{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

PID Notes - Physics 123 PID Notes 1 PID Notes REV 01...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 123: PID Notes 1 PID Notes REV 0 1 March 11, 2008. Contents 1 The Problem, Generally... 1 1.1 First, a Reminder of some op amp Jargon . . . . . . . . . . . . . . . . 1 1.2 The compensated op amp . . . . . . . . . . . . . . . . . . . . . . . . . 2 Side effect, by the way: compensated op amp looks like an integrator . . 3 Strange things in the feedback loop can defeat op amp compensation . . 5 1.3 Stabilizing Strategy Generalized... . . . . . . . . . . . . . . . . . . . . 6 Wien Bridge recalls criteria for oscillation, and for stability . . . . . . . 6 2 The PID Motor Control Loop 6 2.1 “P”: Proportional-only Circuit: How much gain can it tolerate? . . . . . 8 “Controller Gain,” “System Gain” . . . . . . . . . . . . . . . . . . . . 8 2.2 Degrees of stability: “Phase margin” . . . . . . . . . . . . . . . . . . . 9 2.3 Add “D:” Derivative . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 How to Calculate the needed Derivative Gain . . . . . . . . . . . . . . 12 2.4 Integral . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 1 The Problem, Generally... The problem is a familiar one: how to keep a feedback loop stable, despite lagging phase shifts within the loop. What’s new in the PID is the application of derivative of the error signal, particularly, in order to stabilize a loop that includes something otherwise de-stabilizing. 1.1 First, a Reminder of some op amp Jargon Figure 1: Curves to remind us of op amp jargon 1 Revisions: correct low-dropout fi gure (C feedback goes to inverting input); add contents (4/06); add 1) plot showing why excess D brings instability, and 2) op amp open-loop phase-shift images; darken faint regions in images (10/05); fi x subscripts to “ subscript ” per Paul’s complaint (10/04).
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Physics 123: PID Notes 2 1.2 The compensated op amp And here’s “compensation” in a nutshell: Figure 2: A reminder concerning op amp “compensation” As you know, a bare op amp, with its multiple stages (each providing a non-zero source impedance driving stray capacitance, to form a low-pass) will show phase shift beginning at -90 degrees for the fi rst low-pass, then -180 at the frequency where the second roll-off occurs, and so on. Since one cannot afford a -180 shift (because it transforms negative feedback into positive 2 ), one has to do something to make even the most straightforward op amp circuit behave. Without the remedy called “compensation,” an op amp follower would oscillate. 2 By the way, do you recall why you can’t outsmart the phase shifts, anticipating the problem by sending the feedback to the non-inverting terminal, then saying, ‘Ha ha: the -180 shift now makes feedback negative !’?
Image of page 2
Physics 123: PID Notes 3 Here is the standard graphic way to describe the problem: Figure 3: Curves showing gain rolloff for op amps, compensated and uncompensated (Text Fig. 4.80) The ’741 is stable, even as a follower, because its designers made sure that the op amp’s gain is down to unity below the frequency where the deadly -180-degree shift occurs 3 . Not so for the “uncompensated” devices. In contrast, the uncompensated ’748 is unstable as a follower. How much circuit gain would it need, in order to be stable, without any additional “compensation”? As the curves above remind us, compensation sacri fi ces op amp gain—a virtue—in order to achieve stability—a minimum requirement.
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern