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In the complex frequency domain a step input can be represented as R(s) and we have...
(a) A Butterworth filter is represented in s-domain circuit as shown in Figure Q. 2 (a)....
(a) A Butterworth filter is represented in s-domain circuit as shown in Figure Q. 2 (a). Proof that the transfer function, H(jo) of the filter can be represented by: Hjo)- 1+j 1 where w and we are the angular frequency and the fixed cutoff angular frequency, respectively. R Y(5) 1/sc Figure Q.2 (a) (5 marks)
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1)...
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
4 C(s) حرام | A system has a block diagram as shown. The input is "R(s)...
4 C(s) حرام | A system has a block diagram as shown. The input is "R(s) and the output is C(s). a) Using only the block diagram reduction method, R(S) find the transfer function of the system. b) Determine the characteristic function and the order of the system c) Find the characteristic roots of the system. d) Find the natural frequency of the system. e) Find the damped natural frequency of the system. 8 * NOTE: All stages of block...
Suppose that the zero-state response to the step input for a plant with transfer function G0(s)...
Suppose that the zero-state response to the step input for a plant with transfer function G0(s) is given by y0(t) for each t 0. Answer the following questions. Your answers are expected to be expressed in terms of y0. 1) What is the zero-state response to the same plant but for the input given by u(t) = t for each t 0 and u(t) = 0 for each t < 0? 2) Consider now the transfer function G(s) = s2G0(s)...
E. If you double the value of kp, what are the new closed-loop pole locations and [5 points] how much overshoot does the step response have? Hint: It is possible to determine the original value...
E. If you double the value of kp, what are the new closed-loop pole locations and [5 points] how much overshoot does the step response have? Hint: It is possible to determine the original value for kp. However, with the knowledge at this point, you can compute the pole locations without actually knowing kp (simply double the zero-order term in the denominator polyno- mial). Problem 2 You are confronted with a process that has the unknown transfer function G(s). It...
Determine the complex transfer function T(s) = V/V; for the circuit shown below. Specify it as...
Determine the complex transfer function T(s) = V/V; for the circuit shown below. Specify it as a function of the complex frequency, s, and the symbols for the resistors and capacitor. On the attached graph, plot the magnitude of the complex transfer function T(jw) in decibels as a function of the frequency f of the source as f varies from 1 Hz to 1 MHz. Assume that the op amp is ideal. Use as the numerical values for the resistors...
Steam-driven power generators rotate at a constant speed via a governor that maintains constant s...
Steam-driven power generators rotate at a constant speed via a governor that maintains constant steam pressure in the turbine. In addition, automatic generation control (AGC) or load frequency control (LFC) is added to ensure reliability and consistency despite load variations or other disturbances that can affect the distribution line frequency output. A specific turbine- governor system can be described only using the block diagram below, in which G (s)- Gg (s)G(s)Gm(s), where is the governor's transfer function 0.2s+1 G.(s)s the...
(a) (i) Show that the sensitivity of the closed-loop transfer function T(s) to variations in the...
(a) (i) Show that the sensitivity of the closed-loop transfer function T(s) to variations in the plant transfer function G(s), in figure 4, is given by 1 SI - SG = 1+G(s)H(s) (ii) If G(s) = and H(s) = 10 (figure 4) and the dc gain of the plant transfer function G(s) changes by 1%, what is the corresponding change in the dc gain of the closed-loop system? [40%] (b) A feedback system is to control output angular position 0....
Question No.2 (CLO 21 10 marks) ) In the circuit shown the input v(O) is a...
Question No.2 (CLO 21 10 marks) ) In the circuit shown the input v(O) is a step voltage of sv and the output is the voltage across the capacitor vot) a. Find the output voltage in Laplace domain. Find the output voltage as a function of time (assume the initial voltage across the capacitor is zero). Sketch the output voltage. Find the time constant and settling time. . c. (b) Given the following system G (s)-=-: i Find the differential...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0,...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
(a) A Butterworth filter is represented in s-domain circuit as shown in Figure Q. 2 (a). Proof that the transfer function, H(jo) of the filter can be represented by: Hjo)- 1+j 1 where w and we are the angular frequency and the fixed cutoff angular frequency, respectively. R Y(5) 1/sc Figure Q.2 (a) (5 marks)
Problem 1 (Problem Solving Workshop 1) For a parallel RL circuit R-10, L 1H Determine 1) 21 3) 4) The transfer function H(s) = (s), the pole-zero map, and the step response. Let L(0) - OA The state and output equations. Let Lt) be the state variable The block diagram of this system. Let (O) = -1 The response (t) due to a step input (t) = (t) A) using a known software. Problem #2 (Problem Solving Workshop 1) For...
4 C(s) حرام | A system has a block diagram as shown. The input is "R(s) and the output is C(s). a) Using only the block diagram reduction method, R(S) find the transfer function of the system. b) Determine the characteristic function and the order of the system c) Find the characteristic roots of the system. d) Find the natural frequency of the system. e) Find the damped natural frequency of the system. 8 * NOTE: All stages of block...
E. If you double the value of kp, what are the new closed-loop pole locations and [5 points] how much overshoot does the step response have? Hint: It is possible to determine the original value for kp. However, with the knowledge at this point, you can compute the pole locations without actually knowing kp (simply double the zero-order term in the denominator polyno- mial). Problem 2 You are confronted with a process that has the unknown transfer function G(s). It...
Determine the complex transfer function T(s) = V/V; for the circuit shown below. Specify it as a function of the complex frequency, s, and the symbols for the resistors and capacitor. On the attached graph, plot the magnitude of the complex transfer function T(jw) in decibels as a function of the frequency f of the source as f varies from 1 Hz to 1 MHz. Assume that the op amp is ideal. Use as the numerical values for the resistors...
Steam-driven power generators rotate at a constant speed via a governor that maintains constant steam pressure in the turbine. In addition, automatic generation control (AGC) or load frequency control (LFC) is added to ensure reliability and consistency despite load variations or other disturbances that can affect the distribution line frequency output. A specific turbine- governor system can be described only using the block diagram below, in which G (s)- Gg (s)G(s)Gm(s), where is the governor's transfer function 0.2s+1 G.(s)s the...
(a) (i) Show that the sensitivity of the closed-loop transfer function T(s) to variations in the plant transfer function G(s), in figure 4, is given by 1 SI - SG = 1+G(s)H(s) (ii) If G(s) = and H(s) = 10 (figure 4) and the dc gain of the plant transfer function G(s) changes by 1%, what is the corresponding change in the dc gain of the closed-loop system? [40%] (b) A feedback system is to control output angular position 0....
Question No.2 (CLO 21 10 marks) ) In the circuit shown the input v(O) is a step voltage of sv and the output is the voltage across the capacitor vot) a. Find the output voltage in Laplace domain. Find the output voltage as a function of time (assume the initial voltage across the capacitor is zero). Sketch the output voltage. Find the time constant and settling time. . c. (b) Given the following system G (s)-=-: i Find the differential...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
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