In this article we focus on the balanced truncation linear quadratic regulator (LQR) with constrained states and inputs. For closed-loop, we want to use the LQR to find an optimal control that minimizes the objective function which called “the quadratic cost function” with respect to the constraints on the states and the control input. In order to do that we have used formal asymptotes for the Pontryagin maximum principle (PMP) and we introduce an approach using the so called The Hamiltonian Function and the underlying algebraic Riccati equation. The theoretical results are validated numerically to show that the model order reduction based on open-loop balancing can also give good closed-loop performance.

The article presents research on modelling fracture in softwood bent elements. This kind of timber is the one most exploited for construction. Authors present a brief review on the subject with emphasis on three basic attempts: Linear Elastic Fracture Mechanics (LEFM), Continuum Damage Mechanics (CDM) and Hill’s Function (HF). Proposed 3D solution bases on Hill’s Function applied in the ABAQUS FEM code. The new idea includes isolating theoretical compression and tension zones in a model. Then, it is possible to distinguish between compressive and tensile strength and predict a real behaviour of bent elements. Introducing general dependencies between material properties leads to the need of determining only longitudinal elastic modulus (EL) and modulus of rupture (MOR). It is practical because these parameters are the main reported in a scientific and technical literature. Authors describe all of the assumptions in details. The experimental tests and Digital Image Correlation method (DIC) validate the FEM model.

Thiswork presents results of comparative studies of the optical absorption coefficient spectra of ion implanted layers in silicon. Three nondestructive and noncontact techniques were used for this purpose: spectroscopic ellipsometry (SE), modulated free carriers absorption (MFCA) and the photo thermal radiometry (PTR). Results obtained with the ellipsometric method are the proof of correctness of the results obtained with the MFCAandPTRtechniques. These techniques are usually used for investigations of recombination parameters of semiconductors. They are not used for investigations of the optical parameters of semiconductors. Optical absorption coefficient spectra of Fe+ and Ge+ high energy and dose implanted layers in silicon, obtained with the three techniques, are presented and compared.