A well-known method by Anderson and Moore for optimal quadratic feedback design with guaranteed constant convergence rate for linear time-invariant systems is generalised to linear complex-valued time-varying systems and time-varying convergence rates. The resulting method is readily applicable to observer design for state-affine systems and unifies methods developed there with the classical quadratic optimal state estimation and control. A pre-assigned time-varying convergence rate is shown to significantly improve the observer's transients in comparison with a constant one being employed for flux estimation in induction machines.

Identification of all the electrical parameters of Induction Machines (IMs) is a prerequisite for successful model-based control and/or fault detection. Most of the existing identification methods of symmetrical IMs are, strictly speaking, valid only at stationary conditions, which limitation results in either poor dynamics excitation or gross approximation errors, depending on the working conditions of the motor. In this paper, the topic of identification of all electrical parameters of faulty IMs is addressed for the first time. A method for on-line observer-based estimation of all electrical parameters of IMs with faulty stator is presented aiming primarily at fault tolerant control and fault detection. The approach does not rely on any assumptions regarding the rotor angular speed and/or acceleration.

In this paper, two dynamical models of the induction machine (IM) subject to electrical faults in the stator and rotor respectively are validated against experimental data. The considered stator faults are inter-turn short circuit in one of the phases and increased phase winding resistance. The rotor model is validated against an IM with one broken rotor bar, but otherwise healthy. The model parameters are estimated by the Gauss-Newton method and the obtained estimates are compared and discussed. The validation results show, for each of the considered faults, very good agreement between simulations and experiments. This makes the models promising in various applications involving asymmetric IM such as fault tolerant motor drives and motor condition monitoring.

A well-known method by Anderson and Moore for optimal quadratic feedback design with guaranteed convergence rate for linear time-invariant systems is generalized to linear complex-valued time-varying systems and convergence rates. The resulting method is applied to observer design and illustrated by solving the problem of flux estimation in induction machines. A pre-assigned time-varying convergence rate is shown to improve the observer's transients in comparison with a constant one. The suggested design technique can be readily utilized for nonlinear state-affine systems

In this paper, a low differential order model describing the dynamics of IMs with faulty stator is developed. The modelling is performed under well established idealizing assumptions regarding the magnetic and electrical properties of the motor. Typical motor faults as inter-turn short circuit and increased winding resistance are taken into account. The resulting model can be handled analytically and serve as a ground for fault detection and fault tolerant control of the IM. For each of the considered faults, very good agreement between simulations and experimental data collected from mass-produced industrial IMs is observed.

This thesis covers a broad range of subjects pertaining to induction machines, faulty as well as healthy ones. Firstly, a completely new and unconventional methodology for deriving simplest possible, yet sufficiently accurate, mathematical models for induction machines with general electrical faults is presented. Examples of common faults covered are inter-turn short circuit and increased resistance in one or more stator phases. Some common rotor faults treated in the thesis are broken rotor bars and broken end rings. Another fault that is encompassed by the modeling approach is diminished air-gap in front of one or more stator and/or rotor phases. Although straightforward to consider, it is unlikely in practice that more than one fault would occur at a time. Therefore, the modeling technique is explicitly used for arriving at two different models, where it is assumed that there is an electrical fault in either one stator phase or in one rotor phase. Interestingly, complexity of the resulting models is comparable to that of conventional models for healthy induction machines. The two models are validated against data collected from real-life induction machines with faults on purpose imposed upon them, with excellent agreement between the simulated and measured signals. Secondly, system properties of the two derived models, such as dissipativity, observability and controllability, are analyzed. It is shown that neither a stator nor a rotor fault alters these system attributes, except for very special cases. Furthermore, when a healthy induction machine is subject to a constant load and a perfectly balanced stator voltage source, it is proven that the rotor speed cannot be stabilized if the voltage has a spectral content comprising more than two distinct frequencies. Thirdly, the two developed models are used for state and parameter estimation in induction machines. Two kinds of observers are designed. The first one aims at robust stator flux estimation for healthy induction machines. It is shown that exponential convergence of the estimation error can be guaranteed, at a rate independent of the rotor speed. Therefore, the design possesses robustness against disturbance in rotor speed measurements, however with an upper bound on attainable performance. The second observer methodology provides a generalized linear-quadratic optimal framework for linear complex-valued time-varying systems, where an arbitrary, possibly time-varying, guaranteed convergence rate can be assigned. The methodology is thereafter used in a new parameter estimation scheme, both for healthy induction machines and those subject to stator faults, in order to estimate all electrical parameters on-line, under very mild assumptions. Specifically, the scheme can be used for fault detection. Simulations validating the methodology are provided.

In this paper an analysis of observability and controllability of the electrical part of faulty (non-symmetric) induction machines (IMs) is performed. A two-axis model of healthy or faulty IM is studied and the conditions under which it does not degenerate to a descriptor system are obtained. When degeneration does not occur and stator voltages, stator currents and the rotational angle/speed of the rotor are measured, a fault in the IM does not, in general, render the motor neither unobservable nor uncontrollable. However, it turns out that when the rotor resistance is very small, problems with observability and controllability still may arise.

Identification of all the electrical parameters of Induction Machines (IMs) is a prerequisite for successful model-based control and/or fault detection. Various approaches have been proposed previously: off-line experiments under alternating stationary conditions, least squares batch and on-line estimation, to name only a few. Both continuous and discrete time have been considered, all of them utilizing models for symmetrical IMs. Existing methods for identification of the electrical parameters of the IM are strictly speaking valid only at stationary conditions, which limitation results in either poor dynamics excitation or gross approximation errors, depending on the working conditions of the motor. Unrealistic assumptions about the rotor's angular acceleration are also often employed. The topic of identification of all electrical parameters of faulty IMs has not been addressed so far. In this paper, a method for on-line observer-based estimation of all electrical parameters of symmetrical IMs as well as IMs with faulty stator is presented aiming primarily at fault tolerant control and fault detection. The approach does not rely on any assumptions regarding the rotor's angular speed and/or acceleration.

In this report a general framework for developing two-axis models for Induction Machines (IMs) with electrical faults is presented. It produces models that are of reasonably low differential order, suitable for mathematical analysis and can serve as a ground for fault detection and fault tolerant control of the IM. The modelling is performed by applying well established idealizing assumptions regarding the magnetic and electrical properties of the motor. In particular, models describing the IM subject to electrical faults in the stator and rotor are derived. Typical motor faults as inter-turn short circuit, increased winding resistance and broken rotor bars are taken into account. The models are validated against data collected from mass-produced industrial IMs. The validation shows very good agreement between simulations and experiment, for each of the considered faults. Finally, a stability proof for the derived models is presented enabling their use in control and monitoring applications.

A new method for estimation of electrical parameters in Induction Machines (IM) is presented. Evaluation of the parameters is performed by considering the envelope of the stator currents under motor start-up, thus avoiding the high sampling rates necessary for logging the actual currents. The use of start-up data makes the method attractive in the IM control and monitoring applications where the parameter estimates can be used for adjusting the control law or evaluating the motor condition. It is also demonstrated that the use of a simplified decoupled dynamic model of the IM in the estimation algorithm does not significantly worsen the quality of the obtained parameter estimates. Both simulations and experiments show fast convergence of the suggested algorithm.