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What is Block diagram?

A diagram of a control system that shows each element as a box (block) containing its transfer function, the flow of signals as arrows, the addition and subtraction of signals as summing points and the branching of signals as pickoff points. Blocks in series combine into the product of their transfer functions and blocks in parallel into the sum, and a negative-feedback loop can be replaced by a single block G/(1 + GH). Repeating such equivalent transformations gives the transfer function from the setpoint or a disturbance to the output.

Japanese name: ブロック線図

Block diagram appears in 1 practice question across 1 topic, including Control Engineering Basics.

Field: Control Engineering Basics

Try it: questions about Block diagram

In a negative-feedback block diagram, the forward path has the transfer function G(s) and the feedback path has the transfer function H(s). Which of the following is the closed-loop transfer function Y(s)/R(s) from the setpoint R(s) to the output Y(s)?

  1. AG(s)/(1 − G(s)H(s))
  2. BG(s)H(s)/(1 + G(s)H(s))
  3. CG(s)/(1 + G(s)H(s))
Show answer and explanation

Answer: C. G(s)/(1 + G(s)H(s))

The error is E(s) = R(s) − H(s)Y(s) and the output is Y(s) = G(s)E(s). Eliminating E(s) from the two equations gives Y(s) = G(s)R(s) − G(s)H(s)Y(s), and so Y(s)/R(s) = G(s)/(1 + G(s)H(s)). The term G(s)H(s) in the denominator is the transfer function that a signal sees going once around the loop, called the loop transfer function (open-loop transfer function). With unity feedback, H(s) = 1, it becomes G(s)/(1 + G(s)).

Questions that mention Block diagram (1)

  1. In a negative-feedback block diagram, the forward path has the transfer function G(s) and the feedback path has the transfer function H(s). Which of the following is the closed-loop transfer function Y(s)/R(s) from the setpoint R(s) to the output Y(s)?

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Related terms

Transfer function Bode plot Feedback control Feedforward control First-order system Gain margin Integral windup Laplace transform Overshoot PID control

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