Homework Answers
a. In polynominal form simply replace 'jw' by 's'. The transfer function is
0.1 s + 100
------------------------
1e-06 s^2 + 0.0052 s + 1
b. Matlab code for bode plot:
s=tf('s');
g=100*(1+0.001*s)/((1+0.005*s)*(1+0.0002*s));
margin(g)
c. From the transfer function the lower cutoff frequency is
1000Hz.
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3. You are given a system transfer function belowl 20 points): 100 (1 +0.001 je) TF(a) a. Convert...
For the system transfer function given by: s +10 $2 x (82100.+10) 1. Identify each term in the tr...
For the system transfer function given by: s +10 $2 x (82100.+10) 1. Identify each term in the transfer function (constant, poles, zeros) (a) For any constant terms, what is the dB magnitude? What is the phase angle? (b) For any real poles not at the origin, what is the break frequency? (c) For any real zeros not at the origin, what is the break frequency? 2. Give the value of the DB magnitude and phase angle at w =...
For each filter mentioned in the following cases, first simulate the circuit using Multisim. You can get a plot of the transfer function that is called the Bode plot. From the right toolbar, select &...
For each filter mentioned in the following cases, first simulate the circuit using Multisim. You can get a plot of the transfer function that is called the Bode plot. From the right toolbar, select "Bode Plotter". Change initial (I) and final (F frequencies to 1Hz and 200 KHz, respectively. Use a Voltage AC source as the input signal. You do not need to change any parameter from voltage AC source Connect "Bode Plotter" to input and output of your circuit...
Problem 3 (20 points) A Bode plot is a graph of the frequency response of a system. It is a combi...
Problem 3 (20 points) A Bode plot is a graph of the frequency response of a system. It is a combination of a magnitude plot, expressing the magnitude in dB of the frequency response, and a phase plot expressing the phase shift. Both quantities are plotted on a horizontal axis proportional to the logarithm of the frequency. Below is an example of a Bode plot created in Matlab. Bode Diagram 0 -20 3-40 E-60 -80 180 90 10 10 10...
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polyno...
Please do part C only, thank you.
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polynomials, ratios of polynomials, partial fraction expansions and transfer functions: see, for example, the commands roots, poly, conv, residue, zpk and tf (a) Use MATLAB to gener ate the continuous-time transfer function H5+15)( +26(s+72) s(s +56)2(s2 +5s +30) H(s) displaying the result in two forms: as (i) the given ratio of factors and (ii) a ratio of two polynomials. (b) Use...
For all problems -given a transfer function G(s) sketch the magnitude and phase characteristics in the...
For all problems -given a transfer function G(s) sketch the magnitude and phase characteristics in the logarithmic scale (i.e. Bode-plots) of the system using the following rules-of-thumb: i. "Normalize" the G(s) by extracting poles/zeros, substituting s-jw and writing the TF using DC-gain KO and time-constants i. Arange break-points (poles, zeros or on for complex-conjugate poles) in ascending order ii Based on the term Ko(ju)Fk, determine: initial slope of the magnitude-response asymptote for low frequencies as F k 20 dB/dec (e.g....
alpha = 5.0 beta = 7.1 zeta = 6.9 PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the pole...
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
Consider a negative feedback system whose open-loop transfer function is: G(s)H(s)=K/(s(s+1)) Write a MATLAB program to...
Consider a negative feedback system whose open-loop transfer function is: G(s)H(s)=K/(s(s+1)) Write a MATLAB program to obtain the root-locus plot of G(s)H(s). [2 marks] What are the locations of poles when K = 0.19. [2 marks] When K = 0.4, what are the locations of poles? [3 marks] Find values of the damping ratio, % overshoot and frequency when K = 0.4. [3 marks] Write a MATLAB program to obtain a bode plot of G(s)H(s) when K = 1. [2...
Let G,()+3s+5) , K-1 and Ge 1 I Determine the loop transfer function L(s)-KG.G. Use 'margin' command in matlab to generate the Bode Plot for L(s). (a) What are its gain and phase margins (the...
Let G,()+3s+5) , K-1 and Ge 1 I Determine the loop transfer function L(s)-KG.G. Use 'margin' command in matlab to generate the Bode Plot for L(s). (a) What are its gain and phase margins (these should be available in the plots). (b) Convert the gain margin in dB to absolute value. (c) For what value of the gain K would the closed loop system become marginally stable? (d) Show that, for this value of K, the closed loop system does...
Figure 1 Problem 3 For the system shown in the above figure, where G(s) a) Draw...
Figure 1 Problem 3 For the system shown in the above figure, where G(s) a) Draw a Bode diagram of the open-loop transfer function G(s) when K 10. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K-10? c) Determine the value of K such that the phase margin is 30°. What are the gain margin and the crossover frequencies with this K? Note: You can finish problems 2-3 with the help...
Simulation For each filter mentioned in the following cases, first simulate the circuit using Multisim. You can get a plot of the transfer function that is called the Bode plot. From the right toolba...
Simulation For each filter mentioned in the following cases, first simulate the circuit using Multisim. You can get a plot of the transfer function that is called the Bode plot. From the right toolbar, select "Bode Plotter". Change initial (I) and final (F) frequencies to 1Hz and 200 KHz, respectively. Use a Voltage AC source as the input signal. You do not need to change any parameter from voltage AC source. Connect "Bode Plotter" to input and output of your...
For the system transfer function given by: s +10 $2 x (82100.+10) 1. Identify each term in the transfer function (constant, poles, zeros) (a) For any constant terms, what is the dB magnitude? What is the phase angle? (b) For any real poles not at the origin, what is the break frequency? (c) For any real zeros not at the origin, what is the break frequency? 2. Give the value of the DB magnitude and phase angle at w =...
For each filter mentioned in the following cases, first simulate the circuit using Multisim. You can get a plot of the transfer function that is called the Bode plot. From the right toolbar, select "Bode Plotter". Change initial (I) and final (F frequencies to 1Hz and 200 KHz, respectively. Use a Voltage AC source as the input signal. You do not need to change any parameter from voltage AC source Connect "Bode Plotter" to input and output of your circuit...
Problem 3 (20 points) A Bode plot is a graph of the frequency response of a system. It is a combination of a magnitude plot, expressing the magnitude in dB of the frequency response, and a phase plot expressing the phase shift. Both quantities are plotted on a horizontal axis proportional to the logarithm of the frequency. Below is an example of a Bode plot created in Matlab. Bode Diagram 0 -20 3-40 E-60 -80 180 90 10 10 10...
Please do part C only, thank you.
Exercise 1 (Transfer Function Analysis) MATLAB provides numerous commands for working with polynomials, ratios of polynomials, partial fraction expansions and transfer functions: see, for example, the commands roots, poly, conv, residue, zpk and tf (a) Use MATLAB to gener ate the continuous-time transfer function H5+15)( +26(s+72) s(s +56)2(s2 +5s +30) H(s) displaying the result in two forms: as (i) the given ratio of factors and (ii) a ratio of two polynomials. (b) Use...
For all problems -given a transfer function G(s) sketch the magnitude and phase characteristics in the logarithmic scale (i.e. Bode-plots) of the system using the following rules-of-thumb: i. "Normalize" the G(s) by extracting poles/zeros, substituting s-jw and writing the TF using DC-gain KO and time-constants i. Arange break-points (poles, zeros or on for complex-conjugate poles) in ascending order ii Based on the term Ko(ju)Fk, determine: initial slope of the magnitude-response asymptote for low frequencies as F k 20 dB/dec (e.g....
alpha = 5.0
beta = 7.1
zeta = 6.9
PROBLEM 1 (20 points). Given the filter with transfer function +28-1+-2 11(2) = 1-(α/10)2-4 (a2/100):-2 Use MATLAB to Find the zeros and poles of H() Plot the poles and zeros on the -plane. The pot should include the uit circle. Plot the magnitude response (in dB) Plot the phase response. Deliverables: Your MATLAB code used to solve Problem 1 and all the generated plots.
PROBLEM 1 (20 points). Given the filter...
Let G,()+3s+5) , K-1 and Ge 1 I Determine the loop transfer function L(s)-KG.G. Use 'margin' command in matlab to generate the Bode Plot for L(s). (a) What are its gain and phase margins (these should be available in the plots). (b) Convert the gain margin in dB to absolute value. (c) For what value of the gain K would the closed loop system become marginally stable? (d) Show that, for this value of K, the closed loop system does...
Figure 1 Problem 3 For the system shown in the above figure, where G(s) a) Draw a Bode diagram of the open-loop transfer function G(s) when K 10. b) On your plot, indicate the crossover frequencies, PM, and GM. Is the closed-loop system stable with K-10? c) Determine the value of K such that the phase margin is 30°. What are the gain margin and the crossover frequencies with this K? Note: You can finish problems 2-3 with the help...
Simulation For each filter mentioned in the following cases, first simulate the circuit using Multisim. You can get a plot of the transfer function that is called the Bode plot. From the right toolbar, select "Bode Plotter". Change initial (I) and final (F) frequencies to 1Hz and 200 KHz, respectively. Use a Voltage AC source as the input signal. You do not need to change any parameter from voltage AC source. Connect "Bode Plotter" to input and output of your...
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