In 24, Chapter 11, we discussed an EVAD, a device that

Chapter 13, Problem 31

(choose chapter or problem)

In Problem 24, Chapter 11, we discussed an EVAD, a device that works in parallel with the human heart to help pump blood in patients with cardiac conditions. The device has a transfer function

\(G(s)=\frac{P_{a o}(s)}{E_m(s)}=\frac{1361}{s^2+69 s+70.85}\)

where \(E_m(s)\) is the motor's armature voltage, and \(P_{a o}(s)\) is the aortic blood pressure (Tasch, 1990). Using continuous techniques, a cascaded compensator is designed in a unity feedback configuration with a transfer function

\(G_c(s)=\frac{0.5(s+1)}{s+0.05}\)

Selecting to control the device using a microcontroller, a discrete equivalent has to be found for \(G_c(s)\). Do the following:

(a) Find an appropriate sampling frequency for the discretization.

(b) Translate the continuous compensator into a discrete compensator using the sampling frequency found in Part a.

(c) Use Simulink to simulate the continuous and discrete systems on the same graph for a unit step input. There should be little difference between the compensated continuous and discrete systems.