The error detector element in a control system gives
The difference of the reference signal and the feedback signal
The error detector — the summing junction at the input of every closed loop — subtracts the feedback signal from the reference :
\(E(s)=R(s)-B(s)\qquad\text{where}\qquad B(s)=H(s)\,C(s)\)
which is option 3.
Two details separate the right answer from the near miss.
First, subtraction, not addition. Negative feedback is what makes a closed loop stable and self-correcting: if the output exceeds the reference, the error goes negative and the controller reduces its drive. Adding the two signals (options 1 and 2) would give positive feedback, and the loop would run away to a limit rather than settle.
Second, the feedback signal, not the output. This is why option 4 is wrong. The feedback path contains the sensor and its conditioning, described by \(H(s)\), so what returns to the junction is \(H(s)C(s)\) and not \(C(s)\) itself. The two coincide only in a unity-feedback system, where \(H=1\) — a special case, not the general one. Physically the distinction matters because the reference and the output are usually different kinds of quantity: a thermostat compares a set-point voltage with a thermocouple voltage, not with a temperature.
The closed-loop transfer function follows directly from that subtraction :
\(C=GE=G\left(R-HC\right)\quad\Rightarrow\quad \dfrac{C}{R}=\dfrac{G}{1+GH}\)
The \(1+GH\) in the denominator — the source of every benefit feedback brings — exists only because the junction subtracts. Had it added, the denominator would be \(1-GH\), which vanishes when \(GH=1\) and gives the Barkhausen condition for an oscillator.
| Signal | Symbol |
|---|---|
| Reference / set point | R(s) |
| Feedback | B(s) = H(s)C(s) |
| Error | E(s) = R(s) − B(s) |
| Output | C(s) |
Practical error detectors take many forms — a potentiometer bridge, a differential amplifier, a synchro pair for shaft angles, or simply a subtraction in software — but all perform the same operation, and the steady-state value of E is what the error constants Kp, Kv and Ka quantify.
Hence, the error detector gives the difference of the reference signal and the feedback signal.
Similar Questions
Read the following statements about the transfer function of a system :
(a) The transfer function provides complete insight into the structure of the system.
(b) It offers a symbolic picture about the dynamic characteristics of the system.
(c) It does not give any insight into the structure of the system.
(d) If the transfer functions of individual components of the system are known, the overall characteristics of the system can be determined just by taking their product.
Which of the above statements are correct ?
The mass-spring-damper system shown in the following figure represents :
Three blocks having transfer functions \(G_1(s) = \frac{1}{s+2}\), \(G_2(s) = \frac{1}{s+5}\) and \(G_3(s) = \frac{s+1}{s+3}\) are cascaded. The equivalent transfer function is:
Important Questions from Basics of Control Systems
- Match the LIST-I with LIST-IIChoose the correct answer from the options given below:
LIST-I LIST-II A. Nyquist Criterion I. Polar Plots B. Bode Plot II. Rectangular Plots C. Phase Margin III. Amount of additional phase lag at the gain crossover frequency required to bring the system to the verge of instability D. Gain Margin IV. It is the reciprocal of the magnitude $|G(j\omega)|$ at the frequency at which the phase angle is $-180^\circ$. - Which of the following statement is not correct in respect of Transfer Function of linear Time Invariant System
A. In any open loop control system, the output is not compared with the reference input.
B. Traffic control by means of signals operated on a time basis is an example of closed loop control.
C. Closed loop control always implies the use of feedback control action in order to reduce system error.
D. Washing machine is an example of open loop system.
E. Stability is a major concern in open loop control system.
Choose the correct answer from the options given below:
Read the following statements about the transfer function of a system :
(a) The transfer function provides complete insight into the structure of the system.
(b) It offers a symbolic picture about the dynamic characteristics of the system.
(c) It does not give any insight into the structure of the system.
(d) If the transfer functions of individual components of the system are known, the overall characteristics of the system can be determined just by taking their product.
Which of the above statements are correct ?
The mass-spring-damper system shown in the following figure represents :
