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A4. What is time response of the control system? (around 50 words) (5 marks) A5. A unity feedback system has Open loop Transfer system (s+1). What is its Closed loop Transfer function? (5 marks) A6. A unity feedback system has Open loop Transfer system s/(s+1). What is its Closed loop Transfer function? (5 marks)

Answer 1

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A4: Ans- TIME RESPONSE OF THE CONTROL SYSTEM:-

Time response of a control system is defined as the output of a control system when subjected to an input which is function of time. The analysis of the system with respect to time ( Studying properties of the system with respect to time) is called time response analysis.

Time Response can be classified into two types:-

1. Transient Response               2. Steady state Response

Transient Response :- The output of the system before it settles down to a final value is called transient Response . In transient Response delay time, rise time , peak overshoot, settling time etc. are studied.

Steady State Response :- The output of the system after it settles down to a final value is called steady state response.

For example shown in the image below in 2nd order system Time response: (The Transfer function in the box is the standard 2nd order transfer function where omega n is natural frequency and zeta is damping ratio)

Date Page Example of Time Response : Let us considen a 2nd Onder Control system with unit step input the time response of output is : I/P ulf) 4) м2 / Р ult) 5²+28 Wust wohl 1 t Time Полролдо ар Output : - भार 1 Transient Response t Steady state Пол Роу) е

AS- Unity feedback system t :: H(s) = 1 Open loop Transfer function, GCS)= 5+] IP openloop G(s) op H(S) feedback Let us consider negative feedback Then the closed loop transfer function is given by ICS) GC5) 1 +90) HOO) こ FLS) = st1 1 +(5+1)-1 TIS) - S+1 S+2 closed doop transfert function

Page A6 Now, Given Open loop Transfer function, GUS) - S st 166) = Considering negative feedback system 1905) / JIP THE TES) = GCS) 1+GHCU) I(S) - S st1 1 ts x 1 st1 T05) - S S+ 1 + S TUS) = S 25+ 1 → closed loop Transfer function Note: To calculate for Positive feedback Control system use the formula T(S) 1-GC) HOS).

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