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In the complex frequency domain a step input can be represented as R(s) and we have...
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...
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...
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)...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) fil...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
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...
As a process engineer with the Complex Pole Corporation, you are assigned a unit with an exothermic chemical reacto...
As a process engineer with the Complex Pole Corporation, you are assigned a unit with an exothermic chemical reactor, In order to learn more about the dynamics of the process, you decide to make a step change in the input variable, the coolant temperature, from 10 °C to 15 C. Assume that the reactor was operating initially at steady state. You obtain the following plot (FIGURE Q2) for the output variable, which is the reactor temperature. 290 285 280 275...
(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...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
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...
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...
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...
1. Pole-zero placement. We wish to design a stable and causal second-order discrete-time (DT) filter (i.e., having two poles and two zeros, including those at 0 and oo) using pole-zero placement. (a) [5 pts] Where might you place the poles and zeros to achieve the following magnitude frequency response? Sketch the pole-zero plot in the complex z-plane. -Π -Tt/2 0 (b) [3 pts] Give an expression for the transfer function H(z). Justify your answer. (c) [2 pts] Write an expression...
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...
As a process engineer with the Complex Pole Corporation, you are assigned a unit with an exothermic chemical reactor, In order to learn more about the dynamics of the process, you decide to make a step change in the input variable, the coolant temperature, from 10 °C to 15 C. Assume that the reactor was operating initially at steady state. You obtain the following plot (FIGURE Q2) for the output variable, which is the reactor temperature. 290 285 280 275...
(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...
Problem 2: (40 pts) Part A: (20pts) A third-order system has an of Y(s)-L[y(t) corresponding to a unit step input u(t) is known to be input of u(t) and an output of y(t). The forced response portion 1 Ys) (3 +3s2+ 4s +5) = a) Determine the input-output differential equation for the system b) From your result in a), determine the transformed free response Yee (s) corresponding to initial conditions of: y(0)= y(0) = 0 and ý(0)-6 Part B (20pts)...
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...
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