Feedback control diagram

Systems & feedbackField guide · Systems & feedback · 5 of 6

How does anything stay near a target?

Over the causal loop diagram’s marks, a feedback control diagram shows each variable’s role above its name, and a stock with its flows where the controlled variable accumulates.

Marks

• variable

• polarity

• delay

• loop

• reinforcing loop

• balancing loop

• boundary

• external driver

• gapa role, written above its variable's name

• nonlinear effect

• evidence coding

• behavior note

• behavior-over-time graph

• stock

• flow

• cloud

• signal

• stock equation

• targeta role, written above its variable's name

• corrective actiona role, written above its variable's name

• controlled variablea role, written above its variable's name

• measured valuea role, written above its variable's name

• feedforward

• saturation

• deadband

• overridea role, written above its variable's name

How each mark is drawn and read: chapter 8, What the notation expresses.

A line with an arrowhead

A thin line with an arrowhead is a signal: an effect carrying a reading or a setting, not material, that changes the variable at its head. Where the controlled variable is a stock, its flows’ double lines move material.

A house kept warm on a winter evening

B1 heating runs from temperature gap through boiler output, room temperature and thermometer reading; outdoor temperature, an external driver, acts on room temperature from outside the loop (chapter 8’s house).

When to draw one

Draw one when someone has chosen a value for a quantity to stay near, when the quantity and its reading can disagree, or when something outside keeps pushing it away (chapter 8’s signals).

When not to draw one

With no target, as when tea cools toward the room’s temperature, a causal loop diagram does; when the reading and the quantity can’t come apart, as with a cistern’s float, a sentence does (chapter 8, what stays informal).

Reasoning and polish

• Reasoning4 of 5
• Polish4 of 5signal sketch → nested control loops

1. Target, gap, corrective action, controlled variable and measured value
2. External drivers, delays, saturation and nested loops
3. Feedforward, adaptation, stability, and failure modes

Related types

• A feedback control diagram is drawn as a causal loop diagram is, with a role written above each variable that plays one, its effects called signals.
• Where the controlled variable accumulates, it is drawn on a feedback control diagram with a stock & flow diagram’s stock, flows and signals, the roles written above them.

In this book

• Chapter 8, Sense, Compare, Correct: target and gap, measured value, corrective action, controlled variable, control loops, external drivers, delays, control with accumulation and the engineering names; exercises FC 01–05.
• Chapter 9, Anticipation, Limits, and Nested Control: feedforward, sampling and filters, deadband, saturation, competing targets, nested loops, override and false alarms; exercises FC 06–10.

Sources

• Donella H. Meadows, Thinking in Systems: A Primer (Chelsea Green, 2008), chapter 2, A Brief Visit to the Systems Zoo, on the thermostat drawn as one stock, the room’s temperature, with two competing balancing loops.
• Karl Johan Åström and Richard M. Murray, Feedback Systems: An Introduction for Scientists and Engineers, second edition (Princeton University Press, 2021), chapter 1, on feedback, the parts of a feedback system, a thermostat’s on-off rule, feedforward and nested loops; chapter 3, on how engineers draw boxes and lines; and chapter 11, on a throttle held at its limit on a steep hill.
• Stephen Boyd, “Feedback Control Systems: Static Analysis”, lecture 12 of EE102 (Stanford University), on the names engineers give a feedback system’s parts.
• James K. Roberge, Operational Amplifiers: Theory and Practice (MIT), section 2.2, the source of the engineering name for where the target and the measured value meet.