Towards Efficient Maximum Likelihood Estimation of LPV-SS Models

How to efficiently identify multiple-input multiple-output (MIMO) linear parameter-varying (LPV) discrete-time state-space (SS) models with affine dependence on the scheduling variable still remains an open question, as identification methods proposed in the literature suffer heavily from the curse of dimensionality and/or depend on over-restrictive approximations of the measured signal behaviors. However, obtaining an SS model of the targeted system is crucial for many LPV control synthesis methods, as these synthesis tools are almost exclusively formulated for the aforementioned representation of the system dynamics. Therefore, in this paper, we tackle the problem by combining state-of-the-art LPV input-output (IO) identification methods with an LPV-IO to LPV-SS realization scheme and a maximum likelihood refinement step. The resulting modular LPV-SS identification approach achieves statical efficiency with a relatively low computational load. The method contains the following three steps: 1) estimation of the Markov coefficient sequence of the underlying system using correlation analysis or Bayesian impulse response estimation, then 2) LPV-SS realization of the estimated coefficients by using a basis reduced Ho-Kalman method, and 3) refinement of the LPV-SS model estimate from a maximum-likelihood point of view by a gradient-based or an expectation-maximization optimization methodology. The effectiveness of the full identification scheme is demonstrated by a Monte Carlo study where our proposed method is compared to existing schemes for identifying a MIMO LPV system

Feature-based motion control for near-repetitive structures

In many manufacturing processes, production steps are carried out on repetitive structures which consist of identical features placed in a repetitive pattern. In the production of these repetitive structures one or more consecutive steps are carried out on the features to create the final product. Key to obtaining a high product quality is to position the tool with respect to each feature of the repetitive structure with a high accuracy. In current industrial practice, local position sensors such as motor encoders are used to separately measure the metric position of the tool and the stage where the repetitive structure is on. Here, the final accuracy of alignment directly relies on assumptions like thermal stability, infinite machine frame stiffness and constant pitch between successive features. As the size of these repetitive structures is growing, often these assumptions are difficult to satisfy in practice. The main goal of this thesis is to design control approaches for accurately positioning the tool with respect to the features, without the need of the aforementioned assumptions. In this thesis, visual servoing, i.e., using machine vision data in the servo loop to control the motion of a system, is used for controlling the relative position between the tool and the features. By using vision as a measurement device the relevant dynamics and disturbances are therefore measurable and can be accounted for in a non-collocated control setting. In many cases, the pitch between features is subject to small imperfections, e.g., due to the finite accuracy of preceding process steps or thermal expansion. Therefore, the distance between two features is unknown a priori, such that setpoints can not be constructed a priori. In this thesis, a novel feature-based position measurement is proposed, with the advantage that the feature-based target position of every feature is known a priori. Motion setpoints can be defined from feature to feature without knowing the exact absolute metric position of the features beforehand. Next to feature-to-feature movements, process steps involving movements with respect to the features, e.g., engraving or cutting, are implemented to increase the versatility of the movements. Final positioning accuracies of 10 µm are attained. For feature-to-feature movements with varying distances between the features a novel feedforward control strategy is developed based on iterative learning control (ILC) techniques. In this case, metric setpoints from feature to feature are constructed by scaling a nominal setpoint to handle the pitch imperfections. These scale varying setpoints will be applied during the learning process, while second order ILC is used to relax the classical ILC boundary of setpoints being the same every trial. The final position accuracy is within 5 µm, while scale varying setpoints are applied. The proposed control design approaches are validated in practice on an industrial application, where the task is to position a tool with respect to discrete semiconductors of a wafer. A visual servoing setup capable of attaining a 1 kHz frame rate is realized. It consists of an xy-stage on which a wafer is clamped which contains the discrete semiconductor products. A camera looks down onto the wafer and is used for position feedback. The time delay of the system is 2.5 ms and the variation of the position measurement is 0.3 µm (3s)

Controlled switching in Kalman filtering and iterative learning controls

“Switching is not an uncommon phenomenon in practical systems and processes, for examples, power switches opening and closing, transmissions lifting from low gear to high gear, and air planes crossing different layers in air. Switching can be a disaster to a system since frequent switching between two asymptotically stable subsystems may result in unstable dynamics. On the contrary, switching can be a benefit to a system since controlled switching is sometimes imposed by the designers to achieve desired performance. This encourages the study of system dynamics and performance when undesired switching occurs or controlled switching is imposed. In this research, the controlled switching is applied to an estimation process and a multivariable Iterative Learning Control (ILC) system, and system stability as well as system performance under switching are investigated. The first article develops a controlled switching strategy for the estimation of a temporal shift in a Laser Tracker (LT). For some reason, the shift cannot be measured at all time. Therefore, a model-based predictor is adopted for estimation when the measurement is not available, and a Kalman Filter (KF) is used to update the estimate when the measurement is available. With the proposed method, the estimation uncertainty is always bounded within two predefined boundaries. The second article develops a controlled switching method for multivariable ILC systems where only partial outputs are measured at a time. Zero tracking error cannot be achieved for such systems using standard ILC due to incomplete knowledge of the outputs. With the developed controlled switching, all the outputs are measured in a sequential order, and, with each currently-measured output, the standard ILC is executed. Conditions under which zero convergent tracking error is accomplished with the proposed method are investigated. The proposed method is finally applied to solving a multi-agent coordination problem”--Abstract, page iv

Review of the mathematical foundations of data fusion techniques in surface metrology

The recent proliferation of engineered surfaces, including freeform and structured surfaces, is challenging current metrology techniques. Measurement using multiple sensors has been proposed to achieve enhanced benefits, mainly in terms of spatial frequency bandwidth, which a single sensor cannot provide. When using data from different sensors, a process of data fusion is required and there is much active research in this area. In this paper, current data fusion methods and applications are reviewed, with a focus on the mathematical foundations of the subject. Common research questions in the fusion of surface metrology data are raised and potential fusion algorithms are discussed

Iterative learning control: algorithm development and experimental benchmarking

This thesis concerns the general area of experimental benchmarking of Iterative Learning Control (ILC) algorithms using two experimental facilities. ILC is an approach which is suitable for applications where the same task is executed repeatedly over the necessarily finite time duration, known as the trial length. The process is reset prior to the commencement of each execution. The basic idea of ILC is to use information from previously executed trials to update the control input to be applied during the next one. The first experimental facility is a non-minimum phase electro-mechanical system and the other is a gantry robot whose basic task is to pick and place objects on a moving conveyor under synchronization and in a fixed finite time duration that replicates many tasks encountered in the process industries. Novel contributions are made in both the development of new algorithms and, especially, in the analysis of experimental results both of a single algorithm alone and also in the comparison of the relative performance of different algorithms. In the case of non-minimum phase systems, a new algorithm, named Reference Shift ILC (RSILC) is developed that is of a two loop structure. One learning loop addresses the system lag and another tackles the possibility of a large initial plant input commonly encountered when using basic iterative learning control algorithms. After basic algorithm development and simulation studies, experimental results are given to conclude that performance improvement over previously reported algorithms is reasonable. The gantry robot has been previously used to experimentally benchmark a range of simple structure ILC algorithms, such as those based on the ILC versions of the classical proportional plus derivative error actuated controllers, and some state-space based optimal ILC algorithms. Here these results are extended by the first ever detailed experimental study of the performance of stochastic ILC algorithms together with some modifications necessary to their configuration in order to increase performance. The majority of the currently reported ILC algorithms mainly focus on reducing the trial-to-trial error but it is known that this may come at the cost of poor or unacceptable performance along the trial dynamics. Control theory for discrete linear repetitive processes is used to design ILC control laws that enable the control of both trial-to-trial error convergence and along the trial dynamics. These algorithms can be computed using Linear Matrix Inequalities (LMIs) and again the results of experimental implementation on the gantry robot are given. These results are the first ever in this key area and represent a benchmark against which alternatives can be compared. In the concluding chapter, a critical overview of the results presented is given together with areas for both short and medium term further researc