Question: The purpose of an artificial pacemaker is to regulate heart rate in those patients in which the natural feedback system malfunctions. Assume a unity-feedback system

The purpose of an artificial pacemaker is to regulate heart rate in those patients in which the natural feedback system malfunctions. Assume a unity-feedback system with a forward path,

1352k G(s) = %3D s(s+ 8)(s+20)

as a simplified model of a pacemaker (Neogi, 2010).

a. Convert the pacemaker model to a discrete system with a sampling rate of 0.01 second.

b. Draw the root locus of the system using a computer program.

c. Use the root locus in Part b to find the range of k for which the system is closed-loop stable.

d. Use the root locus from Part b to find the value of k that will yield a 5% overshoot for a step input.

e. Simulate the unit-step input of your discretized system to verify your design.

1352k G(s) = %3D s(s+ 8)(s+20)

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