(Solved): 4) Determine the steady-state error for constant and ramp inputs for canonical systems with the fo ...

Expert Answer

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Steady-state error:

It is the error when the time reaches   of its value. By making use of final value theorem, the steady-state error (ess) is used to compute.

For an error signal, the steady-state error, ess =   s.E(s)

For a system, the error signals is obtained from its block diagram as




The input signal : R(s)

The output signal : C(s)

The error signal, E(s) = R(s) - H(s) . C(s)

Also, C(s) = E(s) . G(s)

Then,

E(s) = R(s) - H(s) . E(s) . G(s)

E(s) =    --------------> (1)
The steady-state error is given as ess = e(  ) =   s.   ---------------> (2)



The error function is depends upon the applied input signal and the open loop transfer function (G(s)) and the feedback transfer function (H(s)).