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You are working at a medical device company, and are helping to design a new needle system that pricks the skin of a patient so that a drop of blood becomes available for a glucose test. The needle tip position x can be modeled as a system with the transfer function: Kw2 H(s) = X(s)/F(s) = s² +26wns+w²/2 Here, f(t) is an input force. It is constrained to be a step function with amplitude 1 (e.g. f(t) = u(t). Given all the current design parameters, the response that the team is getting is shown below: Position x, mm 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.02 0.04 Step Response 0.06 0.08 Time (seconds) 0.1 0.12 0.14 Unfortunately, the problem is that the needle needs to reach a maximum position of 1.5 mm, but then after the over- shoot, retract to a position of 0.5 mm. The peak time should be exactly 0.2 seconds. Given that you can control the damping ratio (, the natural frequency wn, and the gain K, write in a few sentences a proposed strategy for modifying the design to meet the stated objectives. Please make the justification for the strategy clear.

You are working at a medical device company, and are helping to design a new needle system that pricks the skin of a patient so that a drop of blood becomes available for a glucose test. The needle tip position x can be modeled as a system with the transfer function: Kw2 H(s) = X(s)/F(s) = s² +26wns+w²/2 Here, f(t) is an input force. It is constrained to be a step function with amplitude 1 (e.g. f(t) = u(t). Given all the current design parameters, the response that the team is getting is shown below: Position x, mm 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0.02 0.04 Step Response 0.06 0.08 Time (seconds) 0.1 0.12 0.14 Unfortunately, the problem is that the needle needs to reach a maximum position of 1.5 mm, but then after the over- shoot, retract to a position of 0.5 mm. The peak time should be exactly 0.2 seconds. Given that you can control the damping ratio (, the natural frequency wn, and the gain K, write in a few sentences a proposed strategy for modifying the design to meet the stated objectives. Please make the justification for the strategy clear.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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3. You are working at a medical device company, and are helping to design a new needle system that pricks the skin of a patient so that a drop of blood becomes available for a glucose test. The needle tip position a can be modeled as a system with the transfer function: Position x, mm Here, f(t) is an input force. It is constrained to be a step function with amplitude 1 (e.g. f(t) = u(t). Given all the current design parameters, the response that the team is getting is shown below: 1.4 1.2 1 0.8 0.6 0.4 0.2 0 H(s) = X(s)/F(s) = 0 Kw2/20 s² + 25wns + w²/12 0.02 0.04 Step Response 0.06 0.08 Time (seconds) 0.1 0.12 0.14 Unfortunately, the problem is that the needle needs to reach a maximum position of 1.5 mm, but then after the over- shoot, retract to a position of 0.5 mm. The peak time should be exactly 0.2 seconds. Given that you can control the damping ratio , the natural frequency wn, and the gain K, write in a few sentences a proposed strategy for modifying the design to meet the stated objectives. Please make the justification for the strategy clear.
Transcribed Image Text:3. You are working at a medical device company, and are helping to design a new needle system that pricks the skin of a patient so that a drop of blood becomes available for a glucose test. The needle tip position a can be modeled as a system with the transfer function: Position x, mm Here, f(t) is an input force. It is constrained to be a step function with amplitude 1 (e.g. f(t) = u(t). Given all the current design parameters, the response that the team is getting is shown below: 1.4 1.2 1 0.8 0.6 0.4 0.2 0 H(s) = X(s)/F(s) = 0 Kw2/20 s² + 25wns + w²/12 0.02 0.04 Step Response 0.06 0.08 Time (seconds) 0.1 0.12 0.14 Unfortunately, the problem is that the needle needs to reach a maximum position of 1.5 mm, but then after the over- shoot, retract to a position of 0.5 mm. The peak time should be exactly 0.2 seconds. Given that you can control the damping ratio , the natural frequency wn, and the gain K, write in a few sentences a proposed strategy for modifying the design to meet the stated objectives. Please make the justification for the strategy clear.
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