TY - JOUR
T1 - Identification of Linear Time-Invariant Systems
T2 - A Least Squares of Orthogonal Distances Approach
AU - Cantera-Cantera, Luis Alberto
AU - Garrido, Rubén
AU - Luna, Luis
AU - Vargas-Jarillo, Cristóbal
AU - Asiain, Erick
N1 - Publisher Copyright:
© 2023 by the authors.
PY - 2023/3
Y1 - 2023/3
N2 - This work describes the parameter identification of servo systems using the least squares of orthogonal distances method. The parameter identification problem was reconsidered as data fitting to a plane, which in turn corresponds to a nonlinear minimization problem. Three models of a servo system, having one, two, and three parameters, were experimentally identified using both the classic least squares and the least squares of orthogonal distances. The models with two and three parameters were identified through numerical routines. The servo system model with a single parameter only considered the input gain. In this particular case, the analytical conditions for finding the critical points and for determining the existence of a minimum were presented, and the estimate of the input gain was obtained by solving a simple quadratic equation whose coefficients depended on measured data. The results showed that as opposed to the least squares method, the least squares of orthogonal distances method experimentally produced consistent estimates without regard for the classic persistency-of-excitation condition. Moreover, the parameter estimates of the least squares of orthogonal distances method produced the best tracking performance when they were used to compute a trajectory-tracking controller.
AB - This work describes the parameter identification of servo systems using the least squares of orthogonal distances method. The parameter identification problem was reconsidered as data fitting to a plane, which in turn corresponds to a nonlinear minimization problem. Three models of a servo system, having one, two, and three parameters, were experimentally identified using both the classic least squares and the least squares of orthogonal distances. The models with two and three parameters were identified through numerical routines. The servo system model with a single parameter only considered the input gain. In this particular case, the analytical conditions for finding the critical points and for determining the existence of a minimum were presented, and the estimate of the input gain was obtained by solving a simple quadratic equation whose coefficients depended on measured data. The results showed that as opposed to the least squares method, the least squares of orthogonal distances method experimentally produced consistent estimates without regard for the classic persistency-of-excitation condition. Moreover, the parameter estimates of the least squares of orthogonal distances method produced the best tracking performance when they were used to compute a trajectory-tracking controller.
KW - least squares method
KW - least squares of orthogonal distances method
KW - motion control
KW - parameter identification
KW - servo system
UR - http://www.scopus.com/inward/record.url?scp=85149859713&partnerID=8YFLogxK
U2 - 10.3390/math11051238
DO - 10.3390/math11051238
M3 - Artículo
AN - SCOPUS:85149859713
SN - 2227-7390
VL - 11
JO - Mathematics
JF - Mathematics
IS - 5
M1 - 1238
ER -