Why Close the Loop

Part 3 · Control Loops

Key point: the load needs \(V_{\mathrm{out}}\) to stay within a specified tolerance. Without feedback the output droops by \(\Delta I\,R_{\mathrm{out}}\). Feedback compares \(V_{\mathrm{out}}\) to \(V_{\mathrm{ref}}\) and fights to hold regulation.

Click a step, or Next, to set the lab. The sliders wait until you have walked it.

1
Green is the spec.
3.3 V ±5% here. Idle is trimmed to \(V_{\mathrm{ref}}\). The load does not care how you got there — only that you stay in the band.
2
Open loop droops \(\Delta I\,R_{\mathrm{out}}\).
Drive is trimmed at idle. Extra load current through the plant’s \(R_{\mathrm{out}}\) is volts you lose, and nothing pulls them back. Watch \(V_{\mathrm{out}}\) go red.
3
Close it: error drives the plant.
\(e = V_{\mathrm{ref}} - F\,V_{\mathrm{out}}\). Compensator \(C\) (here a number \(K\), not yet Type II) and plant \(P\) sit in the forward path. Same current, smaller droop — still red.
4
\(K\) divides the droop.
Closed-loop, \(\Delta V = \Delta I\,R_{\mathrm{out}}/(1+K)\). \(K=40\). The step stays blue.
5
Hard load: moderate \(K\), bigger \(\Delta I\).
\(K\) drops to 4 and the step jumps to 1.2 A. Same idea: more amps through \(R_{\mathrm{out}}\) → more volts. Red again.

K is a number here. Later pages give C poles and zeros, and ask whether a large K is still stable.

Load step vs the window

Top: \(V_{\mathrm{OUT}}\) vs ±5% · Bottom: \(I_{\mathrm{LOAD}}\)

Gain K

droop \(\Delta I R_{\mathrm{out}}/(1+K)\) → —

vs open-loop \(\Delta I R_{\mathrm{out}}\) → —

Load step ΔI (A) Plant Rout (Ω)

K = 0 is open loop: idle is trimmed to 3.3 V. The step drops Vout by ΔI·Rout. Nothing pulls it back.

Forward: \(C\) then \(P\). Return is open — \(K=0\).

Vout · blue in-spec · red out · green = ±5%

Iload · step up, then release

Vout in spec Vout out of spec Vref Iload playhead

Control loop algebra

Error at the summer is \(e = V_{\mathrm{ref}} - F V_{\mathrm{out}}\). The forward chain is \(L = C P\). Then

\[ \Delta V = \frac{\Delta I\,R_{\mathrm{out}}}{1+K} \]

Idle is trimmed to \(V_{\mathrm{ref}}\). Extra load current through the plant’s \(R_{\mathrm{out}}\) is a disturbance. Closed-loop it is divided by \(1+K\). Open loop (\(K=0\)) takes the full \(\Delta I R_{\mathrm{out}}\) hit. A later page puts a pole at the origin so even the leftover DC error goes to zero, and asks whether a large \(K\) is still stable.