Question

A unity feedback system has open loop transfer functionG(s) = {K/s(s+√2 K}Find K so that tₛ=1 sec for a 2% tolerance.Your answer must be an integer.

Answer 1

To find the value of K so that the settling time is 1 second for a 2% tolerance in a unity feedback system, the damping factor ζ is necessary.

Step-by-step explanation:

To find the value of K so that the settling time is 1 second for a 2% tolerance, we need to use the formula for settling time in a unity feedback system:

t_s = -ln(0.02)/(ζω_n)

where ζ is the damping factor and ω_n is the undamped natural frequency. In this case, the open loop transfer function is G(s) = K/(s(s+√2 K)). The undamped natural frequency is ω_n = √2 K and we need to find the value of K that satisfies t_s = 1. Plugging these values into the settling time formula:

1 = -ln(0.02)/(ζ√2 K)

From this equation, we can see that the value of ζ has been omitted. Without the value of ζ, we cannot determine K to satisfy the given settling time condition. Therefore, more information is required to find the exact value of K.