Parameter adaptation of simplified switched reluctance motor model using Newton and Gauss-Newton signal fitting methods

Abstract

Purpose

The paper is concerned about parameter adaptation of a novel, simplified and nonlinear switched reluctance motor (SRM) model. The purpose of the presented on-line procedure is to give an opportunity to set the model parameters’ values to obtain a relatively good convergence with the real control object. This is important when a reference model is used for control (e.g. optimal) or object state classification (e.g. fault detection) purposes. The more convergent the real object model is, the better operation quality may be expected.

Design/methodology/approach

In the paper, a 12/8 pole’s SRM as a control object is analyzed. The model equations were verified experimentally by comparing phase current model estimations with reference (measured) ones at different operational points. Differential equations of motor winding currents were chosen as an approximation function in the fitting (parameter adaptation) process using the Newton and Gauss–Newton methods. The structure of the adaptation system is presented along with the implementation in simulation environment.

Findings

It was confirmed in the simulation tests that Newton and Gauss–Newton methods of nonlinear model parameters’ adaptation may be used for the SRM. The introduced fitting structure is well suited for implementation in real-time, embedded systems. The proposed approximation function could be used in process as an expansion to Jacobian and Hessian matrices. The χ² (chi²) coefficient (commonly used to measure the quality of the signal fitting) reduced to a low value during the adaptation process. Another introduced quality coefficient shows that the Newton method is slightly better in scope of the entire adaptation process time; however, it needs more computational power.

Research limitations/implications

The proposed structure and approximation function formula in the parameters’ adaptation system is appropriate for sinusoidal distribution of the motor phase inductance value along the rotor angle position. The inductance angular shape is an implication of the mechanical construction – with appropriate dimensions and materials used. In the presented case, the referenced model is a three-phase SRM in 12/8 poles configuration used as a main drive part of Maytag Neptune washing machine produced by Emerson Motors.

Practical implications

The presented method of parameter adaptation for novel, simplified and nonlinear SRM model provides an opportunity for its use in embedded, real-time control systems. The convergent motor model, after the fitting procedure (when the estimations are close to the measurements from real object), may be used for solving many well-known control challenges such as detection of initial rotor position, sensorless control, optimal control, fault-tolerant control end in fault detection (FD) systems. The reference model may be used in FD in the way of deducing signals from the difference between the estimated and measured ones.

Originality/value

The paper proposed a new system of parameter adaptation for the evaluated nonlinear, simplified 12/8 poles SRM model. The relative simplicity of the proposed model equations provides the possibility of implementing an adaptation system in an embedded system that works in a real-time regime. A Two adaptation methods – Newton and Gauss–Newton – have been compared. The obtained results shown that the Newton fitting method is better in the way of the used quality indicator, but it consumes more computational power.

Citation

Fabianski, B. and Zawirski, K. (2017), "Parameter adaptation of simplified switched reluctance motor model using Newton and Gauss-Newton signal fitting methods", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 36 No. 3, pp. 602-618. https://doi.org/10.1108/COMPEL-10-2016-0446