Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach
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, h...
| Main Authors: | , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2023-03-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/11/5/1238 |
| _version_ | 1797614889538158592 |
|---|---|
| author | Luis Alberto Cantera-Cantera Rubén Garrido Luis Luna Cristóbal Vargas-Jarillo Erick Asiain |
| author_facet | Luis Alberto Cantera-Cantera Rubén Garrido Luis Luna Cristóbal Vargas-Jarillo Erick Asiain |
| author_sort | Luis Alberto Cantera-Cantera |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-11T07:17:44Z |
| format | Article |
| id | doaj.art-818823ef06644b33a5b894854f9b1062 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T07:17:44Z |
| publishDate | 2023-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-818823ef06644b33a5b894854f9b10622023-11-17T08:10:06ZengMDPI AGMathematics2227-73902023-03-01115123810.3390/math11051238Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances ApproachLuis Alberto Cantera-Cantera0Rubén Garrido1Luis Luna2Cristóbal Vargas-Jarillo3Erick Asiain4Automation and Control Engineering Department, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos, Zacatenco, Av. Luis Enrique Erro s/n, Mexico City 07738, MexicoAutomatic Control Department, CINVESTAV-IPN, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico City 07360, MexicoCentro de Estudios Científicos y Tecnológicos No. 9, Instituto Politécnico Nacional, Mexico City 11400, MexicoAutomatic Control Department, CINVESTAV-IPN, Av. Instituto Politecnico Nacional 2508, Col. San Pedro Zacatenco, Mexico City 07360, MexicoCentro de Estudios Científicos y Tecnológicos No. 9, Instituto Politécnico Nacional, Mexico City 11400, MexicoThis 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.https://www.mdpi.com/2227-7390/11/5/1238servo systemparameter identificationleast squares methodleast squares of orthogonal distances methodmotion control |
| spellingShingle | Luis Alberto Cantera-Cantera Rubén Garrido Luis Luna Cristóbal Vargas-Jarillo Erick Asiain Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach Mathematics servo system parameter identification least squares method least squares of orthogonal distances method motion control |
| title | Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach |
| title_full | Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach |
| title_fullStr | Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach |
| title_full_unstemmed | Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach |
| title_short | Identification of Linear Time-Invariant Systems: A Least Squares of Orthogonal Distances Approach |
| title_sort | identification of linear time invariant systems a least squares of orthogonal distances approach |
| topic | servo system parameter identification least squares method least squares of orthogonal distances method motion control |
| url | https://www.mdpi.com/2227-7390/11/5/1238 |
| work_keys_str_mv | AT luisalbertocanteracantera identificationoflineartimeinvariantsystemsaleastsquaresoforthogonaldistancesapproach AT rubengarrido identificationoflineartimeinvariantsystemsaleastsquaresoforthogonaldistancesapproach AT luisluna identificationoflineartimeinvariantsystemsaleastsquaresoforthogonaldistancesapproach AT cristobalvargasjarillo identificationoflineartimeinvariantsystemsaleastsquaresoforthogonaldistancesapproach AT erickasiain identificationoflineartimeinvariantsystemsaleastsquaresoforthogonaldistancesapproach |