Question

The transfer function for a plant in a motor position control is given by G(s)= A/s(s+α)

Find A and a such that the unity feedback control system has a static velocity error constant, Kv-20 and damping ratio of 0.707.

Answer 1

To find A and α for a motor position control system with a given static velocity error constant and damping ratio, substitute the transfer function into the equations for Kv and ζ and solve them simultaneously.

Step-by-step explanation:

The transfer function for a motor position control system is given by G(s) = A/s(s+α). To find the values of A and α such that the unity feedback control system has a static velocity error constant Kv-20 and damping ratio of 0.707, we need to solve the following equations:

Kv = lims->0 sG(s) = -20, ζ = 0.707

By substituting the given transfer function into the equation for Kv, we get -20 = A/α. And by substituting the given transfer function into the equation for ζ, we get ζ = 1/(2√(α)). Solving these equations simultaneously will give us the values of A and α.