Below is given the forward transfer function of a unity-feedback system.a) Determine the position, velocity, and acceleration error constants Kp, Kv, and Ka and the steady-state error for step, ramp, and parabolic inputs;b) If possible, use a proportional controller to give a steady-state error for ramp input of e_ss(ramp) ≤ 0.01;c) Determine the controller necessary to give zero steady-state error for a ramp input;d) Determine the controller necessary to give zero steady-state error for aparabolic input. The image presents a transfer function in control systems, expressed in the Laplace domain:\[ G(s) = \frac{20(0.2s + 1)}{s(2s + 1)} \]### Explanation:- **Numerator**: The numerator of the transfer function is \(20(0.2s + 1)\). This represents the zeros and gain of the system. - **Denominator**: The denominator is \(s(2s + 1)\), indicating the poles of the system.### Components:1. **Zeros**: A zero at \(s = -5\) derived from \(0.2s + 1 = 0\).2. **Poles**: - One pole at \(s = 0\). - Another pole at \(s = -\frac{1}{2}\) from \(2s + 1 = 0\).This type of function is used to model and analyze the behavior of dynamic systems.

Answered: Below is given the forward transfer…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

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Below is given the forward transfer function of a unity-feedback system.
a) Determine the position, velocity, and acceleration error constants Kp, Kv, and Ka and the steady-state error for step, ramp, and parabolic inputs;
b) If possible, use a proportional controller to give a steady-state error for ramp input of e_ss(ramp) ≤ 0.01;

c) Determine the controller necessary to give zero steady-state error for a ramp input;
d) Determine the controller necessary to give zero steady-state error for a
parabolic input.

The image presents a transfer function in control systems, expressed in the Laplace domain:

\[ G(s) = \frac{20(0.2s + 1)}{s(2s + 1)} \]

### Explanation:

- **Numerator**: The numerator of the transfer function is \(20(0.2s + 1)\). This represents the zeros and gain of the system.
- **Denominator**: The denominator is \(s(2s + 1)\), indicating the poles of the system.

### Components:

1. **Zeros**: A zero at \(s = -5\) derived from \(0.2s + 1 = 0\).
2. **Poles**:
- One pole at \(s = 0\).
- Another pole at \(s = -\frac{1}{2}\) from \(2s + 1 = 0\).

This type of function is used to model and analyze the behavior of dynamic systems.

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