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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]

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]