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

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Physics 123: PID Notes 1 PID Notes REV 0 1 March 11, 2008. Contents 1 The Problem, Generally. .. 1 1 . 1 F i r s t ,aR em i n d e ro fs om eo pam pJ a r g o n ................ 1 1 . 2 T h ec p e n s a t e do p ......................... 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 “C o n t r o l l e rG a i n , ”“S y s t emG a i n ” .................... 8 2.2 Degrees of stability: “Phase margin”. .................. 9 2 . 3 A d d“D : ”D e r i v a t i v e ........................... 1 1 H ow t oC a l c u l a t e t h en e e d e dD e r i v a t i v eG a i n .............. 1 2 2 . 4 I n t e g r a l.................................. 1 5 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 f 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); f x subscripts to “ subscript ”perPaul’s complaint (10/04).
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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 f 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 !’?
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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.
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This note was uploaded on 04/07/2008 for the course PHYSICS 123 taught by Professor Hayes during the Spring '07 term at Harvard.

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

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