Design an observer for the plant Gs 10 s 3s 7s 15

Chapter 12, Problem 19

(choose chapter or problem)

For a specific individual, the linear time-invariant model of the hypothalamic-pituitary adrenal axis of the endocrine system with five state variables has been found to be (Kyrylov, 2005)

\(\left[\begin{array}{c} \dot{x}_1 \\ \dot{x}_2 \\ \dot{x}_3 \\ \dot{x}_4 \\ \dot{x}_5 \end{array}\right]=\left[\begin{array}{ccccc} -0.014 & 0 & -1.4 & 0 & 0 \\ 0.023 & -0.023 & -0.023 & 0 & 0 \\ 0.134 & 0.67 & -0.67 & 0.38 & 0.003264 \\ 0 & 0 & 0.06 & -0.06 & 0 \\ 0 & 0 & 0.0017 & 0 & -0.001 \end{array}\right]\)

\(\times\left[\begin{array}{l} x_1 \\ x_2 \\ x_3 \\ x_4 \\ x_5 \end{array}\right]+\left[\begin{array}{l} 1 \\ 0 \\ 0 \\ 0 \\ 0 \end{array}\right] d_0\)

The State-variable definitions were given in Problem 23, Chapter 3.

a. Use MATLAB to determine if the system is controllable.

b. Use MATLAB to express the matrices A and B in phase-variable form.