Nishant Mandal responds of the second order system.pptx

translet responds of the secound order system

1. Transient response of the second order systems Submitted by NISHANT MANDAL (BWU/BEC/21/008 ) BRAINWARE UNIVERSITY Course Name – Control System Course Code – ESCR302

2. Transient Response Definition In control systems, a transient response (which is also known as a natural response) is the system response to any variation from a steady state or an equilibrium position. The examples of transient responses are step and impulse responses which occur due to a step and an impulse input respectively. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING

3. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING Cont … Damping Oscillation: A typical Transient Response Example

4. Time Constant of Second Order System Definition – The time it takes, in seconds, for the decaying exponential to be decreased to e-1 =0.368 of its initial value. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING Because e -t/T = e -1  when t=T, it can be observed that:

5. Transient Response of Second Order System This very common transfer function to represent the second order system can be reduced to the standard form. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING Where ω n =undraped natural frequency ζ = damping ratio 2 ω n S 2 + 2 ζω n s + 2 ω n G(s) =

6. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING Cont … For a unit step input which is R(s) =1/s, the transform of the output would be 2 ω n ) s(S 2 + 2 ζω n s + 2 ω n C (s) = The characteristic equation would be s 2 +2 ζω n s+ =0 ω n 2

7. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING Cont … These system poles depend on ζ The characteristic equation would be s 2 +2 ζω n s+ =0 ω n 2 ζ > 1 : overdamped : s 1,2 = − ζω n ± ωn√ζ 2 − 1

8. DEPARTMENT OF ELECTRONICS & COMMUNICATION ENGINEERING Cont … ω n - ω n - ζω n j ω jω n √1- ζ 2

9. THANK YOU