Verica Radisavljevic-Gajic

Recent Trends in Stabilization and Control of Distributed Parameter Dynamic Systems

The field of control and stabilization of distributed parameter systems described by partial differential equations has recently seen an increasing number of results published by very respected researchers in excellent control engineering and applied mathematics journals. This paper presents a survey of control and stabilization results with emphasis on controls. Various distributed parameter dynamic control and stabilization problems have been studied corresponding to heat conduction, wave propagation, Schrodinger equation, crowd (swarm) dynamics, magneto-hydro-dynamic channel flow, string and beam equations, viscous Burger equation, and general diffusion equations. Various techniques have been used for control and stabilization of such systems: Lyapunov stabilization, backstepping, gain scheduling, singular perturbations, sliding mode control, observer driven controller, tracking control, sampled-data control, neural networks. The field still remains widely open for future research. Applications of surveyed results to various areas including robots, aircraft, networks, transmission lines, electrochemical processes in energy systems are indicated.Copyright

Optimal Parallel Controllers and Filters for a Class of Second-Order Linear Dynamic Systems

Matrix second-order damped linear dynamic systems are frequently encountered in mechanical, structural, electrical, civil, and aerospace engineering. This class of systems also comes from the distributed parameter dynamic systems (systems described by partial differential equations) when they are approximated by linear dynamic systems. In this paper, we show how to design, for this class of systems, the globally optimal linear-quadratic controller and the globally optimal Kalman filter in terms of locally optimal linear-quadratic controllers and locally optimal scalar second-order Kalman filters. This simplifies computational requirements and allows full parallelism in information processing and feedback loop implementation. Conditions are established under which the presented procedure is applicable. Examples are included to demonstrate the efficiency of the proposed technique.

Simplified derivations of time-weighted quadratic functionals used in optimal control and filtering applications

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.

Natural Gas Hydrogen Reformer Controller Design With Disturbance Rejection

In this paper we present a controller design for a linearized model of a fuel cell hydrogen gas reformer, which produces hydrogen from natural gas. We design two feedback control loops, one of them with an integrator and another one with proportional state feedback. In the third step, a feed-forward controller is designed whose role is to off-set for the impact of the disturbance represented by the fuel cell current. Both the feedback controller and the feedforward controller are obtained through a rigorous dynamic optimization process of a quadratic performance criterion along trajectories of a linear dynamic system. According to the presented simulation results, the proposed controller copes well with the disturbance and reduces its impact within a few seconds from the time when the disturbance occurs, despite large jumps in the fuel cell current (disturbance).Copyright

Two-Stage Design of Linear Feedback Controllers for a Proton Exchange Membrane Fuel Cell

The paper considers the eighth-order proton exchange membrane (PEM) fuel-cell mathematical model and shows that it has a multi-time scale property, indicating that the dynamics of three model state space variables operate in the slow time scale and the dynamics of five state variables operate in the fast time scale. This multi-scale nature allows independent controllers to be designed in slow and fast time scales using only corresponding reduced-order slow (of dimension three) and fast (of dimension five) sub-models. The presented design facilitates the design of hybrid controllers, for example, the linear-quadratic optimal controller for the slow subsystem and the eigenvalue assignment controller for the fast subsystem. The design efficiency and its high accuracy are demonstrated via simulation on the considered PEM fuel cell model.Copyright

Full- and Reduced-Order Linear Observer Implementations in Matlab\/Simulink [Lecture Notes]

The design of observers is usually considered a graduate-level topic and therefore tends to be taught in a graduate-level control engineering course. However, several recent editions of standard undergraduate controlsystem textbooks cover full-order, and even reduced-order, observers [1]-[9]. Observers are also used in their own right to strictly observe the state variables of a dynamic system rather than to be used for feedback control (for example, in an experiment whose state variables have to be monitored, observed, or estimated at all times).

A Simplified Two-Stage Design of Linear Discrete-Time Feedback Controllers With Applications to Systems With Slow and Fast Modes

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 (multi-time 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.Copyright

A Lyapunov approach to second-order sliding-mode boundary control of an unstable heat system with spatiotemporal-varying parameters under boundary disturbances

This paper considers a boundary stabilization problem of an unstable heat system incorporated with spatial and temporal varying coefficients subjected to boundary uncertainties. The system model is governed by a second-order parabolic partial differential equation (PDE). By taking the Volterra integral transformation, we can obtain a target PDE with asymptotic stability characteristics in the new coordinates when an appropriate backstepping boundary control input is applied. The implicated backsteeping control law can be further integrated into the matched boundary disturbance. The associated Lyapunov function can then be used for designing an in nite-dimensional sliding surface, on which the system exhibits exponential stability, invariant of the bounded matched disturbance. Based on the Lyapunov method, a second-order sliding-mode boundary control, constructed by the integration of discontinuous signal, is employed to maintain the robustness to matched boundary disturbance. The closed-loop stability of the controlled system is also verified. Simulation results are provided to demonstrate the feasibility of this proposed control scheme.

Non-linear integral control of photon power transients in optical communication networks with erbium-doped fibre amplifiers

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.

Modeling of solid oxide fuel cells (SOFCs): An overview

In this paper, the authors present an overview for modeling of solid oxide fuel cells. Even though, a large amount of literature of SOFCs has been published in the last decade, most of them has focused on electrochemical characteristics such as cell components, new materials, reaction mechanisms, etc. The review of modeling for SOFCs helps to simulate and understand effects of changing loads, temperature, fuel and air supply, diffusion, and design algorithms and feedback loops to control these variables.