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# Instrumentation and Control Lab

### Ex 3: Identification of Linear System From Frequency Response Test

#### 3.1 Objective:

To plot the gain and phase angle with frequency of an unknown linear system and to determine the transfer function of the system from the graph.

#### 3.2 Apparatus:

(i) Black box (ii) Audio frequency oscillator (iii) CRO

#### 3.3 Procedure and Experimental Results:

(i) The black box, provided for the experiment, is a single input single output (SISO) electrical system. Since one terminal is common between the input and output, it is a two port three terminal system.

(ii) Connect the oscillator and CRO with the input and output of the black box. Apply sinusoidal voltage in input terminal.

(iii) Now vary the input sinusoidal signal’s frequency from low (say 1Hz) to high (say 100KHz) keeping the input voltage fixed (say 5V).

(iv) Observe the output voltage and phase at each frequency. Plot frequency (in rad/sec) versus gain and frequency versus phase angle in a semilog graph paper.

(v) Fit asymptotes of the gain vs frequency plot and from the corner points and slope identify the transfer function of the system.

(vi) Plot the theoretical phase angle vs frequency graph to identified system. Is that matching with the experimentally obtained one?

#### 3.4 Few Questions for Viva Voce:

(i) What is Liasajous figure?
(ii) What are the step and ramp response of the identified system?
(iii) If there is delay in the system how it can be expressed using in transfer function?
(iv) Why sinusoid input is used instead of triangular or other kind of function?

#### 3.5 Reference:

(i) Katsuhiko Ogata, “Modern Control Engineering”, Prentice-hall Of India Pvt Ltd, 4th edition, 2007.