Question

The output in response to a unit step input for a particular continuous control system is c(t)= 1-e^-t. What is the delay time Td?

(a) 0.36

(b) 0.18

(c) 0.693

(d) 0.289

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Question is from Time Response of Second Order Systems in section Time Response Analysis, Design Specifications and Performance Indices of Control Systems

Answer 1

Correct answer is (c) 0.693

Easiest explanation: The output is given as a function of time. The final value of the output is limn->∞c(t)=1; . Hence Td (at 50% of the final value) is the solution of 0.5=1-e^-Td, and is equal to ln 2 or 0.693 sec.