determine error coefficient and static error for unity and non unity feedback system represented by g(s) = (s+2)/(s.(s+1)(s+10)) and h(s)=1
To determine the error coefficient and static error for the unity and non-unity feedback systems, the system can be represented in control system block diagrams and the relevant formulas can be applied.
Given the transfer function of the system is G(s) = (s + 2) / (s * (s + 1) * (s + 10)) and H(s) = 1 for unity feedback.
1. Unity feedback system:
The system can be represented in a control system block diagram as follows:
G(s) --> + -->|G(s)|--> C(s) --> + --> E(s) --> y(s)
^ | |
| + V
| - H(s) = 1
+------<----------
Where:
- G(s) is the transfer function of the system.
- H(s) is the transfer function of the feedback.
- C(s) is the controller (input).
- E(s) is the error signal.
- y(s) is the output signal.
The transfer function of the closed-loop system with unity feedback is given by:
T(s) = G(s) / (1 + G(s) * H(s))
Substitute the given transfer functions into the equation:
T(s) = (s + 2) / (s * (s + 1) * (s + 10) + (s + 2))
To determine the error coefficient:
Kp = lim(s->0) G(s) * H(s)
Kp = lim(s->0) (s + 2) / (s * (s + 1) * (s + 10))
Kp = 2 / (0 * 1 * 10)
Kp = 0
To determine the static error:
Ess = 1 / (1 + Kp)
Ess = 1 / (1 + 0)
Ess = 1
Therefore, for the unity feedback system, the error coefficient is 0, and the static error is 1.
2. Non-unity feedback system:
For the non-unity feedback system with H(s) = 1, the same steps as above can be followed to determine the error coefficient and static error. The main difference will be in the block diagram representation.
The transfer function of the closed-loop system in the non-unity feedback case would be:
T(s) = G(s) / (1 + G(s) * H(s))
The error coefficient and static error can be calculated in the same way as done for the unity feedback system.
By following these steps, the error coefficient and static error for the non-unity feedback system with G(s) = (s + 2) / (s * (s + 1) * (s + 10)) and H(s) = 1 can be determined.