Solve the following without the use of AI. Show all steps. Thank You! Consider the closed-loop transfer function of a system, where the input ofthe system is u:G(s) ==U(s)Y(s)1s(s² + 3s + 2)Derive the state-space representation of the system and express it in a matrix form.Assume outputs of interest for the state-space representation are the displacement andvelocity, y and y. (Hint: the differential equation is y + 3y + 2y = u.)

Step 1:To derive the state-space representation from the transfer…

Answered: Consider the closed-loop transfer…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

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A mechanical system is described by the following transfer function -4s H(s) = sª-2s² + s-17 If u is the input, and y the output, Cast this system into the state variable format. (Do not find the solution for the system) Y
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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…
For the following state-space representation,define the:– State Vector– System Matrix– Feedforward Matrix– Input Matrix & Input Vector– Output Matrix & Output Vector
T:06)
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