B. Newman et A. Kassem, ANALYTICAL RELATIONSHIPS FOR LINEAR-QUADRATIC AEROELASTIC FLIGHT CONTROL EIGENVALUES, Journal of guidance, control, and dynamics, 20(6), 1997, pp. 1149-1156
Several obstacles limiting the use of contemporary control design tech
niques in production vehicles are noted. These obstacles restrict one
from obtaining insight into the control law augmentation of the vehicl
e. For example, with the linear quadratic (LQ) state feedback method,
detail effects from cost function weight adjustment are not easily und
erstood. Further, the role of each feedback loop is not readily appare
nt. Fundamental to overcoming this problem is factoring of the LQ char
acteristic polynomial. Useful analytical expressions, and ultimately t
he relationships they represent, are sought between basic design param
eters of the system and the closed-loop eigenvalues, An approximate an
alytical factoring technique, previously developed for open-loop appli
cations, is considered as a tool for this closed-loop problem. The fir
st two terms of a Taylor series are used to capture the polynomial coe
fficient dependencies on the polynomial factors. By analytically inver
ting the first-order sensitivity matrix, corrections to preliminary ap
proximate factors are generated. Expressions for the closed-loop facto
rs are in terms of basic parameters such as stability and control deri
vatives, structural vibration damping ratio and natural frequency, and
cost function weights, allowing key relationships to be uncovered bet
ween the design knobs and important closed-loop features.