In this paper the expansion of discrete time signals in the Laguerre functions is studied in comparison to the expansion in the pulse functions. The order of excitation of the expansion coefficients is investigated and related to the excitation order of the time domain signals. A general definition of the concept of excitation order is presented that provides a convenient tool for determining the excitation properties of, e.g., finite data sets. Examples are included to illustrate the prospects of this new definition. Furthermore, bounds on parameters associated with the regression matrix are given for either basis.

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.

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.

This paper deals with estimation and control of foam level in dynamic foaming. An improved foam level estimation methodology from a microphone signal and its automatic calibration is presented. The dynamical reaction of the foam level on air lance movements is modelled using system identification. Based on the resulting mathematical model, a controller for foam level stabilisation is designed and applied to a water model, representing the LD converter process. It is shown that the foam level can be controlled using a microphone as the measurement device and air lance movement as the actuator.