Time-Varying System Identification Using Modulating Functions and Spline Models With Application to Bio-Processes

Time dependent parameters are frequently encountered in many real processes which need to be monitored for process modeling, control and supervision purposes. Modulating functions methods are especially suitable for this task because they use the original continuous-time differential equations and avoid differentiation of noisy signals. Among the many versions of the method available, Pearson–Lee method offers a computationally efficient alternative. In this paper, Pearson–Lee method is generalized for non-stationary continuous-time systems and the on-line version is developed. The time dependent parameters are modeled as polynomial splines inside a moving data window and recursion formulae using shifting properties of sinusoids are formulated. The simple matrix update relations considerably reduce the number of computations required when compared with repeatedly using FFT. The method is illustrated for estimating the kinetic rates and yield factors as time-varying parameters in a fermentation process. The Monod law along with temperature dependency models were used to simulate the data. The simulation study shows that it is not necessary to assume a growth model in order to estimate the kinetic rate parameters

Optimal input design and parameter estimation for continuous-time dynamical systems

Diese Arbeit behandelt die Themengebiete Design of Experiments (DoE) und Parameterschätzung für zeitkontinuierliche Systeme, welche in der modernen Regelungstheorie eine wichtige Rolle spielen. Im gewählten Kontext untersucht DoE die Auswirkungen von verschiedenen Rahmenbedingungen von Simulations- bzw. Messexperimenten auf die Qualität der Parameterschätzung, wobei der Fokus auf der Anwendung der Theorie auf praxisrelevante Problemstellungen liegt. Dafür wird die weithin bekannte Fisher-Matrix eingeführt und die resultierende nicht lineare Optimierungsaufgabe angeschrieben. An einem PT1-System wird der Informationsgehalt von Signalen und dessen Auswirkungen auf die Parameterschätzung gezeigt. Danach konzentriert sich die Arbeit auf ein Teilgebiet von DoE, nämlich Optimal Input Design (OID), und wird am Beispiel eines 1D-Positioniersystems im Detail untersucht. Ein Vergleich mit häufig verwendeten Anregungssignalen zeigt, dass generierte Anregungssignale (OID) oft einen höheren Informationsgehalt aufweisen und mit genaueren Schätzwerten einhergeht. Zusätzlicher Benefit ist, dass Beschränkungen an Eingangs-, Ausgangs- und Zustandsgrößen einfach in die Optimierungsaufgabe integriert werden können. Der zweite Teil der Arbeit behandelt Methoden zur Parameterschätzung von zeitkontinuierlichen Modellen mit dem Fokus auf der Verwendung von Modulationsfunktionen (MF) bzw. Poisson-Moment Functionals (PMF) zur Vermeidung der zeitlichen Ableitungen und Least-Squares zur Lösung des resultierenden überbestimmten Gleichungssystems. Bei verrauschten Messsignalen ergibt sich daraus sofort die Problematik von nicht erwartungstreuen Schätzergebnissen (Bias). Aus diesem Grund werden Methoden zur Schätzung und Kompensation von Bias Termen diskutiert. Beitrag dieser Arbeit ist vor allem die detaillierte Aufarbeitung eines Ansatzes zur Biaskompensation bei Verwendung von PMF und Least-Squares für lineare Systeme und dessen Erweiterung auf (leicht) nicht lineare Systeme. Der vorgestellte Ansatz zur Biaskompensation (BC-OLS) wird am nicht linearen 1D-Servo in der Simulation und mit Messdaten validiert und in der Simulation mit anderen Methoden, z.B., Total-Least-Squares verglichen. Zusätzlich wird der Ansatz von PMF auf die weiter gefasste Systemklasse der Modulationsfunktionen (MF) erweitert. Des Weiteren wird ein praxisrelevantes Problem der Parameteridentifikation diskutiert, welches auftritt, wenn das Systemverhalten nicht gänzlich von der Identifikationsgleichung beschrieben wird. Am 1D-Servo wird gezeigt, dass ein Deaktivieren und Reaktivieren der PMF Filter mit geeigneter Initialisierung diese Problematik einfach löst.This thesis addresses two topics that play a significant role in modern control theory: design of experiments (DoE) and parameter estimation methods for continuous-time (CT) models. In this context, DoE focuses on the impact of experimental design regarding the accuracy of a subsequent estimation of unknown model parameters and applying the theory to real-world applications and its detailed analysis. We introduce the Fisher-information matrix (FIM), consisting of the parameter sensitivities and the resulting highly nonlinear optimization task. By a first-order system, we demonstrate the computation of the information content, its visualization, and an illustration of the effects of higher Fisher information on parameter estimation quality. After that, the topic optimal input design (OID), a subarea of DoE, will be thoroughly explored on the practice-relevant linear and nonlinear model of a 1D-position servo system. Comparison with standard excitation signals shows that the OID signals generally provide higher information content and lead to more accurate parameter estimates using least-squares methods. Besides, this approach allows taking into account constraints on input, output, and state variables. In the second major topic of this thesis, we treat parameter estimation methods for CT systems, which provide several advantages to identify discrete-time (DT) systems, e.g., allows physical insight into model parameters. We focus on modulating function method (MFM) or Poisson moment functionals (PMF) and least-squares to estimate unknown model parameters. In the case of noisy measurement data, the problem of biased parameter estimation arises immediately. That is why we discuss the computation and compensation of the so-called estimation bias in detail. Besides the detailed elaboration of a bias compensating estimation method, this work’s main contribution is, based on PMF and least squares for linear systems, the extension to at least slightly nonlinear systems. The derived bias-compensated ordinary least-squares (BCOLS) approach for obtaining asymptotically unbiased parameter estimates is tested on a nonlinear 1D-servo model in the simulation and measurement. A comparison with other methods for bias compensation or avoidance, e.g., total least-squares (TLS), is performed. Additionally, the BC-OLS method is applied to the more general MFM. Furthermore, a practical issue of parameter estimation is discussed, which occurs when the system behavior leaves and re-enters the space covered by the identification equation. Using the 1D-servo system, one can show that disabling and re-enabling the PMF filters with appropriate initialization can solve this problem

Automatic face recognition using stereo images

Face recognition is an important pattern recognition problem, in the study of both natural and artificial learning problems. Compaxed to other biometrics, it is non-intrusive, non- invasive and requires no paxticipation from the subjects. As a result, it has many applications varying from human-computer-interaction to access control and law-enforcement to crowd surveillance. In typical optical image based face recognition systems, the systematic vaxiability arising from representing the three-dimensional (3D) shape of a face by a two-dimensional (21)) illumination intensity matrix is treated as random vaxiability. Multiple examples of the face displaying vaxying pose and expressions axe captured in different imaging conditions. The imaging environment, pose and expressions are strictly controlled and the images undergo rigorous normalisation and pre-processing. This may be implemented in a paxtially or a fully automated system. Although these systems report high classification accuracies (>90%), they lack versatility and tend to fail when deployed outside laboratory conditions. Recently, more sophisticated 3D face recognition systems haxnessing the depth information have emerged. These systems usually employ specialist equipment such as laser scanners and structured light projectors. Although more accurate than 2D optical image based recognition, these systems are equally difficult to implement in a non-co-operative environment. Existing face recognition systems, both 2D and 3D, detract from the main advantages of face recognition and fail to fully exploit its non-intrusive capacity. This is either because they rely too much on subject co-operation, which is not always available, or because they cannot cope with noisy data. The main objective of this work was to investigate the role of depth information in face recognition in a noisy environment. A stereo-based system, inspired by the human binocular vision, was devised using a pair of manually calibrated digital off-the-shelf cameras in a stereo setup to compute depth information. Depth values extracted from 2D intensity images using stereoscopy are extremely noisy, and as a result this approach for face recognition is rare. This was cofirmed by the results of our experimental work. Noise in the set of correspondences, camera calibration and triangulation led to inaccurate depth reconstruction, which in turn led to poor classifier accuracy for both 3D surface matching and 211) 2 depth maps. Recognition experiments axe performed on the Sheffield Dataset, consisting 692 images of 22 individuals with varying pose, illumination and expressions

Using Lidar to geometrically-constrain signature spaces for physics-based target detection

A fundamental task when performing target detection on spectral imagery is ensuring that a target signature is in the same metric domain as the measured spectral data set. Remotely sensed data are typically collected in digital counts and calibrated to radiance. That is, calibrated data have units of spectral radiance, while target signatures in the visible regime are commonly characterized in units of re°ectance. A necessary precursor to running a target detection algorithm is converting the measured scene data and target signature to the same domain. Atmospheric inversion or compensation is a well-known method for transforming mea- sured scene radiance values into the re°ectance domain. While this method may be math- ematically trivial, it is computationally attractive and is most e®ective when illumination conditions are constant across a scene. However, when illumination conditions are not con- stant for a given scene, signi¯cant error may be introduced when applying the same linear inversion globally. In contrast to the inversion methodology, physics-based forward modeling approaches aim to predict the possible ways that a target might appear in a scene using atmospheric and radiometric models. To fully encompass possible target variability due to changing illumination levels, a target vector space is created. In addition to accounting for varying illumination, physics-based model approaches have a distinct advantage in that they can also incorporate target variability due to a variety of other sources, to include adjacency target orientation, and mixed pixels. Increasing the variability of the target vector space may be beneficial in a global sense in that it may allow for the detection of difficult targets, such as shadowed or partially concealed targets. However, it should also be noted that expansion of the target space may introduce unnecessary confusion for a given pixel. Furthermore, traditional physics-based approaches make certain assumptions which may be prudent only when passive, spectral data for a scene are available. Common examples include the assumption of a °at ground plane and pure target pixels. Many of these assumptions may be attributed to the lack of three-dimensional (3D) spatial information for the scene. In the event that 3D spatial information were available, certain assumptions could be levied, allowing accurate geometric information to be fed to the physics-based model on a pixel- by-pixel basis. Doing so may e®ectively constrain the physics-based model, resulting in a pixel-specific target space with optimized variability and minimized confusion. This body of work explores using spatial information from a topographic Light Detection and Ranging (Lidar) system as a means to enhance the delity of physics-based models for spectral target detection. The incorporation of subpixel spatial information, relative to a hyperspectral image (HSI) pixel, provides valuable insight about plausible geometric con¯gurations of a target, background, and illumination sources within a scene. Methods for estimating local geometry on a per-pixel basis are introduced; this spatial information is then fed into a physics-based model to the forward prediction of a target in radiance space. The target detection performance based on this spatially-enhanced, spectral target space is assessed relative to current state-of-the-art spectral algorithms

Identification et commande en ligne des robots avec utilisation de différentiateurs algébriques

This thesis discusses the identification issues of the robot dynamic parameters. Starting with the well-known inverse dynamic identification model, power and energy identification models for robots, it extends the identification model from an energy point of view, by integrating modulating functions with robot power model. This new identification model avoids the computation of acceleration data. As well, the integration procedures are analyzed in frequency domain so that certain groups of modulating functions are selected in order to offer a good low-pass filtering property. Then, a recently developed high order algebraic differentiator is proposed and studied, named Jacobi differentiators. The analyses are done in both the time domain and in the frequency domain, which gives a clear clue about the differentiator filtering property and about how to select the differentiator parameters. Comparisons among different identification models, differentiators, least square techniques are presented and conclusions are drawn in the robot identification issues.Cette thèse traite de l'identification des paramètres dynamiques des robots, en s'appuyant sur les méthodes d'identification en robotique, qui utilisent le modèle dynamique inverse, ou le modèle de puissance, ou le modèle d'énergie du robot. Ce travail revisite le modèle d'énergie en exploitant le caractère intégral des fonctions modulatrices appliquées au modèle de puissance du robot. En outre, les procédures d'intégration sont analysées dans le domaine fréquentiel, et certains groupes de fonctions modulatrices sont sélectionnés afin d'offrir un bon comportement de filtre passe-bas. Ensuite, l'introduction d'un différentiateur algèbrique récemment développé est proposé, nommé différentiateurs de Jacobi. L'analyse est effectuée dans le domaine temporel, et dans le domaine fréquenciel, ce qui met en évidence la propriété de filtrage passe bande et permet de sélectionner les paramètres des différentiateurs. Puis, ces différentiateurs sont appliqués avec succès à l'identification de robot, ce qui prouve leur bonne performance. Les comparaisons entre les différents modèles d'identification, les différenciateurs, les techniques des moindres carrés sont présentées et des conclusions sont tirées dans le domaine de l'identification de robot

Robust Decentralized Control of Power Systems: A Matrix Inequalities Approach

This dissertation presents an extension of robust decentralized control design techniques for power systems, with special emphasis on design problems that can be expressed as minimizing a linear objective function under linear matrix inequality (LMI) in tandem with nonlinear matrix inequality (NMI) constraints. These types of robust decentralized control design problems are generally nonconvex optimizations, and are proven to be computationally challenging. Therefore, this dissertation proposes alternative computational schemes using: i) bordered-block diagonal (BBD) decomposition algorithm for designing LMI based robust decentralized static output feedback controllers, ii) sequential LMI programming method for designing robust decentralized dynamic output feedback controllers, and, iii) generalized parameter continuation method involving matrix inequalities for designing reduced-order decentralized dynamic output feedback controllers. First, this dissertation considers the problem of designing robust decentralized static output feedback controllers for power systems that guarantee connective stability despite the presence of uncertainties among the interconnected subsystems. The design problem is then solved using BBD decomposition algorithm that clusters the state, input and output structural information for the direct computation of the appropriate gain matrices. Moreover, the approach is flexible enough to allow the inclusion of additional design constraints such as the size of the gain matrices and the degree of robust stability while at the same time maximizing the tolerable upper bounds on the class of perturbations. Second, this research considers the problem of designing a robust decentralized fixed-order dynamic output feedback controller for power systems that is formulated as a nonconvex optimization problem involving LMIs coupled through bilinear matrix equation. In the design, the robust connective stability of the overall system is guaranteed while the upper bounds of the uncertainties arising from the interconnection of the subsystems as well as nonlinearities within each subsystem are maximized. The (sub)-optimal robust decentralized dynamic output feedback control design problem is then solved using sequential LMI programming method. Moreover, the local convergence property of this algorithm has shown the effectiveness of the proposed approach for designing (sub)-optimal robust decentralized dynamic output feedback controllers for power systems. Third, this dissertation considers the problem of designing a robust decentralized structure-constrained dynamic output feedback controller design for power systems using LMI-based optimization approach. The problem of designing a decentralized structure-constrained H2/Hinf controller is first reformulated as an extension of a static output feedback controller design problem for the extended system. The resulting nonconvex optimization problem which involves bilinear matrix inequalities (BMIs) is then solved using the sequentially LMI programming method. Finally, the research considers the problem of designing reduced-order decentralized Hinf controllers for power systems. Initially a fictitious centralized Hinf robust controller, which is typically high-order controller, is designed to guarantee the robust stability of the overall system against unstructured and norm bounded uncertainties. Then the problem of designing a reduced-order decentralized controller is reformulated as an embedded parameter continuation problem that homotopically deforms from the centralized controller to the decentralized controller as the continuation parameter monotonically varies. The design problem, which guarantees the same robustness condition of the centralized controller, is solved using a two-stage iterative matrix inequality optimization algorithm. Moreover, the approach is flexible enough to allow designing different combinations of reduced-order controllers between the different input/output channels. The effectiveness of these proposed approaches are demonstrated by designing realistic power system stabilizers (PSSs) for power system, notably so-called reduced-order robust PSSs that are linear and use minimum local-feedback information. Moreover, the nonlinear simulation results have confirmed the robustness of the system for all envisaged operating conditions and disturbances. The proposed approaches offer a practical tool for engineers, besides designing reduced-order PSSs, to re-tune PSS parameters for improving the dynamic performance of the overall system

A new transfer function analyser

This thesis investigates the concept and design of a portable on-line transfer function analyser (TFA). It is eminently suitable for the identification of plants and other controlled feedback systems in which normal operating records are available. A point by point representation in the frequency domain, requiring a maximum of three records, allows Nyquist plots to be carried out, either visually or by plotter facilities. The basic theory relies heavily upon statistical concepts whereby, least squares estimates of the transfer function are obtained from a combination of heterodyning, exact filtering and adaptive loops. The resultant output, on both channels (real and imaginary), is the culmination of the solution to two linear differential equations with stochastic coefficients, so mechanised when the adaptive loops reach a stable equilibrium. Throughout, emphasis is placed upon the electronics combining the best of analog and digital techniques, in order that six parallel paths may be analysed in similar mode. This is especially true of the heterodyning and filtering operations. Practical shortcomings of the instrument noted by comparing estimates with those from the best currently available commercial apparatus, operating on deterministic signals. Examples of a feedback loop, subjected to both deterministic and random stimuli, with and without the presence of extraneous noise sources, are used to illustrate the ease and simplicity by which the instrument can be used in place of complex computing schemes, which tend, in consequence, to be solely of local academic interest. The practical features of the thesis have led to the submission of four papers to the technical press. Two of them deal, exclusively, with a capacitor ratio commutated filter – not apparently described in publications to date - which is also the subject of a proposed patent application in conjunction with NRDC. It is intended, in the near future, to submit the complete instrument as the basis for a second patent proposal

Vision Sensors and Edge Detection

Vision Sensors and Edge Detection book reflects a selection of recent developments within the area of vision sensors and edge detection. There are two sections in this book. The first section presents vision sensors with applications to panoramic vision sensors, wireless vision sensors, and automated vision sensor inspection, and the second one shows image processing techniques, such as, image measurements, image transformations, filtering, and parallel computing