CDS 101/110  PID Control
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CDS 101/110a  Schedule  Recitations  FAQ  () 
Contents 
Overview
Monday: PID Overview (Slides, MP3)
This lecture covers the basic tools in frequency domain control design using proportional + integral + derivative (PID) control. After reviewing the role of the controller on the loop shape and the relationship between the gain and the phase, we introduce PID control and illustrate its use to design a speed controller that satisfies a given set of performance specifications.
Wednesday: PID Analysis (Notes, MP3)
This lecture provides more details on the use of PID control, including the representation of PID controllers in state space. The problems of windup and saturation are also discussed.
Friday: PID Design (Notes, MP3)
This lecture provides additional tools for PID control design, including ZieglerNichols turning and root locus plots for choosing the loop gain. An example system is worked out in detail, using MATLAB.
Handouts
Monday

Wednesday (CDS 110)

Friday

Reading
 K. J. Åström and R. M. Murray,, Preprint, 2006..
Homework
This homework set provides practice in specification and design of control systems in the frequency domain using PID control. The first two problems work through examples similar to the ones used in lecture. The third problem, for CDS 110 students, explores the use of PID control to give a desired level of performance for a simplified balance system.
 Homework #7
 Useful MATLAB commands
 sisotool  display standard linear system plots on a single screen
 feedback  generate a closed loop system from a loop transfer function
FAQ
Monday
Wednesday
Friday
Homework
 A typo in equation (6.24).
 How do I evaluate a certain transfer function at desired frequencies numerically?
 HW 7 Prob 1 Comments
 HW 7 Problem 2
 In MATLAB, use feedback() command to obtain the closed loop transfer function. Do not use L/(1 L).
 Problem 1 b and c  Plot step and freq response
 Problem 1c  ZieglerNichols
 Problem 3d  Pay special attention to low Ti values
 Problem 4c  Settling time
 When evaluating the Bode integral, I am not getting even close to the ideal result (something negative)?