Modal Analysis

You can also perform eigenvalue analysis of the aircraft to characterize its dynamic stability. Instead of calling execute_run, call execute_eigen_mode_calc. To run this type of analysis the aircraft should be in trim, so here we determine the CL necessary for lift = weight. You must also set a velocity before the analysis with ovl.set_parameter("velocity", <velocity>) You can retrieve the eigenvalues and vectors after the analysis with get_eigenvalues and get_eigenvectors.

from optvl import OVLSolver
import numpy as np
import matplotlib.pyplot as plt

def syssho(asys):
    """
    Prints out state-system matrix A in an organized manner.

    Parameters
    ----------
    asys : ndarray (nsys x nsys)
        State matrix A.
    """
    nsys = asys.shape[0]

    # Header
    state_labels = [
        "u", "w", "q", "the",
        "v", "p", "r", "phi",
        "x", "y", "z", "psi"
    ]
    header = " ".join(f"{lab:>10}" for lab in state_labels) + "   |"
    print(header)

    # Rows
    for i in range(nsys):
        row_str = "".join(f"{val:11.4f}" for val in asys[i, :12])
        print(row_str)


ovl = OVLSolver(geo_file="aircraft.avl", mass_file="aircraft.mass",  debug=False)

vel = 10.0

ovl.set_trim_condition("velocity", 10.0)
ovl.set_constraint("Elevator", 0.00, con_var="Cm pitch moment")

ovl.execute_eigen_mode_calc()
Amat = ovl.get_system_matrix(in_body_axis=True)
syssho(Amat)


vals_ovl = ovl.get_eigenvalues()

# plot the eigenvalues
plt.plot(np.real(vals_ovl),np.imag(vals_ovl), 'o')
plt.xlabel('real')
plt.ylabel('imag')
plt.title('Eigenvalues')
plt.grid('on')
plt.show()
# ----------------------------------------------------

The eigenvalues should look like this