CDS 101/110  Loop Shaping
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CDS 101/110a  Schedule  Recitations  FAQ  () 
Contents 
Overview
Monday: Loop Shaping (Slides, MP3)
This lecture describes how to design a control system by converting the performance specifications to constraints on the loop transfer function, and then shaping the loop transfer function to satisfy the constraints. Sensitivity functinos are defined and tradeoffs between different input/output transfer functions are discussed.
Wednesday: Performance Limits (Slides, MP3)
This lecture investigates some of the limits of performance for feedback systems, including the effects of right half plane poles and zeros on the closed loop system performance. A magnetic levitation system and lateral control of the Caltech ducted fan are used to illustrate the basic concepts.
Friday: No class (Thanksgiving holiday)
Handouts
Monday

Wednesday (CDS 110)  Friday

Reading
 K. J. Åström and R. M. Murray,, Preprint, 2006..
Homework
This homework set provides practice in specification, design and limits of control systems using loop shaping. The first problem explores the relationship between the loop transfer function and the closed loop response. The second problem explores some of the effects of right half plane zeros on control performance. The third and fourth problems (CDS 110) are simple design problems for an insect flight control system and a magnetic levitation system.
FAQ
Monday
Wednesday
Friday
Homework
 How is the slope of the gain curve related to robustness?
 HW8 Problem 1 Hints
 HW8 Problem 3
 HW8 problem 4
 Problem 1  What is the value of a?
 Problem 2 (CDS101) Problem 1 (CDS110)
 Problem 2  What does "less negative" mean?
 Problems 3c and 4b  Plot Nyquist plots cooresponding to the loop transfer function