Answered: 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…

Introductory Circuit Analysis (13th Edition)

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Author: Robert L. Boylestad

Publisher: PEARSON

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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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Step 1: Determine the given variables:-

VIEW

Step 2: (a) Calculating the position, velocity, and acceleration error constants:-

VIEW

Step 3: (a) Calculating the steady-state error for step, ramp, and parabolic inputs:-

VIEW

Step 4: (b) If we use a proportional controller:-

VIEW

Step 5: (c) the controller necessary to give zero steady-state error for a ramp input:-

VIEW

Step 6: (d) the controller necessary to give zero steady-state error for a parabolic input:-

VIEW

Solution

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Similar questions

2. Consider the feedback control system shown in Figure 2. a) Determine the steady-state error (ess) for a step input in terms of thed gain, K. b) Determine the steady-state error when K = 4. c) Determine the sensitivity Sg. d) How does the gain K effects the steady-state error in this system? Controller Process K(s + 50) (s + 200) 46.24 R(s) Y(s) s2 + 16.7s + 72.9 Sensor 425 s+ 425 Figure 2. Feedback control system
Problem #3 The following transfer function model was developed for the final control element, process, and measuring element of a feedback control system: G,G,Gm (10s +1)* (a) Determine the necessary and sufficient conditions for closed-loop stability for a PI controller. (b) From the conditions in part-a, obtain a relationship for ti in terms of Ke that will guarantee stability. Are there any values of t¡ that will guarantee stability for all values of Kc?
Q.4. Consider a unity feedback control system with feed forward :transfer function is .Q.4 G(s) 12(s+2.5) s (s² + 5s +11) A) It is desired to make the damping ratio (5) of the dominant closed-loop poles equal to (0.5) and to increase the undamped natural frequency (w) to (5 rad/sec) and the static velocity error constant to (K, = 60 sec-1). Design an appropriate compensator to meet all the performance specifications.? B) Check the stability of this system with compensator and without it? (

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