In Chapter 11, a continuous cascaded compensator for a unity feedback system was designed for the treatment of the HIV-infected patient treated with RTIs (Craig, 2004). The transfer function of the designed compensator was

The linearized plant was given by

The compensated system is overdamped with an approximate settling time of 100 seconds. This system must be discretized for practical reasons: (1) HIV patient cannot be monitored continuously and (2) medicine dosage cannot be adjusted continuously.

a. Show that a reasonable sampling period for this system is T = 8 days (medicine dosage will be updated on a weekly basis).

b. Use Tustin’s method and T = 8 days to find a discrete equivalent to G_c(s).

c. Use Simulink to simulate the continuous and discrete compensated systems for a unit step input. Plot both responses on the same graph.

-2 x 10-4(s2 +0.04s + 0.0048) s(s +0.02) Ge(s) = %3D