In this paper, a control technique is presented for an undamped, pinned-pinned Euler-Bernoulli beam with control inputs and bounded disturbances on one boundary. The control strategy drives the system to its origin at an arbitrary exponential rate in the presence of the disturbances. This is achieved in two main steps. First, a backstepping transformation is used to convert the marginally stable Euler-Bernoulli beam system to a new form that has an exponentially stable homogeneous form. Control inputs are needed to fully convert the system to this form; however, since they are distorted by unknown bounded disturbances, the next step implements a sliding mode controller to account for them. The proposed sliding manifolds require a combination of classical and “second order” techniques in order to avoid discontinuous chattering on the physical system. Therefore, the continuous sliding mode controllers developed return the beam to its origin at an arbitrary exponential rate, and do so in the presence of unknown bounded disturbances on the boundary. The main contributions of this paper with respect to previous backstepping designs for the Euler-Bernoulli beam are that all three of the following goals are accomplished together: (i) steady-state position is the origin, (ii) decay rate has no theoretical restrictions, and (iii) is robust to bounded disturbances.

In this paper, we present some initial results about vulnerability of control systems that can be used in Internet of Things (IoT) applications. Up to our best knowledge, this paper is the first study about vulnerability of applied control systems in general, and especially in the IoT environment. The purpose of this paper is to examine fundamentals of linear control systems and consider vulnerability of its main features and concepts used in IoT applications under potential malicious attacks. We examine vulnerabilities of system stability, controllability, observability, design of feedback loops, and design and placement of sensors and controllers (actuators). The detailed study is limited to the most important vulnerability issues in time-invariant, unconstrained, deterministic, and linear physical systems. Several interesting and motivating examples are provided. We have outlined also some basic vulnerability studies for time-invariant nonlinear unconstrained systems, and indicate that such a study is particularly needed for distributed parameter systems that are very prone to outside physical and cyber-attacks.

This paper presents the development of a full-state observer for an Euler-Bernoulli beam system with simply supported boundary conditions. This problem is motivated by the necessity of estimators in control and diagnostic applications. The observer is developed using a backstepping procedure. The full state observer cannot be completed with a single observer system, and hence this paper presents the synthesis of two observer structures that together provide the desired convergence. The necessary feedback information is limited to the slope and the shear force of the beam at one boundary, which are practically measurable values on a physical system. The observer estimates the full infinite dimensional beam system without any discretization of the model. The result of the technique developed in this paper is that the infinite dimensional observer estimates converge to the plant system states (representing the actual beam displacement) at an arbitrary exponential rate; numerical simulation results validating this behavior are provided.

This paper presents a new technique for design of full-state feedback controllers for linear dynamic systems in three stages. The new technique is based on appropriate partitioning of the linear dynamic system into linear dynamic subsystems. Every controller design stage is done at the subsystem level using only information about the subsystem (reduced-order) matrices. Due to independent design in each stage, different subsystem controllers can be designed to control different subsystems. Partial subsystem level optimality and partial eigenvalue subsystem assignment can be achieved. Using different feedback controllers to control different subsystems of a system has not been present in any other known linear full-state feedback controller design technique. The new technique requires only solutions of reduced-order subsystem level algebraic equations. No additional assumptions were imposed except what is common in linear feedback control theory (the system is controllable (stabilizable)) and theory of three time-scale linear systems (the fastest subsystem state matrix is invertible)). The local full-state feedback controllers are combined to form a global full-state controller for the system under consideration. The presented results are specialized to the three time-scale linear control systems that have natural decomposition into slow, fast, and very fast subsystems, for which numerical ill conditioning is removed and solutions of the design algebraic equations are easily obtained. The proposed three-stage three time-scale feedback controller technique is demonstrated on the eighth-order model of a fuel cell model.

Mathematical models of energy systems have been mostly represented by either linear or nonlinear ordinary differential equations. This is consistent with lumped-parameter dynamic system modeling, where dynamics of system state variables can be fully described only in the time domain. However, when dynamic processes of energy systems display both temporal and spatial evolutions (as is the case of distributed-parameter systems), the use of partial differential equations is necessary. Distributed-parameter systems, being described by partial differential equations, are mathematically (and computationally) much more difficult for modeling, analysis, simulation, and control. Despite these difficulties in recent years, quite a significant number of papers that use partial differential equations to model and control energy processes and systems have appeared in journal and conference publications and in some books. As a matter of fact, distributed-parameter systems are a modern trend in the areas of control systems engineering and some energy systems. In this overview, we will limit our attention mostly to renewable energy systems, particularly to partial differential equation modeling, simulation, analysis, and control papers published on fuel cells, wind turbines, solar energy, batteries, and wave energy. In addition, we will indicate the state of some papers published on tidal energy systems that can be modelled, analyzed, simulated, and controlled using either lumped or distributed-parameter models. This paper will first of all provide a review of several important research topics and results obtained for several classes of renewable energy systems using partial differential equations. Due to a substantial number of papers published on these topics in the past decade, the time has come for an overview paper that will help researchers in these areas to develop a systematic approach to modeling, analysis, simulation, and control of energy processes and systems whose time–space evolutions are described by partial differential equations. The presented overview was written after the authors surveyed more than five hundred publications available in well-known databases such as IEEE, ASME, Wiley, Google, Scopus, and Web of Science. To the authors’ best knowledge, no such overview on PDEs for energy systems is available in the scientific and engineering literature. Throughout the paper, the authors emphasize novelties, originalities, and new ideas, and identify open problems for future research. To achieve this goal, the authors reviewed more than five hundred journal articles and conference papers.

Full- and reduced-order observers have been used in many engineering applications, particularly for energy systems. Applications of observers to energy systems are twofold: (1) the use of observed variables of dynamic systems for the purpose of feedback control and (2) the use of observers in their own right to observe (estimate) state variables of particular energy processes and systems. In addition to the classical Luenberger-type observers, we will review some papers on functional, fractional, and disturbance observers, as well as sliding-mode observers used for energy systems. Observers have been applied to energy systems in both continuous and discrete time domains and in both deterministic and stochastic problem formulations to observe (estimate) state variables over either finite or infinite time (steady-state) intervals. This overview paper will provide a detailed overview of observers used for linear and linearized mathematical models of energy systems and review the most important and most recent papers on the use of observers for nonlinear lumped (concentrated)-parameter systems. The emphasis will be on applications of observers to renewable energy systems, such as fuel cells, batteries, solar cells, and wind turbines. In addition, we will present recent research results on the use of observers for distributed-parameter systems and comment on their actual and potential applications in energy processes and systems. Due to the large number of papers that have been published on this topic, we will concentrate our attention mostly on papers published in high-quality journals in recent years, mostly in the past decade.