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Lоng Questiоn 3 Prоblem StаtementHere is а very simplistic model of а (rear-wheel drive) electric car run by a dc motor.The armature resistance of the motor is R = 1 Ohm, the armature inductance is about 0, the motor torque and back emf constants are both K = 10 , and the rotational inertia of the motor’s armature is 0. The total mass of the car is M = 1000 kg and the car moves in the air with linear air drag cv, where c = 2.When you apply the voltage V to the motor, it provides a motor torque Tm and motor angular speed wm to the input of the transmission. The transmission then delivers the torque Tw and speed ww to the rear wheels. The gear ratio of the (very light & frictionless) transmission is G = 5 . Assume the wheels too are very light and have radius r = 0.25 m, and don’t slip on the road. (All units are SI)Your Objective (4 points) Write the equation relating motor voltage to motor torque and motor angular speed: V= a*Tm + b*wm. Write this equation with numerical values of a and b filled in. And show steps leading to those values. (2 points) Transmission equation relating motor torque to total force on the rear wheels from ground:F = d*Tm. Write this equation with numerical value of d filled in. And show steps leading to that value. (2 points) Transmission equation relating motor speed to car speed:wm = e*v. Write this equation with numerical value of e filled in. And show steps leading to that value. (4 points) Equation of motion of the car:F = f*v + g*vdot. Write this equation with numerical values of f and g filled in. And show steps leading to those values. (8 points) A block diagram showing all these equations graphically. The input of the block diagram should be voltage V and output should be car speed v. I don't need a reduced TF from V to v, I just need the block diagram. You are welcome to use symbols a, b, d, e, f, g, etc. in the diagram, if you are worried your values may not be correct from the previous parts.Clearly label all the signals (lines, wires) and summation junctions. Clearly put proper TFs in each block needed in the diagram. HintsSpeed v of the car, assuming no slipping of the wheel, is related to angular speed of the ww and radius of the wheels as: v=rww.In going from the motor to the wheels through the transmission, while the torque increases by a factor of G (assuming no friction and massless gears), the angular speed decreases by the same factor G. Procedure Work neatly on paper showing FBD, needed equations, algebra, diagrams, etc.Neat + clean + organized = extra credit! Then show your papers to camera for academic integrity. Then type things below. After exam, submit your work as a pdf on canvas. You may get some partial credit if it applies. Type Below (Very Important) Nothing!
Lоng Questiоn 2 Prоblem Stаtement Consider а feedbаck system below with G = 6/(s+6) and H= 2/(s+2). You want to design a controller C(s) and prefilter F(s) to meet all the following specifications below. If r = t (i.e. a unit-sloped ramp) then the y(t) and r(t) should not be farther than 0.5 from each other for large times, i.e., steady state error < 0.5 error in y(t) due to a step disturbance d(u) should be zero! your controller can NOT have more zeros than poles, i.e. it must be proper. This is a strict requirement! For a very specific settling time and overshoot, I want the closed loop TF to have two repeated poles at -5. And no other poles and no zeros. Your Objective Answer the following parts neatly and separately: What do you need from/in the controller C(s) (and if needed F(s)) to meet the ramp error specification? Explain briefly and mathematically using the formulae. (4 points) What do you need from/in the controller C(s) (and if needed F(s)) to meet the disturbance error specification? Explain briefly and mathematically using the formulae. (3 points) By plotting the root locus explain what type of controller is needed to meet all the specifications.i.e., what controller poles and zeros (if any) are needed to meet all the specifications. (5 points) Perform the calculations to find your final controller transfer function C(s), and if needed F(s).i.e. find the numerical values of gain/pole/zeros of C(s) (and if needed F(s)) to get the transfer function. (6 points) What will be the overshoot in y(t) for step r(t)? (2 points) Procedure Work neatly on paper showing all equations, steps, algebra, etc.Neat + clean + organized = extra credit! Then show your papers to camera for academic integrity. Then type things below. After exam, submit your work as a pdf on canvas. You may get some partial credit if it applies. Type Below (Very Important) Final transfer function of K(s) and if needed F(s)
Lоng Questiоn 1 Prоblem Stаtement Consider а feedbаck system below with G = 1/(s+10). You want to design a controller K(s) and if needed a prefilter F(s) to meet all the following specifications below. If r = 1 (i.e. a step) then the y(t) should reach the same value 1 in the steady state, i.e., zero error for step r. the settling time of y(t) response should be less than 1 seconds. the overshoot of y(t) response should be 0% the value of u(t) is finite. D(s) =0. Your Objective Answer the following parts neatly and separately: What do you need from/in the controller K(s) to meet the first specification (steady state y = r)? Explain briefly and mathematically using the formulae. (3 points) Draw the region in the 2D complex plane where the closed loop poles should be so that the settling time and overshoot specifications above are met? Explain briefly and mathematically using the formulae. (4 points) Explain what is needed to meet the finite u(t) specification. (3 points) By plotting the root locus explain what type of controller is needed to meet all the specifications.i.e., what controller poles and zeros (if any) are needed to meet all the specifications. (5 points) Perform the calculations to find your final controller transfer function K(s), and if needed F(s). i.e. find the numerical values of gain/pole/zeros of K(s)/F(s) to get the transfer function. (5 points) Procedure Work neatly on paper showing all equations, steps, algebra, etc.Neat + clean + organized = extra credit! Then show your papers to camera for academic integrity. Then type things below. After exam, submit your work as a pdf on canvas. You may get some partial credit if it applies. Type Below (Very Important) Final transfer function of K(s) and if needed F(s)
1. (B) Briefly explаin whаt hаppens tо the dоmestic exchange rate when gоvernment borrowings increase (holding all other factors constant). (3p)