Question

1. A number of acute upper respiratory viral infections are treated using a combination of antiviral agents as well as antibiotics. Assume that two of these compounds are prescribed for an infected patient. We would like to develop a dosage regimen that maintains viral load at a set level using a linearized infection model. Given the feedback system shown below, determine the range of proportional gain values for which the system has closed-loop stability using the Routh-Hurwitz criterion. Desired Virus Load change + X(s) Virus Load Change Y(s) -520s - 10.3844 53 +2.6817s2 + 0.115 +0.0126

Answer 1

CE=o. 2 83 + 2.6817 82 & 8 Coll_520kc +0.0126-10.3844K) FCRBK2クー Routh Array: - POS 0000 (0.11-520kc) (0.0126-10.38 kg 82 2.6817 160.0126 - 10.3844 KJ 52.6817 (8 11-szok() 2.6817 $0 (0.0126-10:38 Kc) a) bo A m or Routh Assay calculation) :- (6.11-szokolo (0.0126 - 10.38 kc). 8² 2.6817 s! 1384.1K0-0 28 2387 44 goo.0126-10.38ltc. Routh criteria states that; & All elements of 1st column should be positive. This yeildin 1384.1 kc -0.282387 SO → @ 44 and 0.0126 - 10.38 kc do ③ .

solving equation :- - PFIDO 1384.1 kc > 0.282387 > Kc> 0.000 204. solving equation 0.0126) 10.3844 ke. 9 Kc < 0.00121337 combining Ⓡ and ® - 0.000204 <kc co.0012133 28 -OSO.)