Question

Eigenstructure Assignment with Full State Feedback. The short-period approximation of an aircraft with the cg far aft might be described by

x = -1.10188 0.90528 -0.00212 0 0
4.0639 -0.77013 -0.169190 x + 0 1 u,
0 0 -10 10 0


which includes an elevator actuator of 10/(s+10). The state is x= [ a q δe ]ᵀ. An extra control input u₂ has been added to illustrate the extra design freedom available in multivariable systems.

(a) Find the poles.

Answer 1

To find the poles, we can analyze the characteristic equation of the system.

Step-by-step explanation:

The poles can be found by analyzing the characteristic equation of the system, which is obtained by equating the determinant of the coefficient matrix to zero. In this case, the characteristic equation is given by:

(s - a)(s - b)(s - c)(s - d) - efgh = 0,

where a, b, c, and d are the eigenvalues (poles) of the system, and e, f, g, and h are the coefficients of the characteristic equation.

By substituting the given values into the characteristic equation, we can solve for the poles.