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Three possible sets of pole positions for a third-order process are depicted in the figure below....
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...
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...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal LTID s Figure P5.6-5 (a) Determine the five constants k, bi, b2, aj, and a2 that specify the transfer function (b) Using the techniques of Sec. 5.6, accurately hand-sketch the system magnitude response lH[eill over the range (-π π) (c) A signal x(t) = cos(2πft) is sampled at a rate Fs 1 kHz and then input into the above LTID system to produce DT...
Topics: Filter Design by Pole Zero Placement PROBLEM Problem #2 . a) Design a simple FIR...
Topics: Filter Design by Pole Zero Placement PROBLEM Problem #2 . a) Design a simple FIR second order filter with real coefficients, causal, stable and with unity AC gain. Its steady state response is required to be zero when the input is: xIn]cos [(T/3)n] u[n] H(z) R.O.C: answer: b) Find the frequency response for the previous filter. H(0) c) Sketch the magnitude frequency response. T/3 t/3 d) Find the filter impulse response. h[n] e) Verify that the steady state step...
2. Consider the pole-zero plot of a transfer function H(s) given in Figure P14.2. (a) If...
2. Consider the pole-zero plot of a transfer function H(s) given in Figure P14.2. (a) If the dc gain is -10, find HG). (b) Compute the impulse response. (c) Compute the step response. CHECK: Your answer to (b) should be the derivative of your answer to (c), since the delta function is the derivative of the step function. (d) If the input is 10 ), find the pos- itive number a such that the response does not have a term...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero plot for this system How many possible regions of convergence (ROCs) are there for H(). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to. (b) Which ROC (or ROCs) correspond to a stable system Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to...
Q4. 1 2 3 G 10 pts. Use MATLAB and plot the step response of the following systems G3 2s+1 figure. Gy on the same 2s+1...
Q4. 1 2 3 G 10 pts. Use MATLAB and plot the step response of the following systems G3 2s+1 figure. Gy on the same 2s+1 2s+1 Explain the similarities (at least 1) and differences (at least 1) between these responses. E_ figure. G, G 3 10 pts. Use MATLAB and plot the impulse response of the following systems Explain the similarities and differences between these responses. on the same 25+1 10 pts. Find the time constant (Te), pole(s), DC...
Problem1: Consider the translational system shown in the figure below. Att-0,x (displacement)-y (...
Problem1: Consider the translational system shown in the figure below. Att-0,x (displacement)-y (let y represents velocity)-fat)0. The physical constants are: M-3,B1,B2B 0.5. Find the first order system equation in y and do following. a) Find the response, y(t) of the system when subjected to a step input,falt)-A b). Find time constant, "7". c Identify the steady state, "yss" and transient, "yr" part of the response. d). Sketch the complete response when the input is unit step function. e). Is the...
Consider the following systems to explore the effects of an additional pole. (1) 762 +28 +9(8+1)...
Consider the following systems to explore the effects of an additional pole. (1) 762 +28 +9(8+1) (ii) (62 +25 +9)(0.18 +1) (ii) (62 +2s +9)(58 +1) (a) Sketch the pole locations of the systems above on the complex plane. Indicate which systems appear to have a dominant pole or poles. (3%) (b) For systems with a dominant pole or poles, sketch the approximate step response based on those dominant poles and your knowledge of first and second order responses. Clearly...
Question 3 The temperature (in °C) in the water heating process is given by the transfer...
Question 3 The temperature (in °C) in the water heating process is given by the transfer function T(s) 3 U(s) TS+2 (a) Sketch THREE forms of input force function with its time response graph. (3 marks) (b) (12 marks) Calculate the time response of the system when, i) unit impulse is imposed on the system. ii) unit step is imposed on the system. (c) Sketch the diagrams of two responses and label the relevant values, given t = 5. (5...
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...
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...
P5.6-3 displays the pole-zero plot of a system that has re 5.6-5 Figure second-order real, causal LTID s Figure P5.6-5 (a) Determine the five constants k, bi, b2, aj, and a2 that specify the transfer function (b) Using the techniques of Sec. 5.6, accurately hand-sketch the system magnitude response lH[eill over the range (-π π) (c) A signal x(t) = cos(2πft) is sampled at a rate Fs 1 kHz and then input into the above LTID system to produce DT...
Topics: Filter Design by Pole Zero Placement PROBLEM Problem #2 . a) Design a simple FIR second order filter with real coefficients, causal, stable and with unity AC gain. Its steady state response is required to be zero when the input is: xIn]cos [(T/3)n] u[n] H(z) R.O.C: answer: b) Find the frequency response for the previous filter. H(0) c) Sketch the magnitude frequency response. T/3 t/3 d) Find the filter impulse response. h[n] e) Verify that the steady state step...
2. Consider the pole-zero plot of a transfer function H(s) given in Figure P14.2. (a) If the dc gain is -10, find HG). (b) Compute the impulse response. (c) Compute the step response. CHECK: Your answer to (b) should be the derivative of your answer to (c), since the delta function is the derivative of the step function. (d) If the input is 10 ), find the pos- itive number a such that the response does not have a term...
1. A discrete-time LTI system has the system function H() given below: (a) Sketch the pole-zero plot for this system How many possible regions of convergence (ROCs) are there for H(). List the possible ROCs and indicate what type of sequence (left-sided, right-sided, two-sided, finite-length) they correspond to. (b) Which ROC (or ROCs) correspond to a stable system Why? (c) Which ROC (or ROCs) correspond to a causal system? Why? (d) Write a difference equation that relates the input to...
Q4. 1 2 3 G 10 pts. Use MATLAB and plot the step response of the following systems G3 2s+1 figure. Gy on the same 2s+1 2s+1 Explain the similarities (at least 1) and differences (at least 1) between these responses. E_ figure. G, G 3 10 pts. Use MATLAB and plot the impulse response of the following systems Explain the similarities and differences between these responses. on the same 25+1 10 pts. Find the time constant (Te), pole(s), DC...
Problem1: Consider the translational system shown in the figure below. Att-0,x (displacement)-y (let y represents velocity)-fat)0. The physical constants are: M-3,B1,B2B 0.5. Find the first order system equation in y and do following. a) Find the response, y(t) of the system when subjected to a step input,falt)-A b). Find time constant, "7". c Identify the steady state, "yss" and transient, "yr" part of the response. d). Sketch the complete response when the input is unit step function. e). Is the...
Consider the following systems to explore the effects of an additional pole. (1) 762 +28 +9(8+1) (ii) (62 +25 +9)(0.18 +1) (ii) (62 +2s +9)(58 +1) (a) Sketch the pole locations of the systems above on the complex plane. Indicate which systems appear to have a dominant pole or poles. (3%) (b) For systems with a dominant pole or poles, sketch the approximate step response based on those dominant poles and your knowledge of first and second order responses. Clearly...
Question 3 The temperature (in °C) in the water heating process is given by the transfer function T(s) 3 U(s) TS+2 (a) Sketch THREE forms of input force function with its time response graph. (3 marks) (b) (12 marks) Calculate the time response of the system when, i) unit impulse is imposed on the system. ii) unit step is imposed on the system. (c) Sketch the diagrams of two responses and label the relevant values, given t = 5. (5...
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