Question

The short-period approximation of an aircraft with the cg far aft might be described by

x˙= [−1.101884. 0.90528 −0.00212] [0 0]
[ 4.0639 -0.77013 -0.169190] x [0 1] u₁
[ 0 0 -10 ] [10 0]
which includes an elevator actuator of 10/(s+10). The state is x= [α​ 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 of the aircraft's control system, one would calculate the eigenvalues of the system matrix from the state-space representation of the aircraft dynamics.

Step-by-step explanation:

The question concerns the dynamic behavior of an aircraft and involves calculating the poles of a system represented by linear differential equations. This falls under the discipline of control systems engineering, a branch of aerospace engineering which addresses the stability and control of aircraft dynamics. To find the poles of the given system, one can use the state-space representation, where the poles are the eigenvalues of the system matrix A.

In this case, the matrix provided in the state-space form is not complete, but under the assumption that we are provided with the proper matrix (or system of differential equations), the process would involve calculating the eigenvalues of that matrix. Such calculations typically require methods of linear algebra such as characteristic polynomial, determinant, and trace of the matrix to establish the roots of the polynomial equation which corresponds to the eigenvalues/poles of the system.