Parabolic trough collector. A parabolic trough collector

Chapter 12, Problem 45

(choose chapter or problem)

Control of HIV/AIDS. The linearized model of HIV infection when RTIs are used for treatment was introduced in Chapter 4 and repeated here for convenience (Craig, 2004):

\(\left[\begin{array}{c} \dot{T} \\ \dot{T}^* \\ \dot{v} \end{array}\right]=\left[\begin{array}{ccc} -0.04167 & 0 & -0.0058 \\ 0.0217 & -0.24 & 0.0058 \\ 0 & 100 & -2.4 \end{array}\right]\left[\begin{array}{c} T \\ T^* \\ v \end{array}\right]\)

\(+\left[\begin{array}{c} 5.2 \\ -5.2 \\ 0 \end{array}\right] u_1\)

\(y=\left[\begin{array}{lll} 0 & 0 & 1 \end{array}\right]\left[\begin{array}{c} T \\ T^* \\ v \end{array}\right]\)

T represents the number of healthy T-cells, \(T^*\) the number of infected cells, and v the number of free viruses.

a. Design a state-feedback scheme to obtain

(1) zero steady-state error for step inputs

(2) 10% overshoot

(3) a settling time of approximately 100 days

(Hint: the system's transfer function has an open-loop zero at approximately -0.02. Use one of the poles in the desired closed-loop-pole polynomial to eliminate this zero. Place the higher-order pole 6.25 times farther than the dominant pair.)

b. Simulate the unit step response of your design using Simulink.