Answer Happy

The Infection-Quarantine dynamics of a pandemic are as follows: BSI İ N Q=-U-1Q - YI+U I, Q represent infected, quarantine states. B,y are the transmission, recovery rates. • S, N are the susceptible and total population. Initially S = N. The values of the parameters are given to be: 3 = 0.2, y = 0.1. Following is an output feedback strategy to suppress the infection: (1) (2) • At any given instance t, an intervention is made by identifying and se- lecting U = -al individuals for removal from I and moving them into isolation Q, where a is the rate of test and quarantine. Problem 1 This question is on full state feedback control and carries 3.5+9 points. 1. Is the system controllable? Give the necessary steps. 2. In order to control the infections with a rise time of 10, compute the control gain a. 2. Design a lead compensator U = bandwidth of at least 2. Problem 2 This question is on frequency response control and carries 3.5+9 points. 1. Find the transfer function I/U (from Infection-Quarantine dynamics), is the system stable? Kto stabilize the infections with a s+p