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Phase Shift (°) -100 -200 1. Consider an open-loop stable system. In the example below, we will commit to a time constant visualization. One way to see the impact of sensor and measurement dynamics on closed-loop performance is to perform a frequency analysis. For this scenario, we will assume that we have an open-loop transfer function: GLOOP(S) = 10 (5s+1)" Where n is the system order, which may be higher due to sensor dynamics and other closed-loop events (all mysteriously with the same time constant 7 = 5, apparently). Recall that GLoop(s) assumes Kc = 1. 3.1. 3.2. 3. Explain clearly what value for Kc, if any, could de-stabilize the process where n = 2 if placed in closed-loop proportional (P) control. Consider the system for any n > 2. Would a proportional (P) controller with gain Kc = 1 result in a stable output if the system is put into feedback control? Explain clearly how you know. Design a PID controller using the Ziegler-Nichols tuning heuristics for the n = 4 system. Note that the amplitude gain for this system at the crossover frequency is A, = 2.5217.( Make a sketch of Kc prescribed for a Ziegler-Nichols controller (y-axis) versus n (x-axis) for n = 3,4,5,...,10 Specific numbers are not required. Comment on the trend in 1-2 sentences and what it indicates about controlling higher-order processes. 10 Gain (A) 0 10-5 10-3 10 007 10-2 10-1 10º 101 102 103 -300 10-3 10-2 =5 10-1 W السبب 10º Input Frequency w n = 2 n = 3 n = 4 101 102 103

Phase Shift (°) -100 -200 1. Consider an open-loop stable system. In the example below, we will commit to a time constant visualization. One way to see the impact of sensor and measurement dynamics on closed-loop performance is to perform a frequency analysis. For this scenario, we will assume that we have an open-loop transfer function: GLOOP(S) = 10 (5s+1)" Where n is the system order, which may be higher due to sensor dynamics and other closed-loop events (all mysteriously with the same time constant 7 = 5, apparently). Recall that GLoop(s) assumes Kc = 1. 3.1. 3.2. 3. Explain clearly what value for Kc, if any, could de-stabilize the process where n = 2 if placed in closed-loop proportional (P) control. Consider the system for any n > 2. Would a proportional (P) controller with gain Kc = 1 result in a stable output if the system is put into feedback control? Explain clearly how you know. Design a PID controller using the Ziegler-Nichols tuning heuristics for the n = 4 system. Note that the amplitude gain for this system at the crossover frequency is A, = 2.5217.( Make a sketch of Kc prescribed for a Ziegler-Nichols controller (y-axis) versus n (x-axis) for n = 3,4,5,...,10 Specific numbers are not required. Comment on the trend in 1-2 sentences and what it indicates about controlling higher-order processes. 10 Gain (A) 0 10-5 10-3 10 007 10-2 10-1 10º 101 102 103 -300 10-3 10-2 =5 10-1 W السبب 10º Input Frequency w n = 2 n = 3 n = 4 101 102 103

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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please explain and draw the graphs clearly, I am most confused with the graphs thanks

Phase Shift (°) -100 -200 1. Consider an open-loop stable system. In the example below, we will commit to a time constant visualization. One way to see the impact of sensor and measurement dynamics on closed-loop performance is to perform a frequency analysis. For this scenario, we will assume that we have an open-loop transfer function: GLOOP(S) = 10 (5s+1)" Where n is the system order, which may be higher due to sensor dynamics and other closed-loop events (all mysteriously with the same time constant 7 = 5, apparently). Recall that GLoop(s) assumes Kc = 1. 3.1. 3.2. 3. Explain clearly what value for Kc, if any, could de-stabilize the process where n = 2 if placed in closed-loop proportional (P) control. Consider the system for any n > 2. Would a proportional (P) controller with gain Kc = 1 result in a stable output if the system is put into feedback control? Explain clearly how you know. Design a PID controller using the Ziegler-Nichols tuning heuristics for the n = 4 system. Note that the amplitude gain for this system at the crossover frequency is A, = 2.5217.( Make a sketch of Kc prescribed for a Ziegler-Nichols controller (y-axis) versus n (x-axis) for n = 3,4,5,...,10 Specific numbers are not required. Comment on the trend in 1-2 sentences and what it indicates about controlling higher-order processes. 10 Gain (A) 0 10-5 10-3 10 007 10-2 10-1 10º 101 102 103 -300 10-3 10-2 =5 10-1 W السبب 10º Input Frequency w n = 2 n = 3 n = 4 101 102 103
Transcribed Image Text:Phase Shift (°) -100 -200 1. Consider an open-loop stable system. In the example below, we will commit to a time constant visualization. One way to see the impact of sensor and measurement dynamics on closed-loop performance is to perform a frequency analysis. For this scenario, we will assume that we have an open-loop transfer function: GLOOP(S) = 10 (5s+1)" Where n is the system order, which may be higher due to sensor dynamics and other closed-loop events (all mysteriously with the same time constant 7 = 5, apparently). Recall that GLoop(s) assumes Kc = 1. 3.1. 3.2. 3. Explain clearly what value for Kc, if any, could de-stabilize the process where n = 2 if placed in closed-loop proportional (P) control. Consider the system for any n > 2. Would a proportional (P) controller with gain Kc = 1 result in a stable output if the system is put into feedback control? Explain clearly how you know. Design a PID controller using the Ziegler-Nichols tuning heuristics for the n = 4 system. Note that the amplitude gain for this system at the crossover frequency is A, = 2.5217.( Make a sketch of Kc prescribed for a Ziegler-Nichols controller (y-axis) versus n (x-axis) for n = 3,4,5,...,10 Specific numbers are not required. Comment on the trend in 1-2 sentences and what it indicates about controlling higher-order processes. 10 Gain (A) 0 10-5 10-3 10 007 10-2 10-1 10º 101 102 103 -300 10-3 10-2 =5 10-1 W السبب 10º Input Frequency w n = 2 n = 3 n = 4 101 102 103
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