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A brief historical background of the development of the absolute stability theory was presented, and some of its methods and approaches, as well as the results obtained using them, were discussed. The kinds of systems under consideration are named, and applications of the methods and results of the absolute stability theory to other scientific and practical fields for solution of the engineering, mechanical, physical, and other problems were presented.

Essays on the absolute stability theory

The modern power system features high penetration of power converters due to the development of renewables, HVDC, etc. Currently, the controller design and parameter tuning of power converters heavily rely on rich engineering experience and extrapolation from a single converter system, which may lead to inferior performance or even instabilities under variable grid conditions. In this paper, we propose an $\mathcal {H}_{\infty }$ -control design framework to provide a systematic way for the robust and optimal control design of power converters. We discuss how to choose weighting functions to achieve anticipated and robust performance with regards to multiple control objectives. Further, we show that by a proper choice of the weighting functions, the converter can be conveniently specified as grid-forming or grid-following in terms of small-signal dynamics. Moreover, this paper first proposes a decentralized stability criterion based on the small gain theorem, which enables us to guarantee the global small-signal stability of a multi-converter system through local control design of the power converters. We provide high-fidelity nonlinear simulations and hardware-in-the-loop (HIL) real-time simulations to illustrate the effectiveness of our method.

H ∞ -Control of Grid-Connected Converters: Design, Objectives and Decentralized Stability Certificates

This paper deals with the problem of absolute stability and robust stability of a class of neutral systems with sector-bounded nonlinearity and mixed time-varying delays. Some new delay-dependent stability criteria are presented based on Lyapunov stability theory and formulated in terms of strict linear matrix inequalities (LMIs). Neither model transformation nor bounding technique for cross terms is required in obtaining the stability conditions. Since both the neutral- and discrete-delays are taken into account, the obtained criterion is less conservative than the previous ones, which is illustrated by numerical examples.

Stability analysis for a class of neutral systems with mixed delays and sector-bounded nonlinearity

In this work, we present a survey on different topics related to Internal Combustion (IC) engines. The purpose of this work is to show the evolution on modeling, use of biofuels, simulation and/or implementation of different types of control laws applied to the IC engines. In the modeling section, we present a classification of the IC engines models according to their type; in this classification linear, nonlinear, and based on Neural Networks (NN) models are included. In the biofuels section, we included different works classified according to the used biofuel. In this classification, we consider pure biofuels (ethanol, methanol, hydrogen), gasoline-alcohol blends and gasoline-alcohol blend plus hydrogen as additive. In the control section, we include a classification according to the type of control, these are model-based control, observer-based control and intelligent control. Furthermore, in this section we include a review about Fault Diagnosis strategies applied to IC engines. Moreover, we present an overview of the failures provoked by corrosion effects when biofuels are used.

A survey on modeling, biofuels, control and supervision systems applied in internal combustion engines

Technical Communique: A note on absolute stability of uncertain systems

A State-Space Algorithm for Designing H∞ Loop Shaping PlD Controllers

The describing function (DF) method offers a useful a way to analyse the stability of control systems with separable nonlinearities and recently it has been applied to systems with either parametric or norm-bounded perturbations. Here, DFs are employed in an even more general setting, i.e. both types of uncertainty are allowed to enter the system. Furthermore, the high frequency dynamics neglected by the DF technique are also incorporated into the system description. Exploiting some well known results from the robust control literature, computationally tractable stability criteria are derived. Two numerical examples are provided to illustrate the various aspects of these new tools which are, of course, subject to the usual errors and the restrictions of the DF method.

Describing functions in non-linear systems with structured and unstructured uncertainties

Advances in control design for time delay systems are complemented by advances in respective system analysis techniques, and robustness of time delay systems under parametric uncertainties is a topic of active research. We consider uncertain systems subject to time delay, and implicitly compensate for the delay by employing the Internal Model Controller (IMC) design principles. We combine a nominal IMC scheme with an adaptive law in the presence of unknown and possibly time-varying system parameters due to changing operating conditions. The resulting adaptive control structure is used to address the Air Fuel Ratio (AFR) regulation problem which is known to be one of the main control challenges for internal combustion engines.

Adaptive Internal Model Control for Air-Fuel Ratio regulation

As the transportation systems become increasingly complex and crowded, more strict standards are proposed to reduce the levels of emissions produced by motor vehicles and hence the negative effects these emissions have on public health and the environment. The efficiency of three-way catalysts typically employed in Spark Ignition (SI) engines depends primarily on the Air-Fuel Ratio (AFR) regulation performance. The authors implement an Internal Model Controller (IMC) combined with an adaptive law in discrete-time and use this structure to address the AFR control problem despite the presence of parametric uncertainties.

Serkan T. Impram

Papers

Technical Communique: A note on absolute stability of uncertain systems

A State-Space Algorithm for Designing H∞ Loop Shaping PlD Controllers

Describing functions in non-linear systems with structured and unstructured uncertainties

Adaptive Internal Model Control for Air-Fuel Ratio regulation

Air-Fuel Ratio Regulation Using A Discrete-Time Internal Model Controller