Nonlinear-Adaptive Mathematical System Identification
AbstractBy 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
Share & Cite This Article
Sands, T. Nonlinear-Adaptive Mathematical System Identification. Computation 2017, 5, 47.
Sands T. Nonlinear-Adaptive Mathematical System Identification. Computation. 2017; 5(4):47.Chicago/Turabian Style
Sands, Timothy. 2017. "Nonlinear-Adaptive Mathematical System Identification." Computation 5, no. 4: 47.
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.