i) Type of System:
To determine the type of system, we need to find the number of poles at the origin (s=0) in the open-loop transfer function G(s). In this case, the open-loop transfer function G(s) has three poles at the origin (s=0). Therefore, the type of system is a Type 3 system.

ii) Error coefficients:
For a Type 3 system, the error coefficients can be determined using the formula:

Kp = lim(s→0) G(s)
Ki = lim(s→0) sG(s)
Kd = lim(s→0) s^2G(s)

By evaluating the limits, we can find the values of the error coefficients Kp, Ki, and Kd.

iii) Steady State error for input as 1 + 8t + ୲మଶ:
To find the steady-state error for the given input, we can use the final value theorem. The final value theorem states that the steady-state value of the output can be found by evaluating the limit of sG(s) as s approaches 0.

By substituting the given input (1 + 8t + ୲మଶ) into the Laplace transform of the system, we can find the transfer function Y(s)/R(s). Then, by evaluating the limit of sY(s)/R(s) as s approaches 0, we can determine the steady-state error.

Please note that the given transfer function G(s) is not provided in a recognizable format. If you can provide the transfer function in a standard form, I can assist you further in determining the error coefficients and steady-state error.

Question

i) Type of System:
To determine the type of system, we need to find the number of poles at the origin (s=0) in the open-loop transfer function G(s). In this case, the open-loop transfer function G(s) has three poles at the origin (s=0). Therefore, the type of system is a Type 3 system.

ii) Error coefficients:
For a Type 3 system, the error coefficients can be determined using the formula:

Kp = lim(s→0) G(s)
Ki = lim(s→0) sG(s)
Kd = lim(s→0) s^2G(s)

By evaluating the limits, we can find the values of the error coefficients Kp, Ki, and Kd.

iii) Steady State error for input as 1 + 8t + ୲మଶ:
To find the steady-state error for the given input, we can use the final value theorem. The final value theorem states that the steady-state value of the output can be found by evaluating the limit of sG(s) as s approaches 0.

By substituting the given input (1 + 8t + ୲మଶ) into the Laplace transform of the system, we can find the transfer function Y(s)/R(s). Then, by evaluating the limit of sY(s)/R(s) as s approaches 0, we can determine the steady-state error.

Please note that the given transfer function G(s) is not provided in a recognizable format. If you can provide the transfer function in a standard form, I can assist you further in determining the error coefficients and steady-state error.

Knowee AI · Accepted Answer

i) Type of System:
To determine the type of system, we need to find the number of poles at the origin (s=0) in the open-loop transfer function G(s). In this case, the open-loop transfer function G(s) has three poles at the origin (s=0). Therefore, the type of system is a Type 3 system.

ii) Error coefficients:
For a Type 3 system, the error coefficients can be determined using the formula:

Kp = lim(s→0) G(s)
Ki = lim(s→0) sG(s)
Kd = lim(s→0) s^2G(s)

By evaluating the limits, we can find the values of the error coefficients Kp, Ki, and Kd.

iii) Steady State error for input as 1 + 8t + ୲మଶ:
To find the steady-state error for the given input, we can use the final value theorem. The final value theorem states that the steady-state value of the output can be found by evaluating the limit of sG(s) as s approaches 0.

By substituting the given input (1 + 8t + ୲మଶ) into the Laplace transform of the system, we can find the transfer function Y(s)/R(s). Then, by evaluating the limit of sY(s)/R(s) as s approaches 0, we can determine the steady-state error.

Please note that the given transfer function G(s) is not provided in a recognizable format. If you can provide the transfer function in a standard form, I can assist you further in determining the error coefficients and steady-state error.

For the unity feedback system having G(s) = ଶ଴ ሺ௦ ା ସሻ௦ ሺ௦ ା ଶሻሺ௦ ା ଵ଴ሻ .Determinei) Type of Systemii) Error coefficientsiii) Steady State error for input as 1 + 8t + ୲మଶ

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