The concept of least-squares observer is revisited. Robustness properties of this class of observers with respect to norm-bounded measurement noise are investigated and shown to be very much dependent on the operator chosen for the observer implementation. For the case of a harmonic oscillator, an explicit observer parameterization in terms of the implementation operator and the oscillator frequency is obtained, and observer's existence conditions are proven and analyzed
This paper deals with the External Model Repetitive Controller, a structure that combines the classical repetitive disturbance model (in the form of a time delay with a unit feedback) with a feedback of a disturbance estimate. The latter is often termed the External Model Controller and has a broad spectrum of technical applications, e.g., active vibration control. By analyzing the controller performance under the assumption of a disturbance period modeling error, it is shown that an unacceptable performance degradation might occur even for very small values of the modeling error
This paper deals with physical modeling and control of dynamic foaming in the LD-converter process. An experimental setup consisting of a water model, digital signal processor, and PC hardware is built and shown to be useful for studying dynamic foaming. Furthermore, a foam height estimation algorithm is presented and validated through experiments. Finally, sound signals from the LD-converter and water model are compared and similarities between them are found.
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.
A novel approach for monitoring and control of the coal powder injection in a blast furnace is presented and discussed. Image analysis of video recordings is used as a means to estimate the instantaneous coal flow. Initial experiments at the blast furnace no 3 of SSAB Tunnplat AB Lulea, Sweden, have been performed and first hand results on modelling and control of a single injection line are given.
Deals with model-based pressure and flow control of a fine coal injection vessel for the use of the blast furnace injection process. By means of system modeling and identification, the structure and behavior of the coal injection vessel are analyzed. It is shown that by use of model-based design, the control goals can be reached and the control performance can be significantly improved compared to the conventional PI-controllers. Several dynamic models of the plant are developed. A number of control strategies are presented and compared by means of practical tests. The LQG design method is used to design the controllers. All the controllers are validated through experiments on the coal injection plant at SSAB Tunnplat in Lulea, Sweden
This paper deals with model-based pressure and flow control of a fine coal injection vessel for the use of the blast furnace process. A control system should be in place to maintain a constant coal mass flow from the injection vessel to the blast furnace, since irregularities in the coal mass flow cause significant variations in the hot metal quality. By means of system modeling, the structure and behavior of the coal injection vessel are analyzed. It is shown that by use of a model-based design, the control objectives can be reached and the control performance can be significantly improved compared to the proportional integral (PI) controllers. Alternative control strategies are discussed and compared with the conventional design. The linear quadratic Gaussian (LQG) design method is used to design a multi-input multi-output (MIMO) controller which is validated through experiments on the coal injection plant at SSAB Tunnplat, Lulea, Sweden.
This paper deals with a sensitivity analysis of a linear quadratic optimal multivariable controller for a fine coal injection vessel used in the blast furnace process. The multivariable controller from a previous work is briefly presented and the closed-loop system is studied by means of a sensitivity analysis. Effects of disturbances and uncertainty on the closed-loop system are studied based on analysis of the singular values of the sensitivity and the complementary sensitivity functions, the relative gain array, and the minimized condition numbers. Finally, the sensitivity analysis is validated by the use of logged data from test operation at the coal injection plant at SSAB Tunnplat AB, Lulea, Sweden
This paper deals with a sensitivity analysis of an LQ optimal multivariable controller for a fine coal injection vessel used in the blast furnace process. The multivariable controller from a previous work is briefly presented and the closed loop system is studied by means of a sensitivity analysis. Effects of disturbances and uncertainty on the closed loop system are studied based on analysis of the singular values of the sensitivity and the complementary sensitivity functions, the relative gain array and the minimized condition numbers. Finally, the sensitivity analysis is validated by the use of logged data from test operation at the coal injection plant at SSAB Tunnplat Lulea, Sweden
A straightforward method for the estimation of continuous time delays in narrowband signals is proposed. Delay estimation is especially of interest for those areas in signal processing that deal with the time delay of arrival (TDOA). The new method involves a parameterization of the identification problem in the Laguerre functions. This formalism is chosen due to the nature of the signals. Then the delay is obtained from a finite number of input/output Laguerre coefficients by using l2 norm optimal estimation. Estimation bounds are given and experiments from ultrasonic applications are presented
The time delay of arrival (TDOA) is required in many areas in signal processing. In this paper we propose a novel and straightforward method to estimate small continuous time delays in narrowband signals out of a sampled sequence of the input and output signals. It is based on the parameterization of the identification problem in the Laguerre functions. An lp norm optimal estimator is then applied to estimate the delay. Furthermore, estimation bounds are studied and experiments from ultrasonic applications are presented to highlight the performance of the method
The identification of a pressurized tank process is considered. A subspace identification method is employed that identifies the system in question from the Laguerre spectra of the input/output data. The method is presented in a general form and valid in the continuous and in the discrete-time case. Using the input/output Laguerre spectra for identification, instead of the complete input/output data vectors, leads to a considerable data reduction. Furthermore, it is shown by a simulation study that the subspace identification method n4sid works better in Laguerre domain than in the time domain.
A method for detecting and isolating incipient leakages in the valves of a pulverized coal injection vessel for a blast furnace process is presented. Nonlinear physical gray-box models of the plant are developed. Values of the unknown parameters are estimated by identification. Observers are constructed for these models and the residuals are used in a generalized likelihood ratio test. The method is successfully tested with real leakages intentionally introduced in the plant.
The problem of real time metal analysis estimation for the basic oxygen steelmaking process is considered. Nonlinear feedback is applied to a nonlinear process model, thus creating a non linear observer. It is compared to linear feedback on the same process model and is shown to have superior performance. Using real plant data from the converter at SSAB Oxelösund AB, the observer is shown to provide accurate estimates of the carbon content.
By making use of a second-order complex-valued model of the induction machine dynamics, two observer design methods providing a guaranteed estimation error convergence rate at any, probably time-varying, rotor angular velocity are introduced. The design algorithms are based on eigenvector-eigenvalue assignment, alternatively matrix measure assignment and demonstrated to work well in an experiment
A wide class of continuous least-squares (LS) observers is treated in a common framework provided by the pseudodifferential operator paradigm. It is shown that for the operators whose symbols satisfy certain conditions, the continuous LS observer always exists, providing observability of the plant. The general result is illustrated by an LS observer stemming from a sliding-window convolution operator. Applications to state feedback control and fault detection are discussed
A wide class of continuous least-squares (LS) observers is treated in a common framework provided by the pseudodifferential operator paradigm. It is shown that for the operators whose symbols satisfy certain conditions, the continuous LS-observer always exists provided observability of the plant. The general result is illustrated by an LS-observer stemmed from a sliding-window convolution operator. Applications to state feedback control and fault detection are discussed. A wide class of continuous least-squares (LS) observers is treated in a common framework provided by the pseudodifferential operator paradigm. It is shown that for the operators whose symbols satisfy certain conditions, the continuous LS-observer always exists provided observability of the plant. The general result is illustrated by an LS-observer stemmed from a sliding-window convolution operator. Applications to state feedback control and fault detection are discussed. A wide class of continuous least-squares (LS) observers is treated in a common framework provided by the pseudodifferential operator paradigm. It is shown that for the operators whose symbols satisfy certain conditions, the continuous LS-observer always exists provided observability of the plant. The general result is illustrated by an LS-observer stemmed from a sliding-window convolution operator. Applications to state feedback control and fault detection are discussed.
This paper presents a generalization of the Parity Space Method (PSM) for fault detection and isolation by means of pseudodifferential operators. It is shown that a number of recently suggested Parity Space approaches in continuous time can be treated within a generic framework. Disturbance rejection properties of the parity checks written as polynomials in a pseudodifferential operator are studied in terms of 2- and ∞-norms. A consequent analysis demonstrates superior performance of the sliding-window convolution operator-based PSM
Two finite-spectrum-assignment controllers for continuous linear dynamic systems with multiple time delays in input signal are introduced. The controllers are shown to comprise least-squares state estimators. Disturbance attenuation properties stipulated by the choice of shift operator in the observers are studied.
The well-known parity space method for fault detection and isolation is generalized to a continuous-time case. As in the discrete-time case, it is shown that the parity space equations can be implemented using a number of time delays, and are equivalent to a continuous deadbeat observer. Algorithms for isolation of sensor and actuator faults are derived and illustrated by a numerical example. (
A continuous deadbeat observer estimating a linear combination of the state variables is introduced and applied to the problem of detecting and isolating faults in a linear time-invariant system. The existence conditions for the deadbeat observer are shown to be the same as for the functional Luenberger observer.
An application of continuous-time deadbeat observation to fault analysis in linear dynamic systems is discussed. A finite memory residual chosen as a difference of two deadbeat state vector estimates is shown to be independent of both the state vector and control signal. The mapping of the fault mode to the residual is proven to be intrinsically BIBO-stable. Exploiting a decomposition of the “sliding-window” convolution operator, an upper bound for residual norm is derived and a fault detectability condition is obtained. Due to its simple structure, the deadbeat observer does not create a hard computational burden and can be easily implemented in real-time applications.
Deals with stability properties of two known flux observers for induction machines. It is shown that an arbitrary fast convergence rate in one of the observers is achieved at the expense of its robustness against uncertainty in the rotor angular velocity. Another observer is proven to retain stability notwithstanding any error in the angular velocity measurements, but its estimation error convergence rate is limited by the rotor time constant
In this paper, the well-known parity space method is generalized to a continuous-time case both in deterministic and stochastic frameworks. As in the discrete-time case, it is shown that the parity space equations are equivalent to a continuous deadbeat observer or, taking into account measurement/process noise, to a finite-memory smoother. Both structures are infinite-dimensional by nature and can be implemented using a number of time delays. In the deterministic setting there is a significant liberty in choosing the delays. In the stochastic setting, to achieve optimality of the resulting parity equations, the delays are to be computed from the properties of noise.
A continuous observer estimating the state vector of a linear time-invariant system from the measurements of the system's inputs and outputs passed through a bank of finite-memory filters is introduced. System observability is shown to guarantee the existence of the observer. An application of the observer to the problem of detecting and isolating sensor and actuator faults is discussed
A continuous-time deadbeat observation paradigm is discussed. Two observers are shown to estimate the state of a linear dynamic system in continuous time with respectively finite and infinite memory. Among other properties, BIBO-stability is proved for both structures. Based on the theory devised, deadbeat and asymptotic predictors for plants with delayed control are developed and shown to give rise to predictive feedback controllers assigning finite spectrum to the closed-loop system
The paper investigates the possibilities of using a feedforward time-delay structure for state estimation and smoothing in linear continuous dynamic systems. A fixed-lag finite-memory smoother and a continuous deadbeat observer are shown to be described by a linear combination of delayed measurements of the system inputs and outputs. To facilitate implementation of the observer-based controllers an infinite-memory deadbeat observer is introduced. Design methods are illustrated by numerical examples.
A feedforward neural network (FNN) implementation of a finite-memory smoother (FMS) is proposed. For a linear time-invariant dynamic system with measurement and process white noise, a single-layer FNN with delayed inputs is found to possess the same structure as the FMS designed by the least-squares method. The FNN-based FMS features definite speed advantages over conventional approaches and intrinsically finite process memory. Due to its parallel structure and absence of state vector integration, the FNN suffices for real-time applications. A numerical example illustrates the design procedure
A significant class of model-based control approaches uses Kalman filters or Luenberger observers to estimate the plant state vector. Infinite dynamic observer memory inflicts a phenomenon generally referred to as divergence. To overcome this drawback, a structure that intrinsically has finite process memory and does not need state vector integration is proposed in this paper. The observer uses a finite number of delayed input/output measurements to reconstruct the state vector with zero error being provided with a process history over its largest time-delay. This property resembles the deadbeat observer performance for discrete time systems. Moreover, the largest time-delay value puts a natural limit to the observer memory. The Luenberger observer analogy proved to be a useful tool for the observer analysis and paves the way toward observer optimization.
Design aspects of a flux observer for induction machines are discussed. By making use of a second-order, complex-valued, state-space model of the induction machine dynamics, a stability criterion and observer estimation error bounds are obtained. An observer design method providing arbitrary convergence rate of the estimation error by means of a real-valued feedback gain matrix is introduced.
At the Boliden's concentrator in Aitik, bulk flotation constitutes an important part of the process for extracting valuable minerals from the ore. A series of flotation cells consists of five tanks connected in cascade with control valves between the tanks and a slowly varying flow of mineral slurry into the first tank. This paper deals with a comparative study of control strategies for level control in a flotation series in Aitik. The aim is to show the potential performance improvements taking into account couplings between the process state variables. Two control strategies are considered; a decoupling controller and a linear quadratic (LQ) optimal multivariable controller. Experiments with both structures show a significant enhancement of the level control performance as compared to the original SISO design.
At the Boliden's concentrator in Aitik, bulk flotation constitutes an important part of the process for extracting valuable minerals from the ore. A series of flotation cells consists of five tanks connected in cascade with control valves between the tanks and a slowly varying flow of mineral slurry into the first tank. This paper deals with a comparative study of control strategies for level control in a flotation series in Aitik. The aim is to show the potential performance improvements taking into account couplings between the process state variables. Two control strategies are considered; a decoupling controller and a linear quadratic (LQ) optimal multivariable controller. Experiments with both structures show a significant enhancement of the level control performance as compared to the original SISO design
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.
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
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.
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. 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.
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.
The stationary conditions for an induction machine (IM) fed by a voltage source containing more than one frequency are studied. Furthermore, it is shown that given one: harmonic input signal, it is possible to stabilize the angular speed of the IM at a beforehand chosen level, by a special choice of frequency and amplitude of a second signal. A generalization to a broader class of feeding signals is provided. The theoretical results suggest that conventional linear time-invariant identification of electrical parameters of the IM become applicable, since using two different symmetrical signals at once will guarantee sufficiently rich excitation for successful identification. Moreover, the method may be used for a new kind of control, where some control algorithm changes the amplitude and/or frequency of the two symmetrical signals.
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.
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 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.
Model-based closed-loop control of the basic oxygen steelmaking process will give an opportunity to increase process operation performance. By using control algorithms that interact with thermodynamical and physical models capable of making real-time predictions of the effects of control actions, the time delays in order to wait for process response will be eliminated. Existing limitations like pre-set lance programs can be avoided. This paper outlines the concept of a recently started project aiming at model-based closed-loop control as well as present the initial work that has been made on the subject.
This paper describes a method of designing reduced-order observers in the space-phasor flux description of the induction machine. By making use of the second-order complex model of the induction machine, two reduced-order observer structures with time-invariant feedback gains are derived and shown to possess arbitrary convergence rate. Experimental runs facilitate comparison of the suggested reduced-order observers with the well-known full-order time-variant feedback gain observer.
A robust model-based technique for fault detection and isolation in electro-mechanical systems comprising induction machines is introduced. A state observer for reconstructing the magnetic flux components of the induction machine and thereby the electrical torque is used in combination with a robust state estimator for the mechanical load torque based on a model with structured uncertainties. The fault detection and isolation problem is reduced to validation/invalidation of the models representing different fault hypotheses. The practical applicability of the method is demonstrated in a simulation example