Electrical and Electronic Engineering - Research Publications
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ItemIdle speed control using linear time varying model predictive control and discrete time approximations(IEEE, 2010-01-01)This paper addresses the problem of idle speed control of hydrogen fueled internal combustion engine (H2ICE) using model predictive control (MPC) and sampled data control (SDC) theories. In the first step, results from SDC theory and a version of MPC are collectively employed to obtain a rigorously developed new generic control strategy. Here, a controller, based on a family of approximate discrete time models, is designed within a previously proposed framework to have guaranteed practical asymptotic stability of the exact (unknown) discrete time model. Controller design, accomplished using MPC theory, is facilitated by successive online linearizations of the nonlinear discrete time model at each sampling instant. In the second step, the technique is implemented in the idle speed control of hydrogen internal combustion engine (H2ICE). Various conditions under which this theory can be implemented are presented and their validity for idle speed control problem are discussed. Simulations are presented to illustrate the effectiveness of the control scheme.
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ItemExtremum Seeking From 1922 To 2010(IEEE, 2010)Extremum seeking is a form of adaptive control where the steady-state input-output characteristic is optimized, without requiring any explicit knowledge about this input-output characteristic other than that it exists and that it has an extremum. Because extremum seeking is model free, it has proven to be both robust and effective in many different application domains. Equally being model free, there are clear limitations to what can be achieved. Perhaps paradoxically, although being model free, extremum seeking is a gradient based optimization technique. Extremum seeking relies on an appropriate exploration of the process to be optimized to provide the user with an approximate gradient, and hence the means to locate an extremum. These observations are elucidated in the paper. Using averaging and time-scale separation ideas more generally, the main behavioral characteristics of the simplest (model free) extremum seeking algorithm are established.
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ItemA UNIFYING FRAMEWORK FOR ANALYSIS AND DESIGN OF EXTREMUM SEEKING CONTROLLERS(IEEE, 2012-01-01)We summarize a unifying design approach to continuous-time extremum seeking that was recently reported by the authors. This approach is based on a feedback control paradigm that was to the best of our knowledge explicitly summarized for the first time in this form in our recent work. This paradigm covers some existing extremum seeking schemes, provides a direct link to off-line optimization and can be used as a unifying framework for design of novel extremum seeking schemes. Moreover, we show that other extremum seeking problem formulations can be interpreted using this unifying viewpoint. We believe that this unifying view will be invaluable to systematically design and analyze extremum seeking controllers in various settings.
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ItemA Unifying Approach to Extremum Seeking: Adaptive Schemes Based on Estimation of Derivatives(IEEE, 2010-01-01)A unifying, prescriptive framework is presented for the design of a family of adaptive extremum seeking controllers. It is shown how extremum seeking can be achieved by combining an arbitrary continuous optimization method (such as gradient descent or continuous Newton) with an estimator for the derivatives of the unknown steady-state reference-to-output map. A tuning strategy is presented for the controller parameters that ensures non-local convergence of all trajectories to the vicinity of the extremum. It is shown that this tuning strategy leads to multiple time scales in the closed-loop dynamics, and that the slowest time scale dynamics approximate the chosen continuous optimization method. Results are given for both static and dynamic plants. For simplicity, only single-input-single-output (SISO) plants are considered.
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ItemOn a Shubert Algorithm-Based Global Extremum Seeking Scheme(IEEE, 2012)This paper adapts the so-called Shubert algorithm for Extremum Seeking Control (ESC) to seek the global extremum (in presence of local extrema) of general dynamic plants. Different from derivative based methods that are widely used in ESC, the Shubert algorithm is a good representative of sampling optimization methods. With knowledge of the Lipschitz constant of an unknown static mapping, this deterministic algorithm seeks the global extremum. By introducing “waiting time” the proposed Shubert algorithm-based global extremum seeking guarantees the semi-global practical convergence (in the initial states) to the global extremum if compact sets of inputs are considered. Several numerical examples demonstrate how proposed method may be successfully deployed.
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ItemMultidimensional global extremum seeking via the DIRECT method(IEEE, 2012-01-01)This paper adapts the DIRECT method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants - DIRECT is a sampling type global optimisation method for Lipschitz-continuous functions defined over compact multidimensional domains. Finite-time semi-global practical convergence is established based on a deadbeat sampled-data control law, whose sampling period is a parameter which determines the region and accuracy of convergence. A crucial part of the development is dedicated to a robustness analysis of the DIRECT method against bounded additive perturbations on the objective function. A numerical example of global extremum seeking in the presence of local extrema based on DIRECT is presented at the end.
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ItemNon-local stability of a multi-variable extremum-seeking scheme(IEEE, 2011-12-01)This paper considers non-local stability of a simple extremum-seeking (ES) scheme acting on a multiple-input single-output (MISO) plant. The scheme acts to approximately minimise the plant output, utilising a vector of periodic dithers to locally explore a map of the steady-state plant response. In a similar fashion to a previous result for single-input single-output (SISO) plants, semi-global practical asymptotic (SPA) stability (with respect to the design parameters) is demonstrated for the closed-loop system. In order to achieve this result, the dither is required to satisfy a condition similar to persistency of excitation (PE) conditions appearing in the adaptive control literature. A variety of dithers satisfying and failing to satisfy this condition are discussed. A simulation example is used to demonstrate these results.
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ItemExtremum seeking methods for online optimization of spark advance in alternative fueled engines(Elsevier, 2012-01-01)Alternative fueled engines offer greater challenges for engine control courtesy of uncertain fuel composition. This make optimal tuning of input parameters like spark advance extremely difficult in most existing ECU architectures. This paper proposes the use of greybox extremum seeking techniques to provide real-time optimization of the spark advance in alternative fueled engines. The ability and flexibility of the proposed framework is demonstrated through simulation examples. The approaches demonstrated may be extended to other engine inputs requiring online optimization.
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ItemA Systematic Approach to Extremum Seeking Based on Parameter Estimation(IEEE, 2010-01-01)We present a systematic approach for design of extremum seeking (ES) controllers for a class of uncertain plants that are parameterized with unknown parameters. First, we present results for static plants and show how it is possible to combine, under certain general conditions, an arbitrary optimization method with an arbitrary parameter estimation method in order to obtain extremum seeking. Our main results also specify how controller needs to be tuned in order to achieve extremum seeking. Then, we consider dynamic plants and separate our results into the stable plant case and unstable plant case. For each of these cases, we present conditions on general plants, controllers, observers, parameter estimators and optimization algorithms that guarantee semi-global practical convergence to the extremum when controller parameters are tuned appropriately. Our results apply to general nonlinear plants with multiple inputs and multiple parameters.