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Q1:1. Simulate your controller obtained in (1) and (2) using Matlab or Simulink or some other tool on your disposal. You may use the parameters of the plant the same as in your previous assignment (HW1). 2. Show closed loop transients to demonstrate that you achieved the desired error dynamics for a. constant references b. sinusoidal referencesSee Answer
Q2: 0 Compute the divergence of the function \mathbf{v}=(r \cos \theta) \hat{\mathbf{r}}+(r \sin \theta) \hat{\boldsymbol{\theta}}+(r \sin \theta \cos \phi) \hat{\boldsymbol{\phi}} . Check the divergence theorem for this function, using as your volume the inverted hemispherical bowl of radius R, resting on the xy plane and centered at the originSee Answer
Q3: 4. 70 kVA, 24,000/480-V single phase distribution transformers are connected in A/Y. The open-circuit test was performed, and the following data were recorded: Vo-480 V,Io=4.1 A,Po=945 W The short circuit test was performed and the following data were recorded: Vsc=1600 V,Isc=1.6837 A,Psc=1050 W a. Find the equivalent circuit parameter of the transformer referred to the high voltage side. b. Find the voltage regulation of this transformer bank at full load, 0.9 PF Lagging. c. What is the transformer efficiency at the previous conditions.See Answer
Q4: 1. Show that the condition 4a^3+27b^2+0 mod p (which is used to differentiate smooth and singular curves) is fulfilled for the curve y^2 = x^3+2x+2 mod 17.See Answer
Q5: 2. Perform the following point addition using the respective formulations 1 (13,7)+(6,3)in the group of the curve y^2 = x^3+2x+2 mod 17. Make sure you perform themodular operations (especially inversion) carefully.See Answer
Q6: 6. Consider the cyclotron setup below. We supply external fields: static magnetic field Bo and oscillating electric field Eo. The particle has charge qo, mass mo, and initial vertical velocity vo. Because of the influence of Bo and Eo, the particle's speed and direction will change over time. The particle will spend less time in the E field as it gets faster. Please ignore this effect for this problem.Instead, assume the time is the same for mathematical simplicity. (a) Plot the velocity magnitude and phase through the B and E fields as a function of time t. Label values whenever the particle moves from an E field to a B field. For the phase, you are free to consider modulus, i.e. subtract multiples of 2n, if desired. (Two plots) (b) Suppose we make the magnetic field stronger, say 3Bo. Does the particle complete a B field half loop any faster than before? (Short answer) (c) Suppose the cyclotron has a maximum radius of rmax. What is the corresponding maximum velocity an electron can reach in this cyclotron? (Short answer)See Answer
Q7: 4. Suppose we have a stationary external magnetic field Bo. We have a positively charged particle of charge |qo| and mass mo. Initially, it is moving vertically down with speed |vol and no horizontal velocity. The particle can move freely in x and y directions. (a) How does the particle velocity in the vertical and horizontal directions change over time?Provide an expression for v, and vx. (Two plots, two expressions)Vy See Answer
Q8: 3. One process for encoding a secret message is to use certain matrices whose entries are integers and whose inverse also has integer entries. To do this, take a message,assign a number to each letter (e.g. a=1, b=2, etc. and space =27) and arrange the numbers in a matrix from left to right in each row dropping to the next row each time you reach the end of a row. Use 27's to fill in the needed empty entries and encode the message by multiplying on the right by your encoding matrix B. (a) Suppose that you know the encoding matrix B and have received a string of numbers which represent an encoded message. What would need to be done to now decode the message? (b) Suppose the encoding matrix is the matrix B entered earlier. Suppose that you receive the following message that was encoded using the matrix B. Use Matlab to find the decoded matrix and write it on your paper. Now decode the message and write it on your paper. Encoded message =47, 49, -19, 257, 487, 10, -9, 63, 137, 236, 79, 142, -184, 372,536, 59, 70, -40, 332, 588 To get started, arrange the numbers into a matrix of 5 columns (the size of B).See Answer
Q9: 1. A State Fish and Game Department supplies three types of food to take to a lake that supports four species of fish. The following matrix represents the weekly average need of foods for each fish. For example, the 5 means that each fish of Species 2 consumes,each week, an average of 5 units of Food 3. Suppose each week 25,000 units of Food 1, 20,000 units of Food 2, and 40,000 units of Food 3 are supplied to the lake. Assume that all the food is eaten. a) On paper, set up a system of equations where the unknowns x1, x2, . are the numbers of each species of fish. b) Find the augmented matrix of the system, enter the matrix into Matlab, and use the rref command. Write the solution in terms of free variables in matrix form. c) Assume that each unknown (number of fish of each species) is non-negative (i.e.Xi > 0), find restriction(s) on the values of the free variables. On paper, describe how such restrictions affect the values of the other unknowns d) Determine the number of solutions in the solution set under the assumption in part (c).See Answer
Q10: A 230-V shunt motor, having an armature resistance of 0.05 2 and a field resistance of 75 , draws Aline current of 7 A while running light at 1120 rpm. The line current at a given load is 46 A. Determine(a) the motor speed at the given load, (b) motor efficiency, and (c) total core and mechanical losses.Ans. (a) 1110.5 rpm; (b) 83.9%; (c) 903.9 WSee Answer
Q11:2. The inverter below operates with VDD=0.4V and is composed of |Vt| = 0.5V devices. The devices have identical I0 and n. a. Calculate the switching threshold (VM) of this inverter. b. Calculate VIL and VIH of the inverter. See Answer
Q12:3. Consider scaling a CMOS technology by S > 1. In order to maintain compatibility with existing system components, you decide to use constant voltage scaling. In traditional constant voltage scaling, transistor widths scale inversely with S, Wα1/S. To avoid the power increases associated with constant voltage scaling, however, you decide to change the scaling factor for W. What should this new scaling factor be to maintain approximately constant power. Assume long-channel devices (i.e., neglect velocity saturation). How does delay scale under this new methodology? Assuming short-channel devices (i.e., velocity saturation), how would transistor widths have to scale to maintain the constant power requirement? See Answer
Q13:The presentation will be delivered to your supervisor, and perhaps a small audience such as other MSc project students. It is recommended that you use PowerPoint (or similar programme) for your presentation. The presentation should be 10-15 minutes in length. It should cover a summary of your project topic area (which may be informed from your literature review), your aims and objectives for the project, and its time plan. Your presentation will be followed by 5 minutes of Q&A. For 2021, the presentation can be delivered online; using Zoom, MS Teams etc. Some general tips are: Avoid using small print. Check that your figures and text can be seen and are easily readable on a screen. . • ● . . 1- Guidance for MSc Presentation Keep your slides simple, and do not put too much text on each slide. Be enthusiastic. Try to practice so that you are not just reading from notes. Also, do not just read from the slides. Try to engage the audience, talk to them rather than yourself. Make sure you are audible- do not mumble. During the question time, if you do not know the answer to a question, say so. Do not waffle. If you do not understand the question, ask for it to be rephrased. Following your Presentation, please submit your PowerPoint file onto CANVAS for the purposes of marking. II- MSc Presentation Grade Scheme copy of the presentation marking scheme is shown below. This shows how marks are allocated for your presentation. QUALITY OF PRESENTATION Audibility/Use of English/ Interaction with Audience Preparation/Time Keeping Clarity of Diagrams/Slides KNOWLEDGE OF PROJECT Appreciation of the aims of the project/20 Grasp of where the work is leading /20 Ability to answer questions/20 OVERALL MARK/100 /10 /10 /10 /10 /20 /20 /20/nSee Answer
Q14:Problem 1 A ferromagnetic core is shown in Figure P1-2. The depth of the core is 5 cm. The other dimensions of the core are as shown in the figure. Find the value of the current that will produce a flux of 0.005 Wb. With this current, what is the flux density at the top of the core? What is the flux density at the right side of the core? Assume that the relative permeability of the core is 800. 5 cm -10 cm- -20 cm 500 turns Core depth = 5 cm 15 cm + 15 cm + 15 cmSee Answer
Q15:Problem 2 Assume that the voltage applied to a load is V=2082-30° V and the current flowing through the load is I = 2220° A. (a) Calculate the complex power S consumed by this load. (b) Is this load inductive or capacitive? (c) Calculate the power factor of this load? (d) Calculate the reactive power consumed or supplied by this load. Does the load consume reactive power from the source or supply it to the source?See Answer
Q16:Problem 3 A linear machine has a magnetic flux density of 0.5 T directed into the page, a resistance of 0.25 02, a bar length = 1.0 m, and a battery voltage of 100 V. (a) What is the initial force on the bar at starting? What is the initial current flow? (b) What is the no-load steady-state speed of the bar? (c) If the bar is loaded with a force of 25 N opposite to the direction of motion, what is the new steady- state speed? What is the efficiency of the machine under these circumstances? VB = 100 V t=0s X. 0.25 92 www B=0.5 T ImSee Answer
Q17:Problem 1 For the power systen v= 13.8L 0° kV shown, find the powe loss without transfor (Figure a) and with Transformers (Figure V 13.82 0° kV 1:10 T₁ 60Z 60°Q Zline (a) 60Z 60°Q Zjine (b) 10:1 500L 36.87°2 Zload 500Z 36.87°0 ZoadSee Answer
Q18:Problem 2 A 1000-VA 230/115-V transformer has been tested to determine its equivalent circuit. The results of the tests are shown below. Open-circuit test (on secondary side) Voc=115 V Ioc = 0.11 A Poc = 3.9 W Short-circuit test (on primary side) Vsc = 17.1 V Isc = 8.7 A Psc 38.1 W Find the equivalent circuit of this transformer referred to the low-voltage side of the transformer.See Answer
Q19:Question 1 [7 MARKS] A synchronous generator has a resultant air gap flux of 0.08Wb per pole. You are required to find the phase induced voltages and line induced voltages of a 3-phase synchronous generator which has 16 pole and has a coil span of 152° electrical. The flux is distributed sinusoidally over the pole where the stator has 4 slots per pole per phase 8 conductors in two layers. The machine is running at 400rpm.See Answer
Q20:2. A coreless solenoid is 10 CM long with a diameter of 5 CM and 1000 turns of wire. a. What is the magnitude of a magnetic field produced by a DC current of 3 A flowing through the solenoid? b. We add a core of silicon steel and apply a sinusoidal current of 3 A at 60 Hz. Determine the magnetic field as a function.See Answer

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