Mechanical Engineering - Research Publications
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ItemOnline optimization of spark advance in alternative fueled engines using extremum seeking control(Elsevier, 2014-08-01)Alternative fueled engines offer greater challenges for engine control courtesy of uncertain fuel composition. This makes optimal tuning of input parameters like spark advance extremely difficult in most existing ECU architectures. This paper proposes the use of grey-box extremum seeking techniques to provide real-time optimization of the spark advance in alternative fueled engines. Since practical implementation of grey-box extremum seeking methods is typically done using digital technology, this paper takes advantage of emulation design methods to port the existing continuous-time grey-box extremum seeking methods to discrete-time frameworks. The ability and flexibility of the proposed discrete-time framework is demonstrated through simulations and in practical situation using a natural gas fueled engine.
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ItemA Framework for Extremum Seeking Control of Systems With Parameter Uncertainties(Institute of Electrical and Electronics Engineers, 2013-02-01)Traditionally, the design of extremum seeking algorithm treats the system as essentially a black-box, which for many applications means disregarding known information about the model structure. In contrast to this approach, there have been recent examples where a known plant structure with uncertain parameters has been used in the online optimization of plant operation. However, the results for these approaches have been restricted to specific classes of plants and optimization algorithms. This paper seeks to provide general results and a framework for the design of extremum seekers applied to systems with parameter uncertainties. General conditions for an optimization method and a parameter estimator are presented so that their combination guarantees convergence of the extremum seeker for both static and dynamic plants. Tuning guidelines for the closed loop scheme are also presented. The generality and flexibility of the proposed framework is demonstrated through a number of parameter estimators and optimization algorithms that can be combined to obtain extremum seeking. Examples of anti-lock braking and model reference adaptive control are used to illustrate the effectiveness of the proposed framework.
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ItemStability and Persistent Excitation in Signal Sets(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2015-05-01)Persistent excitation (PE) conditions have been widely used to analyze stability properties of various parameter identification algorithms and to establish uniform global asymptotic stability (UGAS) for a large class of nonlinear time-varying systems. In order to generalize such conditions to a more general setting, a new PE condition is proposed with three basic ingredients: a signal set to represent a family of time functions (e.g., trajectories); a pseudo distance measure to describe the convergence; and some binary relations (e.g., state-to-output relations). Closely related to detectability, this PE condition is a necessary condition to guarantee UGAS. Under uniform global stability and an integral inequality, it becomes a sufficient condition of UGAS. A novel concept: M-pair, which aims at simplifying the checking of the PE condition, is introduced. By using M-pair, it is possible to simplify the structure of the referred signal set (in the spirit of the classic Krasovskii-LaSalle theorem) and to extend the dimension of the reference signal set (similar to the Matrosov theorem). Thus, the framework of M-pair not only unifies these well-known results, but also generates more flexibility in checking the PE conditions. When applied to nonlinear switched systems, three new tools to verify the PE condition are obtained. Finally, an example illustrates that a nonlinear time-varying switched system with arbitrary switching can be shown to be UGAS without using a common Lyapunov function.
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ItemMulti-agent source seeking via discrete-time extremum seeking control(PERGAMON-ELSEVIER SCIENCE LTD, 2014-09-01)Recent developments in extremum seeking theory have established a general framework for the methodology, although the specific implementations, particularly in the context of multi-agent systems, have not been demonstrated. In this work, a group of sensor-enabled vehicles is used in the context of the extremum seeking problem using both local and global optimisation algorithms to locate the extremum of an unknown scalar field distribution. For the former, the extremum seeker exploits estimates of gradients of the field from local dithering sensor measurements collected by the mobile agents. It is assumed that a distributed coordination which ensures uniform asymptotic stability with respect to a prescribed formation of the agents is employed. An inherent advantage of the frameworks is that a broad range of nonlinear programming algorithms can be combined with a wide class of cooperative control laws to perform extreme source seeking. Semi-global practical asymptotically stable convergence to local extrema is established in the presence of field sampling noise. Subsequently, global extremum seeking with multiple agents is investigated and shown to give rise to robust practical convergence whose speed can be improved via computational parallelism. Nonconvex field distributions with local extrema can be accommodated within this global framework.
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ItemUnified frameworks for sampled-data extremum seeking control: Global optimisation and multi-unit systems(PERGAMON-ELSEVIER SCIENCE LTD, 2013-09-01)Two frameworks are proposed for extremum seeking of general nonlinear plants based on a sampled-data control law, within which a broad class of nonlinear programming methods is accommodated. It is established that under some generic assumptions, semi-global practical convergence to a global extremum can be achieved. In the case where the extremum seeking algorithm satisfies a stronger asymptotic stability property, the converging sequence is also shown to be stable using a trajectory-based proof, as opposed to a Lyapunov-function- type approach. The former is more straightforward and insightful. This allows for more general optimisation algorithms than considered in existing literature, such as those which do not admit a state-update realisation and/or Lyapunov functions. Lying at the heart of the analysis throughout is robustness of the optimisation algorithms to additive perturbations of the objective function. Multi-unit extremum seeking is also investigated with the objective of accelerating the speed of convergence.
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ItemMultidimensional global extremum seeking via the DIRECT optimisation algorithm(PERGAMON-ELSEVIER SCIENCE LTD, 2013-07-01)DIRECT is a sample-based global optimisation method for Lipschitz continuous functions defined over compact multidimensional domains. This paper adapts the DIRECT method with a modified termination criterion for global extremum seeking control of multivariable dynamical plants. Finite-time semi-global practical convergence is established based on a periodic 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. Extremum seeking involving multiple units is also considered within the same context as a means to increase the speed of convergence. Numerical examples of global extremum seeking based on DIRECT are presented at the end.
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ItemA non-gradient approach to global extremum seeking: An adaptation of the Shubert algorithm(PERGAMON-ELSEVIER SCIENCE LTD, 2013-03-01)The main purpose of this paper is to adapt the so-called Shubert algorithm for extremum seeking control of general dynamic plants. This algorithm is a good representative of the "sampling optimization methods" that achieve global extremum seeking on compact sets in the presence of local extrema. The algorithm applies to Lipschitz mappings; the model of the system is assumed unknown but the knowledge of its Lipschitz constant is assumed. The controller depends on a design parameter, the "waiting time", and tuning guidelines that relate the design parameter and the region of convergence and accuracy of the algorithm are presented. The analysis shows that semi-global practical convergence (in the initial states) to the global extremum can be achieved in presence of local extrema if compact sets of inputs are considered. Numerical simulations for global optimization in the presence of local extrema are provided to demonstrate the proposed approach.
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ItemModel Reduction of Turbocharged (TC) Spark Ignition (SI) Engines(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2011-03-01)This paper proposes a new procedure to reduce the order of control oriented turbocharged (TC) spark ignition (SI) engine models. The starting point of this work is a higher dimensional, fully validated model defined which is not appropriate for control design. The model reduction technique is based on the identification of time scale separation within the dynamics of various engine state variables with pertinent use of perturbation theory. The model reduction is accomplished in two steps and exploits the dynamic and physical characteristics of engine design and operation. In the first step, regular and singular perturbation theories are collectively employed to eliminate temperature dynamics and replace them with their quasi-steady state values. This is followed by the elimination of fast pressures. As a result, a library of engine models is obtained which are associated with each other on a sound theoretical basis and at the same time allow sufficient flexibility in terms of the reduced order modeling. Different assumptions under which this model reduction is justified are presented and their implications are discussed. The approximating properties of the proposed engine models with respect to the original higher dimensional model are quantitatively assessed through comprehensive simulations.
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ItemExtremum seeking of dynamical systems via gradient descent and stochastic approximation methods(Elsevier, 2015-06)Abstract This paper examines the use of gradient based methods for extremum seeking control of possibly infinite-dimensional dynamic nonlinear systems with general attractors within a periodic sampled-data framework. First, discrete-time gradient descent method is considered and semi-global practical asymptotic stability with respect to an ultimate bound is shown. Next, under the more complicated setting where the sampled measurements of the plant’s output are corrupted by an additive noise, three basic stochastic approximation methods are analysed; namely finite-difference, random directions, and simultaneous perturbation. Semi-global convergence to an optimum with probability one is established. A tuning parameter within the sampled-data framework is the period of the synchronised sampler and hold device, which is also the waiting time during which the system dynamics settle to within a controllable neighbourhood of the steady-state input–output behaviour.
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ItemA refinement of Matrosov's theorem for differential inclusions(PERGAMON-ELSEVIER SCIENCE LTD, 2016-06-01)This note presents a refinement of Matrosov's theorem for a class of differential inclusions whose set-valued map is defined as a closed convex hull of finitely many vector fields. This class of systems may arise in the analysis of switched nonlinear systems when stability with arbitrary switching between the given vector fields is considered. Assuming uniform global stability of a compact set, it is shown that uniform global attractivity of the set can be verified by tailoring Matrosov functions to individual vector fields. This refinement of Matrosov's theorem is an extension of the existing Matrosov results which may be easier to apply to certain differential inclusions than existing results, as demonstrated by an example.