Browsing by Subject "Nonlinear systems"

Now showing 1 - 4 of 4
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    Methods Of Distributed And Nonlinear Process Control: Structuredness, Optimality And Intelligence
    (2020-05) Tang, Wentao
    Chemical processes are intrinsically nonlinear and often integrated into large-scale networks, which are difficult to control effectively. The traditional challenges faced by process control, as well as the modern vision of transitioning industries into a smart manufacturing paradigm, requires the instillation of new perspectives and application of new methods to the control of chemical processes. The goal is to realize highly automated, efficient, well-performing and flexible control strategies for nonlinear, interconnected and uncertain systems. Motivated by this, in this thesis, the following three important aspects (objectives) for contemporary process control -- structuredness, optimality, and intelligence -- are discussed in the corresponding three parts. 1. For the control of process networks in a structured and distributed manner, a network-theoretic perspective is introduced, which suggests to find a decomposition of the problem according to the block structures in the network. Such a perspective is examined by sparse optimal control of Laplacian network dynamics. Community detection-based methods are proposed for input--output bipartite and variable-constraint network representations and applied to a benchmark chemical process. 2. For the optimality of control, we first derive a computationally efficient algorithm for nonconvex constrained distributed optimization with theoretically provable convergence properties -- ELLADA, which is applied to distributed nonlinear model predictive control of a benchmark process system. We derive bilevel optimization formulations for the Lyapunov stability analysis of nonlinear systems, and stochastic optimization for optimally designing the Lyapunov function, which can be further integrated with the optimal process design problem. 3. Towards a more intelligent diagram of process control, we first investigate an advantageous Lie-Sobolev nonlinear system identification scheme and its effect on nonlinear model-based control. For model-free data-driven control, we discuss a distributed implementation of the adaptive dynamic programming idea. For chemical processes where states are mostly unmeasurable, dissipativity learning control (DLC) is proposed as a suitable framework of input--output data-driven control, and applied to several nonlinear processes. Its theoretical foundations are also discussed.
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    Modeling, Robust Control, and Experimental Validation of a Supercavitating Vehicle
    (2015-06) Escobar Sanabria, David
    This dissertation considers the mathematical modeling, control under uncertainty, and experimental validation of an underwater supercavitating vehicle. By traveling inside a gas cavity, a supercavitating vehicle reduces hydrodynamic drag, increases speed, and minimizes power consumption. The attainable speed and power efficiency make these vehicles attractive for undersea exploration, high-speed transportation, and defense. However, the benefits of traveling inside a cavity come with difficulties in controlling the vehicle dynamics. The main challenge is the nonlinear force that arises when the back-end of the vehicle pierces the cavity. This force, referred to as planing, leads to oscillatory motion and instability. Control technologies that are robust to planing and suited for practical implementation need to be developed. To enable these technologies, a low-order vehicle model that accounts for inaccuracy in the characterization of planing is required. Additionally, an experimental method to evaluate possible pitfalls in the models and controllers is necessary before undersea testing. The major contribution of this dissertation is a unified framework for mathematical modeling, robust control synthesis, and experimental validation of a supercavitating vehicle. First, we introduce affordable experimental methods for mathematical modeling and controller testing under planing and realistic flow conditions. Then, using experimental observations and physical principles, we create a low-order nonlinear model of the longitudinal vehicle motion. This model quantifies the planing uncertainty and is suitable for robust controller synthesis. Next, based on the vehicle model, we develop automated tools for synthesizing controllers that deliver a certificate of performance in the face of nonlinear and uncertain planing forces. We demonstrate theoretically and experimentally that the proposed controllers ensure higher performance when the uncertain planing dynamics are considered. Finally, we discuss future directions in supercavitating vehicle control.
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    Observer Design for Non-Monotonic Nonlinear Systems and Interesting Contemporary Applications
    (2022-08) Movahedi, Hamidreza
    This dissertation analyzes observer design for non-monotonic nonlinear systems and develops globally stable observer design techniques for such systems. Non-monotonic nonlinear systems are frequently encountered in many practical applications, including vehicle tracking, magnetic position estimation, robotics, state of charge (SoC) estimation in Li-ion batteries, and infectious disease spread dynamics. Very few papers in literature have recognized the challenge that existing nonlinear observer design methods do not work for non-monotonic systems. This dissertation demonstrates that current LMI-based observer design methods do not have feasible solutions for many non-monotonic systems. This motivates the need for new observer design techniques. Such techniques are used in three major applications in this thesis: state of charge estimation in Li-ion batteries, magnetic position estimations, and infectious disease spread dynamics estimation.First, a class of systems in which the process dynamics and output equations contain nonlinear functions of only scalar arguments are considered. A Lyapunov approach is utilized to develop an LMI-based observer design method for this class of nonlinear systems. Then, the failure of LMI-based methods to provide constant observer gains for non-monotonic systems is rigorously analyzed, and it is demonstrated that, no matter how small the Lipschitz constant or the Jacobian bounds of the involved nonlinear functions, these methods cannot provide a stabilizing constant observer gain if all the functions of the system are non-monotonic. Based on this theoretical result, a technique to extend the design method to include switched gain observers is presented and its global asymptotic stability is rigorously proven. The developed observer design methodology is utilized to estimate the SoC in a lithium-ion battery, using measurements of terminal voltage and bulk force. The challenge in this application is that the bulk force applied to the casing of the battery, as a result of Lithium-ion intercalation and deintercalation, is a non-monotonic function of the SoC. Hence, a switched gain observer is devised and applied. Using detailed simulations of possible mismatches in the battery model, the robustness of the observer is compared with that of the extended Kalman filter, and the observer is showed to be less susceptible to these model errors. Experimental results corroborate this finding. Position estimation in electro-hydraulic actuators using non-contacting magnetic sensors is another subject that is considered. Magnetic measurements in this application are all non-monotonic, hence based on the theoretical findings of this dissertation it is clear that more than one magnetic sensor is needed for this estimation problem. Subsequently, the minimum singular values of the observability matrix are utilized as a metric for minimizing the number of sensors and optimizing sensor locations. Extensive experimental results are provided to demonstrate the optimality of the sensor locations and the accuracy of the switched gain observer designed for this application. Next, the hysteresis in Li-ion batteries is analyzed. A nonlinear double capacitor model is used for this problem that contains a measurement equation with two nonlinear functions, one of them being significant hysteresis in voltage of the battery as a function of the SoC. Previously, researchers in this field used a differential equation to model the hysteresis. In this dissertation, it is shown that this popular method loses observability and a modified Preisach method is suggested as an alternative. Then a nonlinear Lipschitz observer is designed for this application, and it is shown that the observer provides accurate SoC estimates based on experimental data in the presence of hysteresis. Another research application explored in this dissertation is centered around infectious disease spread dynamics and the real-time estimation problem of variables characterizing disease spread. The COVID-19 epidemic is studied for this purpose, and a new nonlinear dynamic model is developed to enhance the traditional SEIR epidemic model to include additional variables. Subsequently, a cascaded observer is developed to estimate the real-time values of the infection rate, and the basic reproduction number of COVID-19 spread in Minnesota. Finally, the use of the nonlinear observer design techniques for handling sensor noise and disturbance rejection is considered. A H∞-based globally stable nonlinear observer design technique was explored to provide design flexibility equivalent to the popular locally stable extended Kalman filter which is based on linearization of plant dynamics. Furthermore, comparing with the performance of the extended and unscented Kalman filters in the presence of non-Gaussian pulse disturbances and through detailed simulations, it is shown that the H∞ nonlinear observer performs better and can provide a guaranteed upper bound on the estimation error.
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    Prediction and Prevention of Tripped Rollovers
    (Intelligent Transportation Systems Institute, Center for Transportation Studies, University of Minnesota, 2012-12) Phanomchoeng, Gridsada; Rajamani, Rajesh
    Vehicle rollovers account for a significant fraction of highway traffic fatalities, causing more than 10,000 deaths in the U.S. each year. While active rollover prevention systems have been developed by several automotive manufacturers, the currently available systems address only untripped rollovers. This project focuses on the development of a new real-time rollover index that can detect both tripped and un-tripped rollovers. A new methodology is developed for estimation of unknown inputs in a class of nonlinear dynamic systems. The methodology is based on nonlinear observer design and dynamic model inversion to compute the unknown inputs from output measurements. The developed approach can enable observer design for a large class of differentiable nonlinear systems with a globally (or locally) bounded Jacobian. The developed nonlinear observer is then applied for rollover index estimation. The rollover index estimation algorithm is evaluated through simulations with an industry standard software, CARSIM, and with experimental tests on a 1/8th scaled vehicle. The simulation and experimental results show that the developed nonlinear observer can reliably estimate vehicle states, unknown normal tire forces, and rollover index for predicting both un-tripped and tripped rollovers. The final chapter of this report evaluates the feasibility of rollover prevention for tripped rollovers using currently available actuation systems on passenger sedans.