Scalar Domain Research Articles

On an asymptotic theory of diffraction gratings used in the scalar domain

Starting from the electromagnetic theory, we derive an asymptotic formalism to investigate the behavior of perfectly conducting gratings used at small wavelengths to groove pitch ratios and near normal incidence. The theory is applied to study three classical types of profiles: sinusoidal, lamellar, and blazed gratings. Results are given for both −1 and −2 Littrow (or near Littrow) mounts. The accuracy of the theory and the limits of the domain where it applies are studied by the use of rigorous electromagnetic computations. The role of a finite conductivity of the surface is also investigated.

Approximation in control of nonlinear dynamic systems

AbstractThe type of system approximation in which the system state space x is mapped into a scalar domain V by a quadratic transformation where Q is appropriately determined, is used to develop a suboptimal control procedure for unconstrained lumped parameter dynamic systems via the application of Pontryagin's Maximum Principle. The optimization problem in the scalar domain becomes an initial value problem when the scalar adjoint variable is held constant through out the course of control. The resulting computational scheme includes an effective and simple way to construct the transformation matrix Q and a straightforward minimum seeking approach to locate the best constant overall average scalar adjoint parameter. For the class of problems with quadratic performance index, system equation approximation further reduces the determination of Q to the solution of a matrix Riccati equation.The application of the proposed suboptimal control procedure to four chemical engineering systems shows that the procedure is simple direct, and efficient and works particularly well for problems where the final time is large.