Block diagrams: connecting and reducing systems as blocks
Three calculation rules (series, parallel, feedback) reduce a complex control structure to a single transfer function.
Three rules
| Connection | Combined transfer function |
|---|---|
| Series (G1 then G2) | G1 · G2 |
| Parallel (summed) | G1 + G2 |
| Negative feedback | G / (1 + G·H) |
Closed-loop transfer function
With controller C(s), plant P(s) and sensor H(s) = 1
T(s) = C·P / (1 + C·P)
When the loop gain L = C·P is large, T ≈ 1 and the output follows the target well. The reason feedback is robust to changes in the plant is in this equation.
RoadmapSee where this note sits in Control Engineering→Disturbance input
If a disturbance D is added at the plant input, its effect on the output is
Y/D = P / (1 + C·P)
The larger the loop gain, the smaller the effect of the disturbance.
A real controller as blocks
Drawn out, motor control looks like this.
position target → [position P] → speed target → [speed PI] → current target → [current PI] → voltage → [motor]
Designing by reducing each loop to a block from the inside out is cascade control. A block diagram is also the common language for sharing this structure with a team.