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It's a 2nd order system Since we've two poles.
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IL. Calculation Problems (Total 70 Points). (20 Points) Derive the following RLC fniter's transfer function. What...
Part II: Calculation Problems (Total 70 Points) 1. (12 Points) Find C and simplify C (in...
Part II: Calculation Problems (Total 70 Points) 1. (12 Points) Find C and simplify C (in order to receive a full credit, please write down the logic expression at the output of each gate), and establish the truth table of the following logic A circuit.
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies Wej and Wc2, the bandwidth ß, and quality factor, Q. Co...
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies Wej and Wc2, the bandwidth ß, and quality factor, Q. Compute values for R and L to yield a bandpass filter with a center frequency of 5kHz and a bandwidth of 200Hz, using a 10nF capacitor. (25 points)
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies...
System Modeling and Laplace transform: In this problem we will review the modeling proce- dure for the RLC circuit as shown below, and how to find the corresponding transfer function and step respons...
System Modeling and Laplace transform: In this problem we will review the modeling proce- dure for the RLC circuit as shown below, and how to find the corresponding transfer function and step response Ri R2 Cv0) i2) i,(0) 3.1 Considering the input to be V(t) and the output to be Ve(t), find the transfer function of the system. To do that, first derive the differential equations for al the three loops and then take the Laplace transforms of them. 3.2...
■In Problems il-20, express the quadratic function in stan- dard form, and identify a, b, and...
■In Problems il-20, express the quadratic function in stan- dard form, and identify a, b, and e. In Problems 21-22, write an expression (x) for the result of the given operations on x, and put it in standard form 1. Add 5, multiply by x, subtract 2 22 Subtract 3, multiply by x, add 2, multiply by 5 25. If a company charges x dollars per item, it finds that it can sell 1500-3x of them. Each item costs $5...
1. (20 points). A transfer function has the following zeros and poles: zero at s=-105 and s= poles at s-100 and s--1000. The magnitude of the transfer function at ω= 105 rad/s is equal 100. Find the...
1. (20 points). A transfer function has the following zeros and poles: zero at s=-105 and s= poles at s-100 and s--1000. The magnitude of the transfer function at ω= 105 rad/s is equal 100. Find the transfer function T(s) and sketch Bode plots for the magnitude and phase, ˇ
1. (20 points). A transfer function has the following zeros and poles: zero at s=-105 and s= poles at s-100 and s--1000. The magnitude of the transfer function at ω=...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t)...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t) r*(t ZOH Process zero-order hold, and the process are given by 2s +1 Go(s) =--s G(s) = There parameter a is some real number, and T is the sampling time. (a) (15 points) Determine the discrete-time transfer function G(z).
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y...
Problem 2: (20 points) Consider a unity feedback system with the following forward path transfer function...
Problem 2: (20 points) Consider a unity feedback system with the following forward path transfer function G(s) = - cla_K(s + a)(8+3) s(s2 +1) (1) Construct the root locus for K >0 and a = 5; (2) Construct the root locus for a > 0 and K = 10.
5. Given the following closed-loop system transfer function (20 points) s2 + (1 + 0.1k)s +...
5. Given the following closed-loop system transfer function (20 points) s2 + (1 + 0.1k)s + K a. b. Using Routh's Array criteria, determine the range of K for the system to be stable. The value of K such that the damping ratio is ζ-0.65.
b) Given a second order system with the following open loop transfer function where damping ratio,...
b) Given a second order system with the following open loop transfer function where damping ratio, } = 0.707 and natural frequency, Wn= 2.5. wn? G(S) = S2 + 23wns +wn? i. Determine the steady state error to an appropriate input via a calculation method using the transfer function. Compare your answer with the steady state error from the exact frequency response for this system given in Figure Q4(b). (5 marks) ii. Evaluate the difference of the exact frequency response...
Suppose a company has the following total cost function: TC = 20 + 3x + 54x...
Suppose a company has the following total cost function: TC = 20 + 3x + 54x (3) Where TC represents total cost (in $) and X is the quantity of production. Note, this function is convex. a. Derive the relevant marginal cost function. Show work. (4 pts) b. Solve for the quantity of production which minimizes TC. Show work. (5 pts)
Part II: Calculation Problems (Total 70 Points) 1. (12 Points) Find C and simplify C (in order to receive a full credit, please write down the logic expression at the output of each gate), and establish the truth table of the following logic A circuit.
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies Wej and Wc2, the bandwidth ß, and quality factor, Q. Compute values for R and L to yield a bandpass filter with a center frequency of 5kHz and a bandwidth of 200Hz, using a 10nF capacitor. (25 points)
1. Design a parallel RLC bandpass filter, derive the transfer function H(s). Compute the center frequency, Wo. Calculate the cutoff frequencies...
System Modeling and Laplace transform: In this problem we will review the modeling proce- dure for the RLC circuit as shown below, and how to find the corresponding transfer function and step response Ri R2 Cv0) i2) i,(0) 3.1 Considering the input to be V(t) and the output to be Ve(t), find the transfer function of the system. To do that, first derive the differential equations for al the three loops and then take the Laplace transforms of them. 3.2...
■In Problems il-20, express the quadratic function in stan- dard form, and identify a, b, and e. In Problems 21-22, write an expression (x) for the result of the given operations on x, and put it in standard form 1. Add 5, multiply by x, subtract 2 22 Subtract 3, multiply by x, add 2, multiply by 5 25. If a company charges x dollars per item, it finds that it can sell 1500-3x of them. Each item costs $5...
1. (20 points). A transfer function has the following zeros and poles: zero at s=-105 and s= poles at s-100 and s--1000. The magnitude of the transfer function at ω= 105 rad/s is equal 100. Find the transfer function T(s) and sketch Bode plots for the magnitude and phase, ˇ
1. (20 points). A transfer function has the following zeros and poles: zero at s=-105 and s= poles at s-100 and s--1000. The magnitude of the transfer function at ω=...
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y (t) r*(t ZOH Process zero-order hold, and the process are given by 2s +1 Go(s) =--s G(s) = There parameter a is some real number, and T is the sampling time. (a) (15 points) Determine the discrete-time transfer function G(z).
4. (25 points) Consider a sampled data system shown in the following figure, wherein the transfer function of the y...
Problem 2: (20 points) Consider a unity feedback system with the following forward path transfer function G(s) = - cla_K(s + a)(8+3) s(s2 +1) (1) Construct the root locus for K >0 and a = 5; (2) Construct the root locus for a > 0 and K = 10.
5. Given the following closed-loop system transfer function (20 points) s2 + (1 + 0.1k)s + K a. b. Using Routh's Array criteria, determine the range of K for the system to be stable. The value of K such that the damping ratio is ζ-0.65.
b) Given a second order system with the following open loop transfer function where damping ratio, } = 0.707 and natural frequency, Wn= 2.5. wn? G(S) = S2 + 23wns +wn? i. Determine the steady state error to an appropriate input via a calculation method using the transfer function. Compare your answer with the steady state error from the exact frequency response for this system given in Figure Q4(b). (5 marks) ii. Evaluate the difference of the exact frequency response...
Suppose a company has the following total cost function: TC = 20 + 3x + 54x (3) Where TC represents total cost (in $) and X is the quantity of production. Note, this function is convex. a. Derive the relevant marginal cost function. Show work. (4 pts) b. Solve for the quantity of production which minimizes TC. Show work. (5 pts)
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