Learning Objectives:

• Reduce a block diagram of multiple subsystems to a single block representing the transfer function from input to output.
• Compare and contrast open and closed loop control.

General Layout of a Feedback Control System:

where G\(_1\)(s) is a controller or compensator, G\(_2\)(s) represents a plant model, and H(s) represents the measurement dynamics. Y(s) represents the controlled variable, R(s) represents the reference input, and L(s) represents a disturbance.

Block Diagram Reduction Techniques:

Rule 1: Blocks in cascade (series):

Rule 2: (Combining blocks in parallel):

Rule 3: (Eliminating a feedback loop):

Solved Example: 86-1-01

In an open loop control system:

A. Control input is independent of output

B. Output is independent on control input

C. Only system parameters have effect on the control output

D. None of the above

Correct Answer: A

Solved Example: 86-1-02

For open control system which of the following statements is incorrect ?

A. Less expensive

B. Recalibration is not required for maintaining the required quality of the output

C. Construction is simple and maintenance easy

D. Errors are caused by disturbances

Correct Answer: B

Solved Example: 86-1-03

A control system in which the control action is somehow dependent on the output is known as:

A. Closed loop system

B. Semi-closed loop system

C. Open system

D. None of the above

Correct Answer: A

Solved Example: 86-1-04

In open loop system, the control action:

A. Depends on the size of the system

B. Depends on system variables

C. Depends on the input signal

D. Independent of the output

Correct Answer: D

Solved Example: 86-1-05

A good control system has all the following features except:

A. Good stability

B. Slow response

C. Good accuracy

D. Sufficient power handling capacity

Correct Answer: B

Solved Example: 86-1-06

A closed loop system is distinguished from open loop system by which of the following?

A. Servomechanism

B. Feedback

C. Output pattern

D. Input pattern

A closed loop control system has feedback elements which are absent in open loop control system.

Correct Answer: B

Solved Example: 86-2-01

Find the equivalent transfer function, T(s) = C(s)/R(s), for the system shown in Figure.

A. $\dfrac{1}{s+5}$

B. $\dfrac{5}{s+5}$

C. $\dfrac{s+5}{5}$

D. (s+5)

The transfer function will be given by: \begin{align*} T(s) = \dfrac{C(s)}{R(s)} &= \dfrac{G(s)}{1 + G(s) H(s)}\\ &= \dfrac{\left(\dfrac{1}{s}\right)}{1 + \left(\dfrac{1}{s}\right) (5)}\\ &= \dfrac{\left(\dfrac{1}{s}\right)}{\left(1 + \dfrac{5}{s}\right)}\\ &= \dfrac{1}{s+5} \end{align*}

Correct Answer: A