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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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we show how autonomous vehicles performing a certain task can be controlled from one command center in order to achieve certain goals. The command center provides individual feedback gains to each vehicle in the form of one compounded feedback gain that in fact carries feedback gain information for each individual vehicle. Vehicles may be of different nature: satellites, cars, tanks, drowns, robots, unmanned aircraft, underwater vehicles, and ships. It is assumed that their dynamic is weakly coupled, namely, dynamics of each individual vehicle is weakly coupled to dynamics of all other vehicles and that they have the same control input. The weak coupling among the vehicles is represented either by physical interactions among vehicles or coordinating or communication signals. The results obtained are applicable to vehicles having different mathematical linear/linearized state space models. In the case when no interaction/coordination/communication among vehicles is present, and all feedback signals come from the command center (central controller) controller, the vehicle mathematical models can be identical. An important feature of the presented results is that different local feedback controllers can be facilitated for different vehicles using a unique global feedback controller signal designed by the command center. In this paper, we will consider cases of two and three vehicles, but the presented multistage feedback design methodology can be potentially extended to N vehicles. The presentation is done in continuous time. Similar derivations hold in the discrete-time domain. [ABSTRACT FROM AUTHOR]

This paper is an overview of fundamental linear–quadratic optimal control techniques used for linear dynamic systems. The presentation is suitable for undergraduate and graduate students and practicing engineers. The paper can be used by class instructors as supplemental material for undergraduate and graduate control system courses. The paper shows how to find the solution to a dynamic optimization problem : optimize an integral quadratic performance criterion along trajectories of a linear dynamic system over an infinite time period (steady-state linear–quadratic optimal control problem). The solution is obtained by solving a static optimization problem. All derivations done in the paper require only elementary knowledge of linear algebra and state space linear system analysis. The results are presented also for the observer-driven linear–quadratic steady-state optimal controller, output feedback-based linear–quadratic optimal controller, and the Kalman filter-driven linear–quadratic stochastic optimal controller. Having full understanding of derivations of the linear–quadratic optimal controller, observer-driven linear–quadratic optimal controller, optimal linear–quadratic output feedback controller, and optimal linear–quadratic stochastic controller, students and engineers will feel confident to use these controllers in numerous engineering and scientific applications. Several optimal linear–quadratic control case studies involving models of real physical systems, with the corresponding Simulink block diagrams and MATLAB codes, are included in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we derive an expression for the loss of optimal performance (compared to the corresponding linear-quadratic optimal performance with the instantaneous full-state feedback) when the continuous-time finite-horizon linear-quadratic optimal controller uses the estimates of the state variables obtained via a reduced-order observer. It was shown that the loss of optimal performance value can be found by solving the differential Lyapunov equation whose dimensions are equal to dimensions of the reduced-order observer. A proton exchange membrane fuel cell example is included to demonstrate the loss of optimal performance as a function of the final time. It can be seen from the simulation results that the loss of optimal performance value can be very large. The loss of optimal performance value can be drastically reduced by using the proposed least-square formulas for the choice of the reduced-order observer initial conditions. [ABSTRACT FROM AUTHOR]

This work addresses the control of a pinned-pinned beam represented by the fourth order partial differential equation commonly known as the Euler–Bernoulli beam model. The system under consideration has pinned boundary conditions on one end (displacement and bending moment fixed at zero) and controlled boundary conditions on the other end (displacement and bending moment are prescribed by control functions). There are also unknown bounded disturbances included on the controlled boundary. A backstepping control technique which introduces arbitrary damping into the system is discussed, and a method for applying this control in the presence of unknown disturbances is developed using sliding mode control theory. Sliding mode controllers are developed in a way that does not create a chattering effect, which is a common issue with sliding mode control. Simulation results are presented to show how the system dampens out vibrations at an arbitrarily determined rate and how the control functions respond to unmodeled disturbances. [ABSTRACT FROM AUTHOR]

In this paper we study the pure-slow and pure-fast dynamics of the disparity convergence of the eye movements second-order linear dynamic mathematical model under time varying stimuli. Performing simulation of the isolated pure-slow and pure-fast dynamics, it has been observed that the pure-fast component corresponding to the eye angular velocity displays abrupt and very fast changes in a very broad range of values. The result obtained is specific for the considered second-order mathematical model that does not include any saturation elements nor time-delay elements. The importance of presented results is in their mathematical simplicity and exactness. More complex mathematical models can be built starting with the presented pure-slow and pure-fast first-order models by appropriately adding saturation and time-delay elements independently to the identified isolated pure-slow and pure-fast first-order models. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this article, we present simple alternative derivations for efficient evaluation of a matrix integral that has applications in optimal control and filtering, stability, controllability, observability, and controller design of linear time-invariant systems. The quadratic matrix integral (functional) is computed in terms of solutions of a sequence of algebraic Lyapunov equations. We present also a method to efficiently solve the obtained sequence of algebraic Lyapunov equations. [ABSTRACT FROM AUTHOR]

In this paper, we first review the new algorithm for the two-stage feedback controller design of linear discrete-time systems, and then provide conditions for its applicability. The design algorithm is specialized and simplified for a class of linear systems with slow and fast modes (multitime scale systems or singularly perturbed systems). The proposed design significantly reduces computational full-state feedback design requirements and provides independent and accurate feedback controller design techniques in slow and fast time scales. We present also conditions needed for applicability of the proposed two-stage design in two time scales. The power of the two-stage design lies in the fact that different types of controllers can be designed for different subsystems using the corresponding feedback gains obtained by performing calculations only with the subsystem (reduced-order) matrices. [ABSTRACT FROM AUTHOR]

In this paper, we have shown how to simplify an algorithm for the two-stage design of linear feedback controllers by reducing computational requirements. The algorithm is further simplified for linear discrete-time systems with slow and fast modes (multitime scale systems or singularly perturbed systems), providing independent and accurate designs in slow and fast time scales. The simplified design procedure and its very high accuracy are demonstrated on the eigenvalue assignment problem of a steam power system. [ABSTRACT FROM AUTHOR]

In this study the authors present a novel technique for control of signal power transients caused by signal add/drops in optical communication networks with erbium‐doped fibre amplifiers (EDFAs). The approach utilises the electronic automatic gain control that combines both feedback and feedforward control of EDFA. Feedback control is non‐linear integral control and feedforward control is a steady‐state gain scheduling technique. The feedback non‐linear control requires information about the average inversion level that is obtained via a simple linearised first‐order observer. The scheduling variable used is the nominal pump power needed to keep the average inversion level at the desired value at steady state and the input signal powers given at particular wavelengths. In the simplified gain scheduling version, the scheduling variable is the total input signal power. Simulation examples indicate that the proposed controller completely eliminates at steady state the photon power transients caused by signal add/drops with the steady state being reached within a few milliseconds. [ABSTRACT FROM AUTHOR]

This paper presents a Proton-Exchange Membrane Fuel Cell (PEMFC) transient model in stack current cycling conditions and its partial optimal control. The derived model is used for a specific application of the recently published multistage control technique developed by the authors. The presented control-oriented transient PEMFC model is an extension of the steady-state control-oriented model previously established by the authors. The new model is experimentally validated for transient operating conditions on the Greenlight Innovation G60 testing station where the comparison of the experimental and simulation results is presented. The derived five-state nonlinear control-oriented model is linearized, and three clusters of eigenvalues can be clearly identified. This specific feature of the linearized model is known as the three timescale system. A novel multistage optimal control technique is particularly suitable for this class of systems. It is shown that this control technique enables the designer to construct a local LQR, pole-placement or any other linear controller type at the subsystem level completely independently, which further optimizes the performance of the whole non-decoupled system. [ABSTRACT FROM AUTHOR]