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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:**2. Enter the matrix (a) Create a super augmented matrix named "super" using the command superВ еye(5). (b) Use the rref command to determine the inverse matrix of B. Write the inverse on your paper. (c) Create a matrix D by typing D = inv(B) into Matlab. Write on paper what this command does. Without calculating or using Matlab, what should BD be?See Answer**Q3:**4. Now, turn off your diary file, convert your written work to a pdf, and upload your written work pdf and your diary file into the assignment on blackboard.See Answer**Q4:**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**Q5:**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**Q6:**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**Q7:**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**Q8:**For the elliptic curve y^2 =x^3+2x+2 mod 17, find the min. and max. for the number of points using Hasse's theorem. The number of points is between the ceiling of min. and floor of max.See Answer**Q9:**7. Suppose we equip a wire loop with radius ro with a voltmeter and a resistance Ro embedded for measurement. The loop is fixed in space, and its radius is constant over time. We provide magneticfield B pot pecessarily constan+ (a) Assume B is a triangular wave, i.e. jerky and unlike a sinusoid. Plot the magnetic flux O of the loop and the emf V across Ro as functions of t. (Two plots) (b) The average B field is zero. Should the power dissipated by the resistor be zero? Justify your answer. (Short answer)See Answer**Q10:**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**Q11:**1) A circuit has 4 resistors in series. The voltage source equals 10 volts (V). The resistors are equal to R1 = 500 2, R2 =1 k2, R3 = 1.5 kN and R4 = 2 k2. Draw the circuit diagram for this problem. Label the voltage source, resistors, and voltages across the resistors: VRI, VR2, VR3, VR4. Label a current, I, out of the voltage source. ) Determine the equivalent resistance Reg, that could replace all 4 resistors that are inseries. Determine the current, I, in mA. Determine the electrical power supplied by the 10 V source. Determine the voltages across each of the 4 resistors: VRI, VR2, VR3, VR4. ) Show that Kirchoff's Voltage Law is true here by summing all the voltages around the circuit (i.e. demonstrate that 4 voltages around the circuit sum to 0)See Answer**Q12:**In the case of distribution system line models, explain why the matrices [a],[A] and [d] are unity matrices.See Answer**Q13:**Enumerate some of the advanced distribution planning studies. This topic was discussed during the last zoom session.See Answer**Q14:**Briefly explain what did you learn in this course in not more than 5 bullet points.See Answer**Q15:**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**Q16:**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**Q17:**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**Q18:**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**Q19:**1. For the inverter of the Figure below and an output load of 3 pF: a. Calculate tpth- tphi, and tp b. Are the rising and falling delays equal? Why or why not? c. Compute the static and dynamic power dissipation assuming the gate is clocked as fast as possible.See Answer**Q20:**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

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