CDS 101: Principles of Feedback and Control Lecture 9.1: PID and Root Locus 25 November 2002

Lecture

This lecture describes PID control, including the use of Ziegler-Nichols rules to design the gains. The root locus technique is introduced for determining the loop gain and the effect of pole location on performance is described in this context. Finally, some of the implications of right half plane zeros are discussed using the root locus plot.

• Lecture Presentation

Mud card responses [advanced search]:

• Is there a way to draw out the step response based on the transfer function? ("step" is cheating!)
• What specific modifications are necessary for the control transfer function of a PID controller to add the roll-off poles?
• "Rlocus" in matlab assumes the system gain is the "free parameter". Is there a "simple" way to make it work for any parameters?
• Are the zeroes for L=PC always called zeroes and the roots of L=PC always called roots?
• What is alpha? What happens when it goes to infinity? How come the roots go from the poles of PC to the zeros of PC?
• On slide 9, where did the slopes and bounds come from?
• Are the dominant poles the ones farthest to the right?
• I just discovered that I don't know how to close Nyquist plots with poles on the jw-axis. Can you explain that again?
  i.e. How do I determine which way to close the Nyquist plots if poles or zeros exist on the jw-axis?
• Is there any easy way in MATLAB to plot the tracking error bounds, phase margin bounds, etc that are used on the slides?
• How would one implement a lead compensator? I know how to use the transfer function form, but what does that correspond to? For example, if C(s)=K_i/s comes from u(t)=K_i*integral(e(t)dt), what produces C(s)=K*(s+a)/(s+b)?
• Is L=PC or L=PC/(1+PC) for slide 6?
• Is Kd an operator or a constant?
• How does a pole at high frequency prevent PID amplification of high frequency noise?
• Does cancelling poles/zeros make any difference at all?
• Slide 8: The angle 360/(P-Z) is measured from where?
• How does moving a pole at zero to a small value prevent integrator windup?

Reading Material and Handouts

Handouts from lecture

• Lecture handout
• L91_cruise.m
  
• Homework #8

Required reading

• Astrom, Sec 6.1-6.4, 6.6
  

Supplemental reading

• Packard, Poola and Horowitz, Dynamic Systems and Feedback, Section 13
• A. D. Lewis, A Mathematical Introduction to Feedback Control, Chapter 12 [pdf], Section 13.1 [pdf]
  

Homework

This homework set covers PID and root locus.

• Homework Assignment [pdf]

Modifications to the homework (link above is always the latest version):

• 26 Nov 02: release of remaining CDS 110 problems
• 25 Nov 02: problem set release (first two problems only)

Frequently asked questions on homework and TA hints: