---### Feedback Control System AnalysisFor the given feedback system, we will perform the following tasks:1. **Determine the System Type**2. **Calculate the Static Error Constants**3. **Find the value of \( K \) for a Steady-State Error of 0.01**---#### System Overview:Below is the block diagram of the given feedback control system:```plaintextR(s) --- ( + ) ---> E(s) --> [ K ] ------ ( + ) --> [ 1 / ( s(s^2 + 5s + 6) ) ] ---> C(s) - ^ | | S <-------------------------------- < ```- **\( R(s) \)**: Reference input- **\( E(s) \)**: Error signal- **\( K \)**: Proportional gain- **\( C(s) \)**: Output signal- **\( S \)**: Feedback path, simply \( s \) in this context#### Tasks:**a. Find the System Type**The system type is determined by the number of poles at the origin in the open-loop transfer function.Open-loop transfer function:\[ G(s)H(s) = \frac{K}{s(s^2 + 5s + 6)} \cdot s \]\[ = \frac{K}{s(s^2 + 5s + 6)} \]Taking the denominator:\[ s(s^2 + 5s + 6) = s^3 + 5s^2 + 6s \]There is **1 pole** at \( s=0 \), so the system type is **Type 1**.**b. Find the Value of the Static Error Constants**For a Type 1 system, we consider the velocity error constant \( \text{Kv} \).Velocity error constant \( \text{Kv} \):\[ \text{Kv} = \lim_{s \to 0} s G(s) \]Open-loop transfer function:\[ G(s) = \frac{K}{s(s^2 + 5s + 6)} \]\[ \text{Kv} = \lim_{s \to 0} s \left( \frac{K}{s(s^2 + 5s + 6)} \right) \]\[ \text{Kv} = \lim_{s

Answered: Image /qna-images/answer/1bff32f7-778a-4e7a-9e9c-933ec8370b59.jpg

Given the following feedback system, a. Find the System type b. Find the value of the static error constants c. Find the value of K to have an steady-state error of 0.01 R(s) + E(s) C(s) K 1 s(s2+5s+6) S

Given the following feedback system, a. Find the System type b. Find the value of the static error constants c. Find the value of K to have an steady-state error of 0.01 R(s) + E(s) C(s) K 1 s(s2+5s+6) S

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

See similar textbooks

Related questions

Q: For the unity feedback system shown in figure 1, R(s) + K(s+10)(s+20) (s+30)(s²-20s+200) Figure 1 a.…

A: In this question we need to draw the root locus and find the range of gain K that makes the system…

Q: Q1) Design the value of gain K, for the feedback control system shown in Figure below so that the…

Q: A unity feedback system has the open loop transfer function shown below. Find the imaginary axis…

A: According to the question, for the given functionWe need to find the imaginary axis crossing of the…

Q: Given the uncompensated unity feedback system in Figure 8 below.

Q: A circuit is shown to the right. a. Is this an example of positive feedback or negative feedback? b.…

A: Given: An op-amp circuit. To find: a) Is the given circuit an example of positive feedback or…

Q: Design the state feedback controller so that G(s) is %OS-10% of the system and the settling time…

A: Given data Overshoot percentage, %Mp=10% Settling time, Ts=1 sec Open loop tarnsfer function (OLTF),…

Q: Q3: For the unity feedback system with G(s)= (s+3)(s² +4s+5) Do the following: a). Find the location…

Q: Q.6) For the unity feedback system of Figure below, where Rs) K (s² –3s +2) G(s)= 2. s*+s Sketch the…

Question

---

### Feedback Control System Analysis

For the given feedback system, we will perform the following tasks:

1. **Determine the System Type**
2. **Calculate the Static Error Constants**
3. **Find the value of \( K \) for a Steady-State Error of 0.01**

---

#### System Overview:

Below is the block diagram of the given feedback control system:

```plaintext
R(s) --- ( + ) ---> E(s) --> [ K ] ------ ( + ) --> [ 1 / ( s(s^2 + 5s + 6) ) ] ---> C(s)
- ^ |
| S
<-------------------------------- <
```

- **\( R(s) \)**: Reference input
- **\( E(s) \)**: Error signal
- **\( K \)**: Proportional gain
- **\( C(s) \)**: Output signal
- **\( S \)**: Feedback path, simply \( s \) in this context

#### Tasks:

**a. Find the System Type**

The system type is determined by the number of poles at the origin in the open-loop transfer function.

Open-loop transfer function:
\[ G(s)H(s) = \frac{K}{s(s^2 + 5s + 6)} \cdot s \]

\[ = \frac{K}{s(s^2 + 5s + 6)} \]

Taking the denominator:
\[ s(s^2 + 5s + 6) = s^3 + 5s^2 + 6s \]

There is **1 pole** at \( s=0 \), so the system type is **Type 1**.

**b. Find the Value of the Static Error Constants**

For a Type 1 system, we consider the velocity error constant \( \text{Kv} \).

Velocity error constant \( \text{Kv} \):
\[ \text{Kv} = \lim_{s \to 0} s G(s) \]

Open-loop transfer function:
\[ G(s) = \frac{K}{s(s^2 + 5s + 6)} \]

\[ \text{Kv} = \lim_{s \to 0} s \left( \frac{K}{s(s^2 + 5s + 6)} \right) \]

\[ \text{Kv} = \lim_{s

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1: Given block diagram and what we need to find:

VIEW

Step 2: Finding G(s) Of the system:

VIEW

Step 3: Finding Type of the system and static error constants:

VIEW

Step 4: Finding the value of K:

VIEW

Solution

VIEW

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.

Similar questions

FOLLOW THE FORMAT ON THE NEXT PHOTO NOT FOLLOWING THE FORMAT MEANS DOWNVOTE
For the system shown in the attached image: i. Find the values of "K1" and "a" to produce a settling time of 4 seconds with a 5% overshoot for the step response input. Using transient specifications, find the desired pole location and use this pole location to find the gain K. ii. Find the value of K to yield a major-loop response with a 10% overshoot for the step input. (The dominant pole position for 10% overshoot is -0.935 + j1.28. You can use the magnitude property of the root locus.)
Find the Nyquist plot. ( need only handwritten solution .otherwise downvote.)
Determine the closed-loop transfer function of the system shown in Figure Qla. The plant transfer functions are: (a) g1(s) = 92(s) = s+ 2 and the feedback transfer functions are: h1(s) = 0.25s 1 h2(s) = +1 R(s) C(s) 81(s) 82(s) hi(s) h2(s) Figure Qla (b) (i) Using the Routh-Hurwitz criterion, find the range of values of parameter 'a' for which the system shown in Figure Q1b is stable. I Is the system stable for a = 30? If not, how many positive (unstable) poles does it have? (ii) R(s) E(s) C(s) a s+4 g2 +s+9
8. Prove that Ry S B(R. + R) is the required condition for an optimum design of the voltage-feedback circuit.
An application demands that a sinusoidal pressure variation of 250 Hz be measured with no more than 2% dynamic error. In selecting a suitable pressure transducer from a vendor catalog, you note that a desirable line of transducers has a fixed natural frequency of 600 Hz but that you have a choice of transducer damping ratios of between 0.5 and 1.5 in increments of 0.05. Select a suitable transducer.
For a unity feedback system having K (s2 + 6s + 8) G(s) = %3D s2 + 4s + 13 a) Determine the asymptotes. b) Draw the root locus. c) Find the gain at the point (-3+tj0).
FOLLOW THE FORMAT ON THE NEXT PHOTO NOT FOLLOWING THE FORMAT MEANS DOWNVOTE
I need a detailed solution to this question Do not give me a solution found on the Internet, please and thank you
last 3 digit of id is: 035 so, x= 035
Needs solution now
A unity negative feedback system has an open loop transfer function k s(s+10) for the system to have a damping ratio of 0.25 the value of k must be Select one: a. non of the choices b. 200 c. 10 d. 100 e. 400 G₂