Mechanical Engineering - Research Publications
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ItemNo Preview AvailableOn Singular Perturbation for a Class of Discrete-Time Nonlinear Systems in the Presence of Limit Cycles of Fast Dynamics(IEEE, 2022)This paper extends the existing singular perturbation results to a class of nonlinear discrete-time systems whose fast dynamics have limit cycles. By introducing the discrete-time reduced averaged system, the main result (Theorem 1) shows that for a given fixed time interval, the solutions of the original system can be made arbitrarily close to the solutions of the reduced averaged system and the boundary layer system. From this result, the stability properties of the original system are obtained from the stability properties of the reduced averaged system and the boundary layer system. Simulation results support the theoretical findings.
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ItemControl oriented modeling of turbocharged (TC) spark ignition (SI) engine(SAE International, 2009-01-01)
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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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ItemModel Reduction of Automotive Engines using Perturbation Theory(IEEE, 2009-01-01)In this paper, a new constructive and versatile procedure to systematically reduce the order of control oriented engine models is presented. The technique is governed by the identification of time scale separation within the dynamics of various engine state variables and hence makes extensive use of the perturbation theory. On the basis of the dynamic characteristics and the geometry of engines, two methods for model reduction are proposed. Method 1 involves collective use of the regular and singular perturbation theories to eliminate temperature dynamics and approximate them with their quasi-steady state values, while Method 2 deals with the elimination of fast pressures. The result is a library of engine models which are associated with each other on a sound theoretical basis and simultaneously allow sufficient flexibility in terms of the reduced order modeling of a variety of engines. Different assumptions under which this model reduction is justified are presented and their implications are discussed.
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ItemExtremum Seeking From 1922 To 2010(IEEE, 2010-01-01)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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ItemTrajectory-based proofs for sampled-data extremum seeking control(IEEE, 2013)Extremum seeking of nonlinear systems based on a sampled-data control law is revisited. It is established that under some generic assumptions, semi-global practical asymptotically stable convergence to an extremum can be achieved. To this end, trajectory-based arguments are employed, by contrast with Lyapunov-function-type approaches in the existing literature. The proof is simpler and more straightforward; it is based on assumptions that are in general easier to verify. The proposed extremum seeking framework may encompass more general optimisation algorithms, such as those which do not admit a state-update realisation and/or Lyapunov functions. Multi-unit extremum seeking is also investigated within the context of accelerating the speed of convergence.
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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.