determine error coefficient and static error for unity and non unity feedback system represented by g(s) = 1/(s.(s+1)(s+10)) and h(s)=1
To determine the error coefficient and static error for the unity feedback system represented by G(s) = 1/(s(s+1)(s+10)) and H(s) = 1, we will first identify which type of system it is, whether type 0, type 1, or type 2.
The type of a system is determined by the number of poles at the origin after subtracting the number of zeros at the origin. In this case, there are no zeros at the origin (since the transfer function doesn't have any zeros) and there is one pole at the origin (s), so the system is a type 1 system.
Next, we will calculate the error coefficient for a type 1 system. The error coefficient is given by:
Kp = lim(s->0) G(s)H(s)
Substitute the given transfer functions into the equation:
Kp = lim(s->0) 1/(s(s+1)(s+10))
Kp = 1/(0*(0+1)(0+10)) = 1/0 = ∞
Since the error coefficient is infinity, the system does not have a finite steady-state error when subjected to a unit step input.
For a non-unity feedback system, the static error is given by:
Ess = 1/(1 + Kp)
Ess = 1/(1 + ∞) = 1
Therefore, for the system represented by G(s) = 1/(s(s+1)(s+10)) and H(s) = 1, the error coefficient is infinity and the static error is 1 for a non-unity feedback system.