Question

The step error constant kₚ of a system G(s)=1/(s+2)(s+3)G(s) with unity feedback(H(s) = 1)) is:

a. 0
b. [infinity]
c. 1/6
d. None of the above

Answer 1

The step error constant kₚ for the system G(s)=1/(s+2)(s+3) with unity feedback is 1/6, corresponding to option c.

Step-by-step explanation:

The step error constant k₀ for a system G(s)=1/(s+2)(s+3) with unity feedback (H(s) = 1) is determined by analyzing the given system's type and finding the error coefficient corresponding to a step input. For a type 0 system, which our system is since the system's open-loop transfer function has no free integrators (no poles at the origin), k₀ is given by the DC gain of the system G(s). The DC gain is the value of G(s) as s approaches zero.

In this case, G(0) = 1/(0+2)(0+3) = 1/6. Therefore, the step error constant k₀ is 1/6, which corresponds to option c.