Lab Sheet 6: Performance Analysis of a Three-Phase Induction Motor Objective: Analyze and calculate various performance parameters of a three-phase, 4-pole, 200V, 400Hz induction motor. Understand the effects of electrical properties on motor performance using MATLAB, Python, or Excel. Equipment and Software: MATLAB, Python, or Excel Calculator for manual verification Motor Specifications: Type: Three-phase, 4-pole induction motor Rated Voltage: 200V Frequency: 400Hz Stator Resistance (𝑅𝑠Rs ): 1.71 ohms Stator Reactance (𝑋𝑠Xs ): 0.12 ohms Rotor Resistance (𝑅𝑟Rr ): 0.5 ohms Rotor Reactance (𝑋𝑖′Xi′ ): 0.3 ohms Magnetizing Reactance (𝑋𝑚Xm ): 32 ohms Slip (𝑠s): 2.5% Friction Losses: 100W Negligible Core Losses Tasks: Calculate the Synchronous Speed: Use the formula: 𝑛𝑠=120×𝑓𝑃ns =P120×f Where 𝑓f is the frequency, and 𝑃P is the number of poles. Calculate the Motor Speed at Full Load: Considering the slip (𝑠s), use the formula: 𝑛=𝑛𝑠×(1−𝑠)n=ns ×(1−s) Determine the Total Impedance: Combine stator impedance, rotor impedance referred to the stator, and magnetizing impedance. Use parallel and series combinations as applicable. Calculate the Stator Current and Power Factor: Use Ohm’s law and impedance to find the current: 𝐼𝑠=𝑉𝑝ℎ𝑍𝑡𝑜𝑡𝑎𝑙Is =Ztotal Vph Determine the power factor from the impedance phase angle. Compute Stator and Rotor Copper Losses: 𝑃𝑠𝑐𝑢=3×𝐼𝑠2×𝑅𝑠Pscu =3×Is2 ×Rs 𝑃𝑟𝑐𝑢=3×𝐼𝑟2×𝑅𝑟Prcu =3×Ir2 ×Rr Calculate the Air Gap Power: 𝑃𝑔𝑎𝑝=𝑃𝑟𝑐𝑢/𝑠 Determine the Developed Power and Torque: Subtract rotor copper losses from the air gap power for developed power. Calculate the torque using the developed power and motor speed. Assess Input and Output Power: Input power calculation incorporating power factor. Output power considering friction losses. Evaluate Motor Efficiency: Ratio of output power to input power, expressed as a percentage. Instructions: Students may choose MATLAB, Python, or Excel to perform the calculations. Document all steps, formulas, and intermediate values. Discuss the impact of slip, stator, and rotor resistances on motor performance. Submission: Submit all calculations, code (if applicable) and a discussion on the implications of your findings on motor design and operation. Lab Sheet for Session 5 Objective: Analyse DC motor operations using MATLAB and perform a comprehensive load analysis for an aircraft's electrical system using Excel. Materials: MATLAB software Microsoft Excel Exercise 1: DC Motor Analysis Using MATLAB A DC shunt motor connected to a 460-V supply has an armature resistance of 0.15 Ω. Calculate: (a) The back e.m.f when the armature current is 120 A. (b) The armature current when the back e.m.f. is 447.4 V. A DC shunt motor connected to a 460-V supply takes an armature current of 120 A on full load. Calculate the back e.m.f. at this load given the armature resistance of 0.25 Ω. A 4-pole DC shunt motor takes an armature current of 150 A at 440 V, with an armature resistance of 0.15 Ω. Calculate the back e.m.f. at this load. A 28 V DC motor with an armature resistance of 0.3 ohm, rated at 800 rpm and 5 A, is used to drive a pump. Calculate the no-load speed. Exercise 2: Load Analysis Using Excel Using the provided aircraft electrical data and load profiles, compute the following using Excel: The electrical data for a military aircraft is as follows: Number of generators : 2 (split bus) Number of inverter (for emergency use only) : 1 Number of Transformer Rectifier Unit : 2 Number of battery : 1 Specs: Generator Voltage 115 Frequency 400 Power Factor 0.8 Configuration WYE Max Continuous Power Rating (kVA) 15 Interval Rating (5 s – KVA 24 Interval Rating (5 min – kVA) 18 Inverter Emergency Rating (kVA) 15 Voltage (AC) 115 Frequency 400 Power Factor 0.8 Configuration WYE TRU Rating (amps) 150 Output Voltage (DC) 28 Max Continuous Power Rating (kVA) 150 Interval Rating (5 s – KVA 600 Interval Rating (5 min – kVA) 225 Battery Rating (AH) 40 Output Voltage (DC) 28 There are seven flight profiles. G1 : Start-Up G2 : Taxi G3 : Take Off and Climb G4: Cruise G5 : Landing G6: Ground Alert G7: Double Gen Failure The various AC Loads are as follows: LRU Consumption (VA) Profiles Used Operating Time Fuel Booster Pump 1800 G1, G6 Continuous Fuel Transfer Pump 1628 G1, G6,G7 Continuous Amplifier 10 G1, G3,G7 Continuous Oxygen 9 G2, G3,G4,G7 Continuous Cabin Control 23 G2, G3,G5,G6 Continuous Cockpit Lighting 167 G2, G4,G5,G6 Continuous Heat 270 G1, G2, G5,G6 Continuous Radar 2500 G1, G4, G6 Continuous Avionics Computer 170 G1,G3, G4,G6,G7 Continuous Avionics Sys 1 2700 G3, G7 Continuous Avionics Sys 2 870 G5,G7 Continuous HUD 235 G3,G4,G5 Continuous Fuel Measurement 28 G4,G5 Continuous Weapon System 400 G2, G6 Continuous EW System 3410 G1,G2, G6,G7 Continuous Nav 1` 132 G1,G2, G4,G6,G7 Continuous Nav 2 85.7 G1,G5, G4,G6,G7 Continuous GPS 98.9 G5,G6,G7 Continuous 26 V transformer 82 G2,G5 Continuous Others 4300 G3 Continuous The various DC Loads are as follows: LRU Consumption (Amps) Profiles Used Operating Time VOR/ILS 2 G1, G7 Continuous EW1 5.5 G5, G7 Continuous EW2 1.52 G2, G5,G7 Continuous Controller 0.1 G2, G5, G6 Continuous J Box 0.5 G2, G4,G5,G6 Continuous Air Con 1.8 G3, G4,G5 Continuous Cockpit Lights 4.7 G2, G3,G5,G6,G7 Continuous Anti-Collision Lights 3.4 G1, G4, G3 Continuous Formation Light 0.2 G7, G4, G3 Continuous Landing Light 16.1 G6 Continuous EFIS 2.33 G6,G7 Continuous ADAHRS 0.6 G2 Continuous Transmitter 14.28 G4,G5,G6,G7 Continuous Receiver 3.57 G2, G3,G5,G6,G7 Continuous Standby 4 G3,G5,G6,G4 Continuous Comms Panel 0.3 G4, G3,G5,G6,G7 Continuous AWS 6.9 G2, G5,G7 Continuous SMD 5 G7 Continuous Master Comp 1 G7 Continuous Others 122 G1 Continuous AC Load Analysis: For each flight profile, compute the total consumption in VA. DC Load Analysis: For each flight profile, compute the total consumption in Amps. Evaluate whether the provided generators, inverter, and TRU can cater to these loads under different flight profiles. Questions: How does the back e.m.f. affect the performance of a DC motor? What is the impact of varying the load conditions on the electrical system of an aircraft? Can the aircraft's electrical system handle all operational scenarios without overloading any component? Lab Sheet for Session 4 Objective: Explore the Fourier series representation of square waves and perform detailed harmonic power analysis for inverters in electrical circuits. Materials: Microsoft Excel software Exercise 1: Fourier Series Analysis of a Square Wave Given a square wave of amplitude 3 V and frequency 50 Hz, use MATLAB to compute the Fourier series coefficients up to the 25th harmonic. Sum up to 12th harmonics and up to 2th 5 harmonics plot the two resulting waveform. Observe which waveform (12 vs 25 harmonics) looks more like the original square wave. Questions: Which waveform resembles the original square wave more closely, and why? How does increasing the number of harmonics affect the approximation of the square wave? Exercise 2: Power Analysis for Inverter Circuits Using Excel Using Microsoft Excel, perform a detailed power analysis for a half-bridge and a full-bridge inverter under the following conditions: Load = 20 ohms, DC voltage = 20V, frequency of switching = 200 Hz. Calculate up to the 100th harmonic. Columns: Harmonic Number, Frequency, Voltage at the Harmonic, Resistance, Inductive Reactance, Impedance, Current, Power Factor, and Power. Compute Total Power, Fundamental Power, Total Harmonic Power, and Total Harmonic Distortion (THD). Repeat for the two inverters for Load = 20 ohms, L = 159 mH, DC voltage = 20V, frequency of switching = 200 Hz. Questions: How does the addition of inductance affect the power distribution across the harmonics? What implications do your findings have for the design and operation of inverter systems?

ASSIGNMENT: MATLAB Using Matlab software, do the analysis on the system in Figure 1. 1. If P-Controller, G₁ = K, Obtain the Value of K for damping ratio, & = 0.707? Calculate the maximum overshoot. What is the natural frequency of the system? Plot the time response of this system if it is excited with a step input signal. 2. If I-Controller, Gc= is used, what is the value of K; for damping ratio, { = 0.707? Calculate the maximum overshoot. What is the natural frequency of the system? Plot the time response of this system if it is excited with a step input signal. 3. If PI-Controller, G₁ = K(s+K) is used, what is the value of K and K, for damping ratio, { = 0.707? Calculate the maximum overshoot. What is the natural frequency of the system? Plot the time response of this system if it is excited with a step input signal. 4. Superimpose all the three output responses obtained above and make comparison. Discuss the effect of K; on the root locus and the transient response. U(s) + Gc Figure 1 1 (s + 1)(s + 2)(S + 4) Y(s)

Problem 1. (25 pts) Use the AE5031_HMW1_1.m code to solve the ODE df/dt = -f, f(0) = 1. a) [5 pts] Find the exact solution. b) [10 pts] Use the code for various timesteps 4t and calculate the error= | Exact- Numerical/Exact as a function of the Dt at time time t = 1. c) [10 pts] Plot the error versus the At on a logarithmic scale to confirm that the error decreases proportionally to the 4t (1st order accuracy)

Question 1 20 pts For cruise control, the longitudinal motion of a vehicle on a flat road can be modeled by the first-order nonlinear differential equation mvu - Kv - Kav², where m is the vehicle's mass, v is its speed, u is the tractive force generated by the engine, is the viscous friction force, and is the aerodynamic drag. Suppose m = 4500 lbs, Kf = 2.5N/(m/s), and K = 0.8N/(m/s)². (3+7 + 10 = 20 pts) 1. Define equilibrium values for all variables of interest for the desired equilibrium point where the equilibrium speed is ū=65 mph. 2. Linearize the system around this equilibrium point, defining all variables in the equation clearly, and specify the linearized transfer function (numerical values). 3. Suppose that the custom is at/n3. Suppose that the system is at equilibrium (at 65mph), and the road grade suddenly increases to 3% (see Elevation Grade Calculator (omnicalculator.com) if you need help with this term). The equations will now change to mi = u - K₁v-K₁v² - mgsin(0), and the speed will drop. Can you use linearization to design a control law of the form u=ū+ Au, Au=-kAv, Av=v- i , where k is the gain of the controller that you will choose by "experimentation" (too small a gain and it won't have much effect, too large a gain might cause the throttle to saturate in a real-world scenario) to bring the car speed back (close) to the equilibrium value of 65mph ? If so, show me a simulation for 10 min of the system where the grade abruptly changes from 0 to 3% at 5mins, and then drops back to zero at 7mins. Include 2 subplots, one where there is no feedback control. I.e.. Ava - SO/nequilibrium value of 65mph ? If so, show me a simulation for 10 min of the system where the grade abruptly changes from 0 to 3% at 5mins, and then drops back to zero at 7mins. Include 2 subplots, one where there is no feedback control, i.e., Au = 0, so that u =ū, and a second subplot where you have designed the above controller for an appropriately chosen gain k. Are you able to make the error converge to zero? Why do you think the above controller is unable to do so ? Later on in the course, we will see how to use integral control to make the "steady-state error" (i.e, the error as t → ∞o) zero. Upload Choose a File

3. Go to the [File] menu and move down to [New] and select [M-file]. An M- file is just a text file that contains MATLAB commands. Type in the commands given below, which create a function called GetLine, for returning the equation of a line that connects two input points. function [y,A,B) GetLine (x1, y1, x2, y2); function [y, A, B] = GetLine (x1, y1, x2, y2); If only one set of coordinates is entered, assume the second point is the origin at (0,0). if (nargin=-2) x2 = 0; y2 = 0; end m = (y2-yl)/(x2-x1);&m=slope of line by-axis intercept This function takes two sets of points: (x1, y1) and (x2, y2) and returns the equation of the line connecting them in the variable y. A and B are optional parameters that represent the smallest and largest x coordinates of the points entered. by2m*x2; syms x; y = m*x + b; A B return W- min (x1, x2); max (x1, x2); After you have typed in the commands, save this file as GetLine.m in the directory you created called mymatlab. When calling this function, notice that it returns three variables. If only one variable is given to hold the return value, only the formula of the line is returned. For example: » w = GetLine (2, 5, 1,7) A- -2*x+9 But if the lower and upper limits are needed, then call the functions using: » [w, A, B] = GetLine (2, 5, 1,7) -2*x+9 B = Define x as symbolic y the equation of line 1 A smallest x coordinate B = largest x coordinate 2

2. Start running MATLAB at your computer. The first window that MATLAB loads up is the command window, which is blank except for the prompt »>. Change the current working directory to the mymatlab directory, i.e. type: >> cd c:\temp\mymatlab

The simple all-revolute 4-bar linkage shown below has an input angle of 60 degrees. Write a MATLAB.m file that performs the Newton-Raphson's method to solve for 3 and 4. Submit your code and your answer for full credit. 90'0 2 0.15 m 0.18 m 3 4 0₂ 3 0.08 m Ө.

Throughout the next several weeks you will be developing a computer program to perform a complete analysis of a four-bar linkage. This current assignment only requires the position analysis. Velocity, acceleration, and force analyses will be added in the future. You may use any programming language. I suggest that you will want a procedural language (eg, Matlab, C++, Fortran). Input the rigid dimensions of a four-bar linkage. Your program should be flexible enough to readily accept any dimensions, ie, it should not be hard-wired for only one specific set of dimensions. Perform a position analysis of the linkage for the complete range of motion of the input link. Allow for choice of form of assembly. Inputs: R₁, R₂, R3, R4. Bp. p.Open or crossed, increment of 2 Outputs: 3, 4, and the absolute position of P, all tabulated for the entire range of 2 (b) (c) Rp (d) R₂ Homework 4 ME 3313 Fall 2023 Assigned: 9/5/2023 Bp Y answers. Program listing: P 0₂ 03 R₁ Each programming submission should include the following, submitted as a scanned image or pdf file: (a) R4 04 X Cover memo: This memo should briefly summarize what follows. Describe any known bugs or incorrect This is a text document of the program code, not the MATLAB executable. The program must be documented. Make it easy to understand what is going on. Sample run: Show a sample run with the output of the program using the following data: R₁ = 0.6 m; R₂= 0.2 m; R3 = 0.3 m; R4= 0.4 m; Bp = 0.2 m; p= 35° Verification of answers: It is important to verify your answers. In addition to the penalty for incorrect answers, you can lose another 10% for not knowing that your answers are incorrect. There is no excuse for not checking the validity of your numbers. Don't skip or skimp this part of the assignment. Include documentation that shows your verification. You will want to spot check the results for at least one position, including open and crossed configuration. You will also want to confirm that your range of motion is correct.

Problem #1: Finite element beam problem L=1m Radius of the beam r=2 cm, and elastic modulus E = 200 GPa. Assume the beam is undergoing a small linearly elastic deformation. 8 a) Using MATLAB, analytically compute the deflection at the free end of the beam using the following equation: P = 100 N Px² 6EI (3L - x) b) Using the finite element method (FEM) with five beam elements of equal length: Generate the individual stiffness matrices K₂ for each element of the beam and assemble them into the global stiffness matrix Kg. Print each of the individual matrices and the global stiffness matrix. Calculate and print the displacements and rotations (in degree) for each node of the beam. Calculate and print the reaction forces and moments at each node of the beam. c) On the same figure, plot the vertical deflection throughout the beam for both analytical and FEM solution. Include title, axis labels, legends, and grid. Compare and discuss the two solutions. d) Discuss how you would increase the bending stiffness of the beam when the cross-sectional area and material must be kept the same. e) Perform Model (Frequency) Analysis of the beam in Solidworks. Take screen shot of the first three modal shapes along with their frequencies (make sure the values are readable). f) Validate the 1st natural frequency from part (e) using analytical modal analysis for cantilever beam

Problem 4. (10 pts) Determine the approximate forward difference representation for which is of the 0 (Ax), given evenly spaced grid points as shown in Figure below by means of: a) Taylor series expansion b) Forward difference operators X₂ f₁+2 X1+2 AX-XX X1+5 X

Problem 3. (15 pts) Consider the advection equation du + c(x)=0 with c(x) = x - 1/2 a) [10 pts] Find and sketch the characteristic for the computational domain 0 < x < 1 and 0 < t < 1 b) [5pts] Find the correct number of initial and/ or boundary conditions to specify at x = 0,1 and t = 0,1