Matlab And Simulation
Questions & Answers
Write a short report (3 three pages maximum) on the data analysis. This should concentrate upon what meaningful information you can find from the data, especially the spectral content of the data. You have two thrust settings, try and make some meaningful comment upon the relationship between the sound intensity and the thrust level (if there is one). In your report you need to verify that your data analysis methodology is correct, that is why the square wave signal data have been sampled. Your report needs to include at least one figure showing plotted data. Notes to guide you how to write a technical report are in the file 'write_a_report'.
Required submission: 1 page PDF document and scripts/codes uploaded to Canvas. The purpose of this assignment is to examine how the locations of the nodes zo,1,..., affect the accuracy and robustness of polynomial interpolation. To compute the interpolating polynomial, you will be using the barycentric form described in lectures. For this, you need to download the matlab functions baryweights.m and baryinlerp.m from the computing assignment page in Canvas. The first computes the weights o, ,, of the barycentric form and the second computes the interpolating polynomial. To begin, consider the equally-spaced nodes on [-1, 1], given by Write code to compute the error of the interpolating polynomial -max IP(z)-(z)l. for some suitable range of n (in practice, you should replace this maximum by the maximum on some sufficiently fine grid) and plot log(s) versus n for the test functions: J1 (²) = 5=4²² √2(z)=1+162²" 5-4z Using this, comment on the accuracy of polynomial interpolation at equally spaced nodes. Next, consider the so-called Chebysher nodes on [−1, 1], given by Z₁ =con(ix/n), i=0, ..., n. (2) Repeat the previous experiment with these nodes instead of (1) and test it on the functions above. Note that in this case you should not use the function baryweights.m to find the weights, but instead use the known formula w=½, ™;=(-1)³, j = 1,...,1-1, x=(-1)", (1) 1 (if you don't do this, your computation may result in under/overflow). Is polynomial interpolation at Chebyshev nodes accurate? Is it robust? Finally, use the Chebyshev nodes to approximate the function Js(z) = n(10¹2). Find the smallest value of n (to within ±10) such that e₂ < 10-5.
use a computer to determine and plot the parameters required of an abrupt n-p junction diode. NOTE: The orientation of the
Experiment 3 Fourier Synthesis of Periodic Waveforms Part A A.1) Provide the Matlab code required to synthesise the waveform in equation 12 and the resulting waveform. A.2) Explain the features of the resulting waveform (peak-to-peak amplitude, symmetry, ripple, etc.) A.3) How do you think the waveform would look if an unlimited number of harmonics was available (i.e. n goes to ∞)? To support your answer, provide a couple of figures along with their associated code. A.4) Referring to Equation 3, what is the value of ao? A.5) Find an expression (in terms of n) for an and bn A.6) Plot the spectrum (frequency domain view) of f(t) using cn = Ö(an2 + bn2). Provide the figure and the Matlab code used to obtain it (you can use the stem function from Matlab to plot the frequency components).
B.1) Write f(t) in Fourier synthesis form, i.e. as in Equation 2. B.2) Calculate the first 10 sinewave coefficients (i.e. b1, b2, … , b10 B.3) Synthesise the first 10 harmonics of this waveform and plot the result (provide your Matlab code as well). B.4) Plot in the same figure the original and synthesised sawtooth waveforms (provide your Matlab code). Compare the resulting waveform with what you expected to see and discuss the results. B.5) If the number of harmonics is reduced to 5, comment on the changes that will be observed practically.
C.1) Synthesise the waveforms below. Plot the resulting waveforms and provide the Matlab code used to obtain the plots as well. C.2) Comment on your results for each waveform.
D.1) Synthesise and plot this square wave (provide your Matlab code as well). Calculate the percentage overshoot of the synthesised waveform (compared with the ideal waveform) at the discontinuity. How does this compare with the expected limit of 17.9%? D.2) What is the name of this overshoot? Explain it D.3) Give the Fourier series in each case for the resulting waveform if the above square wave is used as an input for: D.3) (a) A low-pass filter with gain and phase responses as given in Figures 8 and 10 respectivelyD.3) D.3) (b) A low-pass filter with gain and phase responses as given in Figures 8 and 11 respectively (c) A band-pass filter with gain and phase responses as given in Figures 9 and 10 respectively. D.4) Synthesise the above waveforms and draw the obtained waveforms for filters (a), (b) and (c), providing the Matlab code as well.
E.1) For the wave in equation 15, listen to harmonics 1, 2 and 3 individually then as a chord. Plot the chord waveform as well. Provide the Matlab code used to listen to the harmonics/chord and plot the chord E.2) Alter the phase of the third harmonic in equation 15 by 90° and repeat the tasks in the point above. E.3) Discuss the effect of altering the phase of the third harmonic, both on the sound and plot of the chord. Do the sound or plot change as you alter the phase? Why? E.3) Discuss the effect of altering the phase of the third harmonic, both on the sound and plot of the chord. Do the sound or plot change as you alter the phase? Why?
Need the Work as per the Instructions mentioned on the Link Link: http://thomasweldon.com/tpw/courses/eegr4123/e4123p07digitalSignals.html Put Name on 1st Page of Report-->Ali Alqallaf, Ali Alselahy, Omar Alkhaldi
The closed-loop transfer function of a 2nd-order feedback control system is: H_{c l}(s)=\frac{Y(s)}{R(s)}=\frac{K}{s^{2}+2 s+K} (a) Find the range of the constant K for which the unit step response has Mp ≤ 0.163. (b) Find the range of the constant K for which the unit step response has tr≤ 0.9 s. (c) For what value of K will both specifications be met? For this value of K, compute the poles of He(s), the 1% settling time ts, and the peak time tp .
The following equation of motion describes the dynamics of a proportional controller forthe attitude of a satellite that is subject to a damping moment: \ddot{y}(t)+7 \dot{y}(t)+10 K y(t)=10 K r(t) Here, y(t) is the angular position of the satellite, r(t) is the reference angular position, and K is a constant gain. (a) Use this equation of motion to derive the closed-loop transfer function, Hc1(s)Y(s)/R(s).= (b) Determine the range of the gain K that can be used to meet both of these specifications simultaneously: (1) maximum overshoot Mp ≤ 0.043; (2) rise time tr≤ 0.45 sec. (c) Let K = 1. The satellite starts at rest (ỷ(0) = 0) at the angle y(0) = 0 degrees. A reference angle r(t) = 5uç(t) degrees is commanded, where uç(t) is the unit step function. Using your expression for Hel(s) from part (a), explain whether the Final Value Theorem can be applied. If so, apply it to find the steady-state value of y(t).
Suppose that the closed-loop transfer function He(s)control system is given by:= Y(s)/R(s) of a 2nd-order feedback H_{c l}(s)=\frac{K_{1}}{s^{2}+\left(2+K_{1} K_{2}\right) s+K_{1}} (a) Compute the values of the constants K₁ and K₂ that will produce a unit step responsewith maximum overshoot Mp = 0.046 and 2% settling time ts = 1.43 s. (b) Define He(s) in MATLAB and use the function step info ( ) to list the step response characteristics of the system. Submit your code and its output. (c) Plot the unit step response of the closed-loop system in MATLAB using the function step () and display Mp and ts on the plot. Submit your code and plot.
A cruise control model has the 1st-order transfer function H(s)=\frac{Y(s)}{U(s)}=\frac{1 / m}{s+b / m} where the car mass m and damping coefficient b are positive real numbers. What are the rise time t, and the 2% settling time ts of the unit step response of this system?
A water heater draws water from a well at temperature T = 5 °C and uses thermal flux Q from the sun to heat up water to temperature Tin = 60 °C. A schematic is provided below. For this system, the steady-state heat equations reduce to \frac{d^{2} T}{d x^{2}}=-\dot{Q} where Q =50 sin(2pie x), along with the boundary conditions T(x = 0) = Tw = 5 T(x = 1) =T₁n = 60 (a) Start by discretizing Eq. (1) using the second order central difference method \frac{d^{2} T}{\partial x^{2}} \approx \frac{T_{i+1}-2 T_{i}+T_{i-1}}{\Delta x^{2}} and construct the coefficient matrix and solution vectors. Show these matrices for a domain discretized with M = 8 equidistant elements. (b) Solve Eq.(1) using a tri diagonal solver coded in Python or MATLAB. A tri-diagonal solver is a simplified Gaussian elemination solver that makes use of the banded nature of the matrix to reduce the amount of storage and computation required. We give you the following pseudo-code to get started: (I) Store four ID vectors (II)Elimination for i = 1 to N do b(i) = b(i)- c(i-1) *a(i)/b(i-1) d(i)=d(i)-d(i-1)*a(i)/b(i-1) end for III) Back substitution. d(N) = d(N)/b(N) for i N-1 to 0 do d(i) = ((d(i) - c(i)*d(i+1))/b(i)) end for (c) Plot the numerical solution (i.e. T(x) vs x) for M = 4, 8, 16, 32, and 64 alongside the exact analytical solution to Eq. (1). How does the numerical result change with increasing mesh elements M? (d) Conduct a performance study on your tri-diagonal solver by solving Eq.(1) with M = 10, 100, 1000, 5000, 10000 elements and plotting mesh size versus time. Briefly discuss your results.
A system of mass m = 1 kg, stiffness k = 3 N/m, and damping c = 2 N.s/m, changes its governing equations as follow: mx²x+cy = 4xy, mýÿ+x+k sint = 0, x(0) = 0, y(0) = 1, y(0) = -1, 0≤t≤ 1.3 s and, x + xy = cos t, ÿ+ xý = 8, 1.3 ≤ t ≤ 2.3 s where the final conditions from the first set of equations are the initial conditions of the second set of equations.Plot y and y² versus x in one plot, and y versus y below each other. Add labels and legends. Use global command for the first set.
