Tensor product transformation‐based modeling of an induction machine

Abstract

The paper demonstrates a tensor product (TP) model transformation‐based framework for an induction machine (IM). The state space model of an IM is highly nonlinear, thus the Takagi–Sugeno (TS) fuzzy model‐based quasi‐linear parameter‐varying (qLPV) representation can be a good alternative approach of machines modeling. The paper presents the basics of IM state space modeling, how the TP transformation can be applied in details. The control of IM is always a pivotal point; hence, options of feedback control are discussed. The main goal of this paper is to present the whole process of IM TP transformation‐based modeling including a control system.

Performance Improvement of Low-Cost Iterative Learning-Based Fuzzy Control Systems for Tower Crane Systems

“…The main purpose of TP-based model transformation is to map a given Linear Parameter Varying (LPV) or quasi-Linear Parameter Varying (qLPV) state-space model onto a TP model made of Linear Time Invariant (LTI) systems using the Higher Order Singular Value Decomposition. The TP-based model transformation technique was successfully applied recently to tower crane system modeling [92], pendulum cart system modeling [93], [94], black box system modeling [95], induction machine modeling [96], and white noise process modeling [97]. This transformation technique was also used in the TP-based controller design; TP controllers were designed for a big number of processes including more recent ones such as Lotka-Volterra fractional order model [98] and aeroelastic systems [99], but they could be applied to other systems as, for instance, networked control systems [100].…”

Tensor Product Alternatives for Nonlinear Field-Oriented Control of Induction Machines

“…The mentioned control system is a nonlinear state feedback controller completed by the integral action to eliminate the steady-state error of the step response and to attenuate disturbance and noise effects [41,42,50].…”

“…The induction machine nonlinear TP-based controller is complemented by an integral action and observer in [41,42]. The designed controller ensures stable and accurate operation over the full operating range of the machine, taking into account the wide range of temperature values, and possible variations in inductances, which are outside the range of the parameters under consideration.…”

“…In contrast, the TP model transformation-based control is numerical and easy to algorithmize. Therefore, high performance and easy to implement control methods can be achieved by combining FOC and TP transformation, similarly to [40][41][42]. However, the idea of [43] shows that a TP model has a huge number of alternatives.…”