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 model that you are given is more complex this time as the new design has multiple springs and masses and damping elements in series. But you are given a transfer function model: K H(s) = X(s)/F(s) (sc)(sd)(s² + ms + n) Here, f(t) is an input force that can be controlled. It is constrained to be a step function with amplitude A (e.g. f(t)= Au(t). The team wants the system to be stable. What are the constraints (if any) on the parameters K, c, d, m and n? Remember that if you have a stable system, the impulse response will decay to zero over time. Or you can use another justification. For each parameter, list if there is a constraint or not, and what it is (if it exists).

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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 model that you are given is more complex this
time as the new design has multiple springs and masses and damping elements in series. But you are given a transfer
function model:
K
H(s) = X(s)/F(s) =
(sc)(sd)(s² + ms + n)
Here, f(t) is an input force that can be controlled. It is constrained to be a step function with amplitude A (e.g.
f(t) = Au(t). The team wants the system to be stable. What are the constraints (if any) on the parameters K, c, d, m
and n? Remember that if you have a stable system, the impulse response will decay to zero over time. Or you can use
another justification. For each parameter, list if there is a constraint or not, and what it is (if it exists).
Transcribed Image Text: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 model that you are given is more complex this time as the new design has multiple springs and masses and damping elements in series. But you are given a transfer function model: K H(s) = X(s)/F(s) = (sc)(sd)(s² + ms + n) Here, f(t) is an input force that can be controlled. It is constrained to be a step function with amplitude A (e.g. f(t) = Au(t). The team wants the system to be stable. What are the constraints (if any) on the parameters K, c, d, m and n? Remember that if you have a stable system, the impulse response will decay to zero over time. Or you can use another justification. For each parameter, list if there is a constraint or not, and what it is (if it exists).
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