For the transfer functions given in the control system in the figure, find the steady-

Question

For the transfer functions given in the control system in the figure, find the steady-state error (permanent error) for the relevant E(s) and approximately plot the response curve for the respective input. Note: Determine the steady-state error (Ess) and steady-state response (Yss), and on the plotted curve, indicate the rise time (Tr), peak time (Tp), settling time (Ts1), maximum overshoot (M), and steady-state regions.If any informations missing you can assume things in solutions

For the transfer functions given in the control system in the figure, find the steady-state error (permanent error) for the relevant E(s) and approximately plot the response curve for the respective input. Note: Determine the steady-state error (Ess) and steady-state response (Yss), and on the plotted curve, indicate the rise time (Tr), peak time (Tp), settling time (Ts1), maximum overshoot (M), and steady-state regions.If any informations missing you can assume things in solutions

Answer

1. Input Type:

  • Specify the input type (step, ramp, parabolic, etc.) to determine the relevant error constant for G(s).

2. Steady-State Error:

  • Use appropriate error formulas based on the input type and G(s)’s type:
    • For step input: Ess = 1/(1 + Kp), where Kp is the position error constant.
    • For ramp input: Ess = 1/Kv, where Kv is the velocity error constant. (Consider other formulas for different inputs as needed.)

3. Response Curve Approximation:

  • Consider these general characteristics for a step response:
    • Rise Time (Tr): Time for output to rise from 10% to 90% of final value.
    • Peak Time (Tp): Time for output to reach its first peak.
    • Maximum Overshoot (M): Percentage by which output exceeds final value.
    • Settling Time (Ts1): Time for output to settle within a specified tolerance (e.g., 2% or 5%) of final value.
    • Steady-State Region: Time after settling time where output remains essentially constant.
  • Sketch a curve reflecting these characteristics, approximating their values based on system dynamics and assumptions.

Explanation:

Please refer to solution in this step.

4. Additional Considerations:

  • Closed-Loop Transfer Function: Analyze the system’s closed-loop transfer function, T(s) = G(s)H(s) / (1 + G(s)H(s)), for more insights into response characteristics.
  • Simulation Tools: Use simulation software to obtain a more accurate response curve if needed.

5. Desired Information:

  • Specify the input type (step, ramp, etc.) for accurate Ess calculation.

I’m ready to assist further with specific calculations or explanations once you provide the input type.

Explanation:

Please refer to solution in this step.

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