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Q2. (a) For a first order process plant with a time constant of 5 seconds and a gain of 2, determine a controller gain K(s) = K in a unity feedback system such that the closed-loop time constant is placed at TCL = 0.5. (b) Sketch the open-loop and closed-loop time responses of the system in (a) to a unit step input, noting carefully the steady state and time constant of both systems. (c) Given K(s) = K/s, find the closed-loop transfer function and calculate the damping factor and natural frequency for K = 1. Sketch the closed loop response to a unit step for this gain. (d) Find the range of gain K for which the closed-loop system in (c) is under-damped, critically damped or over-damped.

          Q2. (a) For a first order process plant with a time constant of 5 seconds and a gain of 2, determine a controller gain K(s) = K in a unity feedback system such that the closed-loop time constant is placed at TCL = 0.5.
(b) Sketch the open-loop and closed-loop time responses of the system in (a) to a unit step input, noting carefully the steady state and time constant of both systems.
(c) Given K(s) = K/s, find the closed-loop transfer function and calculate the damping factor and natural frequency for K = 1. Sketch the closed loop response to a unit step for this gain.
(d) Find the range of gain K for which the closed-loop system in (c) is under-damped, critically damped or over-damped.

Q2. (a) For a first order process plant with a time constant of 5 seconds and a gain of 2, determine a controller gain K(s) = K in a unity feedback system such that the closed-loop time constant is placed at TCL = 0.5.
(b) Sketch the open-loop and closed-loop time responses of the system in (a) to a unit step input, noting carefully the steady state and time constant of both systems.
(c) Given K(s) = K/s, find the closed-loop transfer function and calculate the damping factor and natural frequency for K = 1. Sketch the closed loop response to a unit step for this gain.
(d) Find the range of gain K for which the closed-loop system in (c) is under-damped, critically damped or over-damped.

Added by Jeffery M.

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