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Control analysis · notation · signals & systems

Boxes, arrows,
circles.

Every control system — thermostats, drones, shooter flywheels, cruise control — gets described in the same three-symbol picture language. Ten minutes here and you'll read a control diagram the way you read a wiring schematic.

→ arrow = a signal on the move ▢ box = a block that transforms it ○ circle = a junction that adds/subtracts
Part 1 / The alphabet

Three symbols. That's the whole language.

Control systems are conversations between values: a target speed, a voltage, a measurement. Describing those conversations in sentences gets tangled fast — so engineers draw them instead. Every diagram on every page of every controls textbook is built from exactly these parts:

setpoint r SIGNAL — a value, flowing + − another signal SUMMING JUNCTION — adds / subtracts difference Block code or physics BLOCK — transforms in → out transformed signal
The anatomy. A value rides in on an arrow, gets combined with another value at a circle, gets transformed by a box, and rides out on another arrow. Information (and, in the plant's case, energy) always flows in the direction of the arrowheads.

Arrows are signals — a number that exists over time: a setpoint in rad/s, a motor voltage, a sensor reading. Boxes are blocks — anything that turns its input signal into an output signal. A block can be code (a controller computing voltage from error) or physics (a motor turning voltage into motion); the notation deliberately doesn't care. Circles are summing junctions — each incoming arrow carries a + or −, and the output is the signed sum. The most famous junction in engineering computes setpoint − measurement, which has a name you'll use forever: the error.

Part 2 / The simplest sentence

Open loop: information flows one way

Chain the symbols left to right and you get the simplest control structure there is. A setpoint enters, a controller block turns it into a control effort (for robots: voltage), the plant — the physical mechanism being controlled — turns voltage into motion, and the result exits stage right:

setpoint r Controller voltage V Plant (motor + flywheel) speed ω
Open-loop control. Every arrowhead points right. Nothing ever flows back — the controller has no idea whether the plant obeyed.

Drive one yourself. The widget below is a live open-loop diagram wired to a real simulated flywheel — you are the controller, and the numbers ride the wires:

Widget 01 — Drive the open loopyou are the controller
Signal in
6.0 V
Signal out
0 rad/s

Trace the causality: your slider is a signal, the plant block is physics, the output is another signal. Now press the friction button — the speed sags, and nothing in the diagram reacts. No arrow flows back, so the system can't know it's wrong. That missing return arrow is the entire motivation for what comes next.

Part 3 / The famous shape

Closing the loop

Now add one path: measure the output with a sensor and route it back to a summing junction at the input, with a minus sign. The junction computes error = setpoint − measurement, and the controller acts on the error instead of the raw setpoint. This shape — the closed loop, or feedback loop — is the most drawn diagram in all of engineering:

setpoint r + − error e Controller acts on error voltage V Plant (motor + flywheel) speed ω Sensor (encoder) measured ω
Closed-loop (feedback) control. Follow one pulse all the way around: forward through code, through physics, back through the sensor, into the minus input. The loop is a circle of cause and effect — the output literally influences its own input.
Why the minus sign matters: subtracting the measurement makes the loop self-correcting — output too low → error positive → push harder. Flip that sign to a + and the loop amplifies its own mistakes instead of fixing them (this is a real and spectacular failure mode: positive feedback). One tiny symbol on the diagram is the difference between cruise control and a runaway.

One more standard citizen of these diagrams: the disturbance — an outside influence that shoves the plant without permission. It enters the picture as an extra arrow summing into the plant's input:

voltage V + + disturbance (ball shot, gust, bump) Plant gets shoved anyway speed ω (now wrong)
Disturbances. The world shoves your plant: a ball rips energy from a flywheel, wind gusts a drone. On the diagram, that's just another signal summing in where you didn't ask for it. Closed loops exist largely to fight this arrow.
Part 4 / Recap

You can now read control diagrams

To read any diagram: find the plant (the physics box), find the setpoint (the arrow entering from the left), then follow the arrows — every path is a chain of cause and effect, and every loop is a system checking its own work. If you can trace one pulse all the way around a closed loop and say what each symbol did to it, you're literate.

arrow — a signal (a value over time)
box — a block (transforms signals)
circle — a summing junction (signed addition)
plant — the physical mechanism
setpoint r — the goal
error e — r − measurement
disturbance — the world shoving back
open loop — no return path
closed loop — output routed back to the input
Pocket glossary — the entire notation, one line each.
Built as an interactive lesson · the open-loop widget runs a real simulated DC-motor flywheel — the numbers on the wires are the actual signals.