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
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
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2587a113-5ca6-415a-ac64-2fd0e756bc9a%2F018145db-72cc-448c-9be6-7ee9c54e64c0%2F2v22lg9_processed.png&w=3840&q=75)
Transcribed Image Text: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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Step 1: Determine the given variables:-
VIEWStep 2: (a) Calculating the position, velocity, and acceleration error constants:-
VIEWStep 3: (a) Calculating the steady-state error for step, ramp, and parabolic inputs:-
VIEWStep 4: (b) If we use a proportional controller:-
VIEWStep 5: (c) the controller necessary to give zero steady-state error for a ramp input:-
VIEWStep 6: (d) the controller necessary to give zero steady-state error for a parabolic input:-
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