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A system has a complex pole pair of (-1+ 2j) and a real zero of (-3). The steady state output to a unit step input is 2. Estimate the transfer function of the system. Q1) a) b). Using the transfer function derived in a) calculate the following i) The damping ratio. ii) The undamped natural frequency. iii) The steady state gain.

A system has a complex pole pair of (-1+ 2j) and a real zero of (-3). The steady state output to a unit step input is 2. Estimate the transfer function of the system. Q1) a) b). Using the transfer function derived in a) calculate the following i) The damping ratio. ii) The undamped natural frequency. iii) The steady state gain.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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A system has a complex pole pair of (-1± 2j) and a real zero of (-3). The steady state output to a unit step input is 2. Estimate the transfer function of the system. Q1) a) b). Using the transfer function derived in a) calculate the following i) The damping ratio. ii) The undamped natural frequency. iii) The steady state gain. iv) The steady state output. v) The output y(t) using inverse Laplace methods. c) A single input single output system with y(t) as output and u(t) as input, is describe by d²y(t) dy(t) + 10y(t) = 5 du(t) -3u(t) dt + 2 %3D dt? dt For an input u(t) with zero initial conditions the above system produces the same output as with no input and with initial conditions dy(t) = -4,y(0) = 1 %3D dt What will be the input u(t)? Hence, Calculate the steady state output. d) Let z(t) be the unit step response of a system with a transfer function K(s + a) G(s) = s+ K If z (0) = 10 and z(0) 100, then what are the values of 'a and 'K? %3D
Transcribed Image Text:A system has a complex pole pair of (-1± 2j) and a real zero of (-3). The steady state output to a unit step input is 2. Estimate the transfer function of the system. Q1) a) b). Using the transfer function derived in a) calculate the following i) The damping ratio. ii) The undamped natural frequency. iii) The steady state gain. iv) The steady state output. v) The output y(t) using inverse Laplace methods. c) A single input single output system with y(t) as output and u(t) as input, is describe by d²y(t) dy(t) + 10y(t) = 5 du(t) -3u(t) dt + 2 %3D dt? dt For an input u(t) with zero initial conditions the above system produces the same output as with no input and with initial conditions dy(t) = -4,y(0) = 1 %3D dt What will be the input u(t)? Hence, Calculate the steady state output. d) Let z(t) be the unit step response of a system with a transfer function K(s + a) G(s) = s+ K If z (0) = 10 and z(0) 100, then what are the values of 'a and 'K? %3D
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