Question

Q1. Consider the unity feedback control system with a PI controller shown below: Gc(s) = k1 + k2/s, G(s) = 1/(s + 10) a) Determine the closed-loop transfer function and the characteristic equation of this system? b) Determine the range of k1 and k2 for which the closed-loop control system is stable. c) Let k1 = 1, k2 = 1, compute the steady-state error ess for a unit-ramp input, U(s) = 1/s^2? d) How woud you modify the PI controller to get ess = 0? Justify your answer.

          Q1. Consider the unity feedback control system with a PI controller shown below:

Gc(s) = k1 + k2/s, G(s) = 1/(s + 10)

a) Determine the closed-loop transfer function and the characteristic equation of this system?
b) Determine the range of k1 and k2 for which the closed-loop control system is stable.
c) Let k1 = 1, k2 = 1, compute the steady-state error ess for a unit-ramp input, U(s) = 1/s^2?
d) How woud you modify the PI controller to get ess = 0? Justify your answer.

Q1. Consider the unity feedback control system with a PI controller shown below:

Gc(s) = k1 + k2/s, G(s) = 1/(s + 10)

a) Determine the closed-loop transfer function and the characteristic equation of this system?
b) Determine the range of k1 and k2 for which the closed-loop control system is stable.
c) Let k1 = 1, k2 = 1, compute the steady-state error ess for a unit-ramp input, U(s) = 1/s^2?
d) How woud you modify the PI controller to get ess = 0? Justify your answer.

Added by Daniel A.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

08/28/2023

Step 1

The controller transfer function is given as G(a) = a + 1/s, and the process transfer function is given as G(s) = k / (s(s+10)). Multiplying these two transfer functions, we get the closed-loop transfer function: G(s) = G(a) * G(s) = (a + 1/s) * (k / Show more…

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Q1. Consider the unity feedback control system with a PI controller shown below: a) Determine the closed-loop transfer function and the characteristic equation of this system. b) Determine the range of k for which the closed-loop control system is stable. c) Let k = l. Compute the steady-state error ess for a unit-ramp input, U(s). d) How would you modify the PI controller to get ess = 0? Justify your answer.