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4. Control of HIV/AIDS. The linearized transfer function relating virus count to a specific retroviral drug administration is R(s) G(s) Y(s) U(s) s3 +2.6817s +0.11s 0.0126 -520s-10.3844 PCs) =- = H(s) And the system operates within the standard feedback scheme we have been considering in class (see diagram). a) Let G(s) P(s), H(s) 1. Obtain the Nyquist plot (in Matlab). Evaluate the system for closed-loop stability b) Let G(s)P(s), H(s) 1. Obtain the Nyquist plot (in Matlab). Evaluate the system for closed-loop stability. Obtain the gain and phase margins.
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- S2os - Jo 3844 S +8.6BI7-X+0.1s+o.oïx CCS) PCS) CCS) PcS)>>c tf([-520 -10.3844],[1 2.6817-519.89 -10.3718]) -520 s - 10.38 SA3 2.682 sA2 - 519.9 s - 10.37 Continuous-time transfer fuplot of (a)

Nyquist Diagram 20 dB 0.04 20dB 10dB 6dB dB2 d㈤dB2 d텨 dB 10:d 6 dB 0.03 0.02 0.01 0.01 0.02 0 03 0.04 0.5 0.5 1.5 Real Axis>> c-tf[520 10.3844]11 2.6817 520.11 10.397]) 520 s +10.38 SA3 +2.682 sA2 +520.1 s 10.4 Continuous-time transfer function. nyplot of (b)

Nyquist Diagram 10 0 $B 2 dB 2 dB 4 dB 4 dB 10 -2 -6 -4 -2 Real Axis

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