   because you would not be able to live them.
   And it's all about living everything.
   Do now live the questions.
   Maybe then at some day you live little by little,
   without noticing, into the answer.
(Rainer Maria Rilke, "Letters to a young poet" )
(translation by Fabian Daub, MAE290a student)