Question

Steady-State Error [4 pts] For the transfer functions in (1) and (2) determine system type, error constants and steadystate error for the inputs: 3.323u(t),2.3323tu(t) and 0.003323t2u(t).

G(s)= 420(s+4)(s+12)(s+15)/ s(s+38)(s²+7s+28)
G(s)= 60(s+3)(s+4)(s+8)// s² (s+6)(2s+17)

Answer 1

To determine the steady-state error for the given transfer functions, we need to determine the system type, error constants, and use the appropriate formulas to calculate the steady-state error.

Step-by-step explanation:

To determine the steady-state error for the given transfer functions, we first need to determine the system type and error constants. For the transfer function G(s), the system type can be found by counting the number of poles at the origin, which is 1. Therefore, the system type is 1. The error constants can be calculated using the formula:

Kp = lim(s→0) G(s)

Kv = lim(s→0) s G(s)

Ka = lim(s→0) s² G(s)

Once the error constants are determined, the steady-state error can be calculated using the formula:

ess = 1 / (1 + Kp) for a unit step input

ess = 1 / Kv for a ramp input

ess = 1 / Ka for a parabolic input