## 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

## 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.