An electric ventricular assist device (EVAD) has been designed to help patients with diminished but still functional heart pumping action to work in parallel with the natural heart. The device consists of a brushless dc electric motor that actuates on a pusher plate. The plate movements help the ejection of blood in systole and sac filling in diastole. System dynamics during systolic mode have been found to be:

The state variables in this model are x, the pusher plate position, v, the pusher plate velocity, and P_ao, the aortic blood pressure. The input to the system is e_m, the motor voltage (Tasch, 1990).

a. Use MATLAB to find a similarity transformation to diagonalize the system.

b. Use MATLAB and the obtained similarity transformation of Part a to obtain a diagonalized expression for the system.

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