Next Article in Journal
A Holistic Scalable Implementation Approach of the Lattice Boltzmann Method for CPU/GPU Heterogeneous Clusters
Previous Article in Journal
Dynamic Data-Driven Modeling for Ex Vivo Data Analysis: Insights into Liver Transplantation and Pathobiology
Article Menu

Export Article

Open AccessArticle
Computation 2017, 5(4), 47;

Nonlinear-Adaptive Mathematical System Identification

Department of Mechanical Engineering, Stanford University, Stanford, CA 94305, USA
Received: 29 September 2017 / Revised: 23 November 2017 / Accepted: 28 November 2017 / Published: 30 November 2017
(This article belongs to the Section Computational Engineering)
Full-Text   |   PDF [3442 KB, uploaded 30 November 2017]   |  


By reversing paradigms that normally utilize mathematical models as the basis for nonlinear adaptive controllers, this article describes using the controller to serve as a novel computational approach for mathematical system identification. System identification usually begins with the dynamics, and then seeks to parameterize the mathematical model in an optimization relationship that produces estimates of the parameters that minimize a designated cost function. The proposed methodology uses a DC motor with a minimum-phase mathematical model controlled by a self-tuning regulator without model pole cancelation. The normal system identification process is briefly articulated by parameterizing the system for least squares estimation that includes an allowance for exponential forgetting to deal with time-varying plants. Next, towards the proposed approach, the Diophantine equation is derived for an indirect self-tuner where feedforward and feedback controls are both parameterized in terms of the motor’s math model. As the controller seeks to nullify tracking errors, the assumed plant parameters are adapted and quickly converge on the correct parameters of the motor’s math model. Next, a more challenging non-minimum phase system is investigated, and the earlier implemented technique is modified utilizing a direct self-tuner with an increased pole excess. The nominal method experiences control chattering (an undesirable characteristic that could potentially damage the motor during testing), while the increased pole excess eliminates the control chattering, yet maintains effective mathematical system identification. This novel approach permits algorithms normally used for control to instead be used effectively for mathematical system identification. View Full-Text
Keywords: Diophantine; Bezout; Aryabhatta; Wiener–Hammerstein; non-minimum phase systems; system identification; nonlinear-adaptive control; self-tuning regulators; pole excess Diophantine; Bezout; Aryabhatta; Wiener–Hammerstein; non-minimum phase systems; system identification; nonlinear-adaptive control; self-tuning regulators; pole excess

Figure 1

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

MDPI and ACS Style

Sands, T. Nonlinear-Adaptive Mathematical System Identification. Computation 2017, 5, 47.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Related Articles

Article Metrics

Article Access Statistics



[Return to top]
Computation EISSN 2079-3197 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top