Patients with a cardio logical illness and less than normal heart muscle strength can benefit from an assistance device. An electric ventricular assist device (EVAD) converts electric power into blood flow by moving a pusher plate against a flexible blood sac. The pusher plate reciprocates to eject blood in systole and to allow the sac to fill in diastole. The EVAD will be implanted in tandem or in parallel with the intact natural heart as shown in Figure AP9.11 (a). The EVAD is driven by rechargeable batteries, and the electric power is transmitted inductively across the skin through a transmission system. The batteries and the transmission system limit the electric energy storage and the transmitted peak power. We desire to drive the EVAD in a fashion that minimizes its electric power consumption [33].
The EVAD has a single input, the applied motor voltage, and a single output, the blood flow rate. The control system of the EVAD performs two main tasks: It adjusts the motor voltage to drive the pusher plate through its desired stroke, and it varies the EVAD blood flow to meet the body's cardiac output demand. The blood flow controller adjusts the blood flow rate by varying the EVAD beat rate. A model of the feedback control system is shown in Figure AP9.11(b). The motor, pump, and blood sac can be modeled by a nominal time delay with T = 1 s. The goal is to achieve a step response with zero steady-state error and percent overshoot P.O. Consider the controller

For the nominal time delay of T = 1 s, plot the step response and verify that steady-state tracking error and percent overshoot specifications are satisfied. Determine the maximum time delay, 7", possible with the PID controller that continues to stabilize the closed loop system. Plot the phase margin as a function of time delay up to the maximum allowed for stability.

V(s) ControllerMolor Motor. pump, and blood sac RUs) voltage Blooc flow ratc Desired t flow rate tby