Given a Bode diagram of a dynamic system, shown in Fig. 4: (a) Find the transfer function of the system G(s) (asymptotes are drawn for you and their slopes are indicated) T (b) Derive the open-loop system response to a harmonic input 2 cos 10t+- (c) Assuming a negative unity feedback configuration: Determine the gain and phase margins of the system Is the system closed-loop stable? Verify your answer using Nyquist plot (use software to generate Nyquist plot and explain how it confirms your conclusion of closed-loop stability/instability) (d) Assuming a proportional controller with gain Kp and negative unity feedback configuration: Can the system be destabilized by a finite gain proportional controller? If yes, find the gain K, that destabilizes the system. If not, explain why not. (e) Find Kp for the system to have a phase margin 20⁰ (f) What is the system phase margin when Kp = 10? At this value of Kp: What is the steady-state error of the closed-loop system to a step input of magnitude A? ● ● ● What is the steady-state error of the closed-loop system to a ramp input of magnitude A? NOTE: parts (b), (c), (e), (f) need to be solved graphically

Given a Bode diagram of a dynamic system, shown in Fig. 4: (a) Find the transfer function of the system G(s) (asymptotes are drawn for you and their slopes are indicated) T (b) Derive the open-loop system response to a harmonic input 2 cos 10t+- (c) Assuming a negative unity feedback configuration: Determine the gain and phase margins of the system Is the system closed-loop stable? Verify your answer using Nyquist plot (use software to generate Nyquist plot and explain how it confirms your conclusion of closed-loop stability/instability) (d) Assuming a proportional controller with gain Kp and negative unity feedback configuration: Can the system be destabilized by a finite gain proportional controller? If yes, find the gain K, that destabilizes the system. If not, explain why not. (e) Find Kp for the system to have a phase margin 20⁰ (f) What is the system phase margin when Kp = 10? At this value of Kp: What is the steady-state error of the closed-loop system to a step input of magnitude A? ● ● ● What is the steady-state error of the closed-loop system to a ramp input of magnitude A? NOTE: parts (b), (c), (e), (f) need to be solved graphically

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: Q5: a) Consider a unity feedback system with the forward transfer function: (s2 + 25) G(s) = %3D…

Q: Consider a unity-feedback system with the process transfer function 1 P(s) (s+1)² Answer the…

A: According to question: a) The integral controller that gives a closed loop pole at s=-a is…

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

Q: Q1 A unity feedback system has the loop transfer function K G(s) s(s+ a) If its time response is to…

A: This question belongs to control system . It is based on the standard specifications of second order…

Q: a : for the unity feedback system G(s)=k/s(s+n). determine k and n such that the response for the…

A: 3 a) The system output and structure of the closed-loop around the system as introduced. The…

Q: Consider the following feedback system: Ris) Cs) C(s) G(s) where C(s) is a phase-lag compensator…

A: Consider the following system : Cs=phase-lag compenstatorwhen uncompenstator Cs=1 Select the most…

Q: Consider a system with open loop transfer function in unity feedback configuration 10 G(s) =…

Q: PROBLEM-2 ( ): Consider a unity negative feedback system with forward transfer function of 9 1…

Q: Given is a feed-forward transfer function G(s) of some system, where K is an adjustable parameter. K…

A: Due to guidelines. we can solve only first three sub part of the question . if you want another…

Q: (2) suppose the open-loop amplifier (or simply the OpAmp) in the above feedback amplifier has the…

A: The magnitude response is the ratio of the output signal's frequency amplitude to the input signal's…

Q: Q5. For the unity feedback system shown in Fig (5), where R(s) Do the following a. Sketch the root…

A: Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: A unity Feedback system is characterized by open loop transfer function G(s) = K / S(S+25) The…

Q: Q3: Consider non-minimum phase unity feedback system with the following open loop transfer function:…

Q: 2) A position control system uses the principle of velocity feedback, as shown in the following…

A: Please refer below pages.If you have any doubts feel free to ask.Explanation:Step 1: Step 2: Step 3:…

Q: The Phono-Solar PS250P-20-U single crystal (module) silicon photovoltaic panel system has dimensions…

Q: Q.2 (a) The open-loop gain of an amplifier is A = 60 dB. If the open-loop gain decreases by 30 pero…

A: a) We know the relation between open loop and closed loop gain as Af=A1+βAdAfAf=11+βA*dAA Given…

Q: ure 5 shows a current series feedback amplifier. The sampled current signal but current, I, flowing…

Q: B) Design a circuit using operational amplifiers, where the output voltage Yis given as, Y=…

A: Operational amplifier: An operational amplifier is an integrated circuit comprised of two input pins…

Q: Figure 1 shows a unity feedback system where the transfer function is given as 1 G(s): s(s² + 100s…

Q: 7.For the unity feedback closed-loop system with forward transfer function K G(s) = 2 +5s +1) (a)…

A: In this question ,we will find range of K for system stable..And staady state error for different…

Q: Use the Nyquist stability criterion to determine the ranges of K > 0 (if any) for which the…

A: For the system represented by the Bode plots, we need to determine the range of K>0 for which…

Q: Bx1000 f 1+j 5x10 , T(f)=

Q: a) The open loop transfer function of a unity feedback system is given by, K (1+0.25s)…

A: Given:Open loop transfer function of a unity feedback system, we need to sketch the root locus of…

Q: Consider a unitary feedback-controlled system with a direct chain transfer function given as. G(p)=-…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: R(s) Cs) 25 2

Q: C(s) A unity feedback system has a forward gain, K and a forward transfer function, G(s) = R(S) G(s)…

Q: fi. Aclosed-loop feedback system is shown in following figure R(s) K C(s) s(s–1)(s+5) 1+s (1) Find…

A: We will find close loop gain , and then we will find characteristics equation to find out range of k…

Q: Q2 Consider the unity feedback system with the open-loop transfor fruction K S(S + 1) [ (5²/₂25…

Q: (2) suppose the open-loop amplifier (or simply the OpAmp) in the above feedback amplifier has the…

A: The magnitude response is the ratio of the frequency amplitude of the output signal to the frequency…

Q: 7.For the unity feedback closed-loop system with forward transfer function K G(s) = 2 +5s +1) (a)…

Q: SemilogPaper.pdf Draw the linear approximation to the log- magnitude on semilog paper for the open…

A: Given

Q: R(s) C(s) K G(s)

A: Gain margin and phase margin is calculated for open loop transfer function GA=M=[G(jw)H(jw)] here we…

Q: 2) The amplifier circuit shown below has the following parameters: Rid = 200k, ro= 2k2, an open loop…

A: Since you have posted the questions with multiple subpart so we are supposed to answer 3 subpart.

Q: Q2) Given the transfer function of the system (plant) as follows: B(s) s+6 A(s) 4s2 – 8s + 5 1-…

Q: Consider following unity feedback system. R(s) K C(s) s(s + 1) (s + 2) Determine the value of K such…

A: determine the value of K such that the natural un damped frequency of dominant complex conjugate…

Q: d) The magnitude and phase shift of the loop-gain for a feedback amplifier are collected in a table…

A: Step 1: Step 2: Step 3: Step 4:

Q: Q4. Consider the unity-feedback system whose open-loop transfer function is [lead-lag compensator] K…

A: Step 1: Step 2: Step 3: Step 4: Step 5: Step 6: Step 7:

Q: In free response systems, as time goes to zero the output approaches infinity. Select one: O True O…

A: Free response system means These are the systems which have 0 studies state value means these…

Q: 3. If the unity feedback system is given by the open loop transfer function G(s) = ks2 / [(s+5)…

A: To calculate phase angle we convert the given transfer function into iw

Question

100%

Given a Bode diagram of a dynamic system, shown in Fig. 4:
(a) Find the transfer function of the system G(s)
(asymptotes are drawn for you and their slopes are indicated)
(b) Derive the open-loop system response to a harmonic input 2 cos 10t+ 44
(c) Assuming a negative unity feedback configuration:
Determine the gain and phase margins of the system
Is the system closed-loop stable? Verify your answer using Nyquist plot (use software
to generate Nyquist plot and explain how it confirms your conclusion of closed-loop
stability/instability)
(d) Assuming a proportional controller with gain K₂ and negative unity feedback
configuration:
Can the system be destabilized by a finite gain proportional controller? If yes, find the
gain Kp that destabilizes the system. If not, explain why not.
(e) Find Kp for the system to have a phase margin 20⁰
(f) What is the system phase margin when K₂ = 10? At this value of Kp:
What is the steady-state error of the closed-loop system to a step input of magnitude
A?
|G(jw)|, dB
●
ø, degrees
●
NOTE:
parts (b), (c), (e), (f) need to be solved graphically
What is the steady-state error of the closed-loop system to a ramp input of magnitude
A?
0
-20
-40
-60
-80
0.01
50
0
-50
-100
-150
0.01
20 dB dec
0.1
0.1
1
1
0 dB/dec
w, rad/sec
w, rad/sec
Figure 4
10
10
↑hump
40 dB/dec
100
100
1000
1000

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2: Solution (a)

Step 3: Solution (b)

Step 4: Solution (c)

Step 5: Solution (c)

Step 6: Solution (d)

Step 7: Solution (e)

Step 8 Solution ( f )

VIEW

Step 9 Solution ( f )

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 9 steps with 3 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

Consider the negative feedback system shown in Figure (We assume that the value of gain K is nonnegative.) For this system, Sketch the root-locus plot. R(s) K s(s+ 1) (s+2) C(s)
Consider an amplifier with the loop gain function T(f), where Bis the feedback gain and fep is the frequency of the dominant pole. B(10*) T(f)=: 1+j 1+j 10 (i) Determine ß such that the amplifier has a low-frequency closcd-loop gain of 50. (ii) Determine frD such that the amplifier has a phase margin of 45 degrees.
Q2. Consider a unity-feedback system whose open-loop transfer function is: Y Ke-0.8s G(s) = R(S) = (s+1) Using the Nyquist plot, determine the critical value of K for stability? (
A unity feedback system is shown in Figure Q1. R(s) C(s) K G(S) Figure Q1 Given that K(s-4s +8) G(s) = (s+4)(s +10) %3D From the given open-loop transfer function, G(s) detemine the following: ) The imaginary erossing of the root locus of the closed-loop transfer function. Hence the gain at that crossing. (i) The arrival angle of the root locus of the closed-loop transfer function. (iii) The breakaway point of the root locus of the closed-loop transfer function is given as s=-6.05. Hence, determine the gain at that point. (iv) Using the information gathered from (i) until (ii), sketch the root locus of the closed- loop transfer fiunction. (v) Hence determine the range of gain K for the underdamped stable system and the critically damped system.
Ex. 440. G(s)=k/ ( (s+5) (s+ 6)) is the FTF of a unity-feedback closed-loop system. respect to k. Determine the number of asymptotes, N. in degrees between the asymptotes. Determine angles, [B,C], in degrees of the asymptotes (let B
I need answer in handwritten
answer fast
A dynamic system in a negative unity feedback configuration has the root locus, shown in Fig. 1. Use the given root locus plot to answer the following questions: (a) What are the open-loop poles and zeros of this system? (b) Is the open-loop transfer function stable? Explain. (c) For what range of values of the gain K is the closed-loop system stable? (d) For K = 4: a. What are the closed-loop poles? b. What are the dominant poles of the closed-loop system (if exist)? c. What is the settling time of the closed-loop system? d. What is the peak time of the closed-loop system? e. What is the max. overshoot of the closed-loop system? (e) What is the maximum damping of the dominant closed-loop poles (f) For what value of K does the closed-loop system have a minimum settling time? (g) For the value of K in (f): a. What is the natural frequency of the dominant poles of the system? b. List all the poles of the closed-loop system (h) For what value(s) of the gain K does the closed-loop system…
3) An amplifier has an open-loop gain given by AOL = 1 1+jf/10* 100 (1+√√√3) and a feedback fraction ß = Use the graphical method to plot the closed-loop frequency response of Av. i) Determine the phase margin of this amplifier and write down the expression for "rate of closure (ROC)" in this context. ii) Analyze the stability if ROC ≥ 40 dB/dec.
as a = 12/ ( 5² + 85 + 12) Suppose the plant in a closed- loop feedback control System is modelled second order system with transfer function defined as: Gr(s) = ((s)/R(S) ⒸSketch the closed loop feedback control system diagram 1 showing the input rtt), controller Gr(s), plant Gris), output (it) and unity feedback. the system. the system if a unit Sketch the zero-pole location diagram of Ⓒ find the output response c(t) of step input ult) is applied to the system. Find the most suitable sampling frequency and the period that must be used for this system to sensor delay of 0.055 1695 13 meet a Q3
Q2. For the unity feedback system blow, K where G(S) S(5+3) (5+5) find the range of gain, K, for stability, instability and the value of K for maginal Stability. For marginal Stability, also find the frequency of ocillation. Use the Nyquist Criterion.