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A proportial controller Kₚ is being used with a 1ˢᵗ -order system G(s) = K/(Ts+1) in unity feedback system. Increasing Kₚ will

A. increase the time constant and decrease the eₛₛ to step inputs
B. decrease the time constant and decrease the eₛₛ to step inputs
C. decrease the time constant and increase the eₛₛ to step inputs
D. increase the time constant and increase the eₛₛ to step inputs

1 Answer

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Final answer:

Increasing the proportional gain Kp in a unity feedback control system with a first-order process will decrease the steady-state error ess to step inputs, but will not affect the time constant of the system. The correct answer is option B.

Step-by-step explanation:

The question pertains to the effect of changing the proportional gain, Kp, on a first-order system described by the transfer function G(s) = K/(Ts+1), where K is the system gain and T is the system time constant, when used within a unity feedback control system. Increasing Kp impacts the system's response to step inputs, particularly in terms of its time constant and steady-state error ess.

When Kp is increased, the overall system gain increases. This does not change the time constant T of the system, which is a property of the system itself. Thus, an increase in Kp does not affect the time constant. However, for a step input, the steady-state error ess is inversely related to the overall system gain. Therefore, increasing Kp will ultimately decrease the steady-state error ess but will not change the time constant.

The correct answer to the question is B. Increasing Kp will decrease the steady-state error ess to step inputs but will not change the time constant of the system.

User Marco Ferrari
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