Bulletin of the Polish Academy of Sciences Technical Sciences

Simple necessary and sufficient conditions for robust stability of the positive linear discrete-time systems with delays with linear uncertainty structure in two cases: 1) unity rank uncertainty structure, 2) non-negative perturbation matrices, are established. The proposed conditions are compared with the suitable conditions for the standard systems. The considerations are illustrated by numerical examples.

The synthesis problem for optimal control systems in the class of discrete controls is under consideration. The problem is investigated by reducing to a linear programming (LP) problem with consequent use of a dynamic version of the adaptive method of LP. Both perfect and imperfect information on behavior of control system cases are studied. Algorithms for the optimal controller, optimal estimators are described. Results are illustrated by examples.

A complete parametric approach is proposed for the design of the Luenberger type function Kx observers for descriptor linear systems. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, parametric expressions for all the coefficient matrices of the observer are derived. The approach provides all the degrees of design freedom, which can be utilized to achieve some additional design requirements. An illustrative example shows the effect of the proposed approach.

New tests (criterions) for checking the reachability and the observability of positive linear-discrete-time systems are proposed. The tests do not need checking of rank conditions of the reachability and observability matrices of the systems. Simple sufficient conditions for the unreachability and unobservability of the systems are also established.

In the paper finite-dimensional stationary dynamical control systems described by linear stochastic ordinary differential state equations with single point delay in the control are considered. Using notations, theorems and methods taken directly from deterministic controllability problems, necessary and sufficient conditions for different kinds of stochastic relative controllability are formulated and proved. It will be proved that under suitable assumptions relative controllability of a deterministic linear associated dynamical system is equivalent to stochastic relative exact controllability and stochastic relative approximate controllability of the original linear stochastic dynamical system. Some remarks and comments on the existing results for stochastic controllability of linear dynamical systems with delays are also presented. Finally, minimum energy control problem for stochastic dynamical system is formulated and solved.

The paper deals with the problems of designing observers and unknown input observers for discrete-time Lipschitz non-linear systems. In particular, with the use of the Lyapunov method, three different convergence criteria of the observer are developed. Based on the achieved results, three different design procedures are proposed. Then, it is shown how to extend the proposed approach to the systems with unknown inputs. The final part of the paper presents illustrative examples that confirm the effectiveness of the proposed techniques. The paper also presents a MATLAB® function that implements one of the design procedures.

The paper presents the method for multicriteria design of a synchronous generator voltage regulator. The results of the voltage regulator polyoptimisation are compromise sets for a classic controller of type PI and fuzzy logic controller of type Takagi-Sugeno-Kang. A genetic algorithm is used to solve the polyoptimisation problem.

The paper deals with linear circuits synthesis with periodic parameters. It was proved that the time-varying voltages and currents of inner branches of such circuits can be calculated using linear recursive equations with periodic coefficients if signals on port are given. The stability theorem of periodic solution was formulated. Hereby described the synthesis problems appear when compensation of power supply systems is considered.

The paper concerns the two-machine non-preemptive flow shop scheduling problem with a total late work criterion

and a common due date (F2|dj = d|Y ). The late work performance measure estimates the quality of a solution with regard

to the duration of late parts of activities performed in the system, not taking into account the quantity of this delay. In the

paper, a few theorems are formulated and proven, describing features of an optimal solution for the problem mentioned, which is

NP-hard. These theorems can be used in exact exponential algorithms (as dominance relations reducing the number of solutions

enumerated explicitly), as well as in heuristic and metaheuristic methods (supporting the construction of sub-optimal schedules

of a good quality).

The manufacture and consumption of market products show ever growing trends, and this means not only the supply and demand volume but also, to a higher and higher extent, searching for new products distinguishable from the variety of products on the market. Thus, it is necessary to find methods of functional, logical and structural combination of the so far existing engineering applications like CAx, RP/RT/RE, PDM/TDM, PPC/ERP, CE/SE and RDBMS techniques. A new challenge imposed on manufacturers by the competitive market is the so-called “product customization”, i.e. attending to an individual customer’s requirements in the features of a series manufactured product. The general objective of customisation is to elaborate features of a product, manufacturing processes, documentation and production organisation in such a way that the product’s individual features meet the customer’s requirements and its manufacturing process, price and service do not stray from series manufactured products.

The paper contains a description of a multiscale algorithm based on the boundary element method (BEM) coupled with a discrete atomistic model. The atomic model uses empirical pair-wise potentials to describe interactions between atoms. The Newton-Raphson method is applied to solve a nanoscale model. The continuum domain is modelled by using BEM. The application of BEM reduces the total number of degrees of freedom in the multiscale model. Some numerical results of simulations

at the nanoscale are shown to examine the presented algorithm.

This paper is an overview of the application potential and design challenges of micro air vehicles (MAVs), defined as small enough to be practical for a single-person transport and use. Four types of MAVs are considered: 1) fixed-wing, 2) rotarywing, 3) ornithopters (bird-like flapping) and 4) entomopters (insect-like flapping). In particular, advantages of a propeller-driven delta wing configuration for type 1 are discussed. Some detail is also given for type 4, the least understood of the four, including a new concept of manoeuvre control for such MAVs. The paper concludes with a brief prognostic of the future of each MAV type.

The paper presents the application of the newly developed method of the solution of nonlinear equations to the adaptive modelling and computer simulation. The approach is suitable when the system of equations can be arranged in such a way that it consists of a large number of linear equations and a smaller number of nonlinear equations. This situation occurs in the case of adaptive modelling of mechanical systems using finite elements or finite differences techniques. In this case the classical least square method becomes very effective. The paper presents several examples of the application of the method. A solution to the, so called, “black box” problem is also presented.

In the paper the thermal processes proceeding in the solidifying metal are analyzed. The basic energy equation determining the course of solidification contains the component (source function) controlling the phase change. This component is proportional to the solidification rate ¶ fS/¶ t (fS Î [0, 1], is a temporary and local volumetric fraction of solid state). The value of fS can be found, among others, on the basic of laws determining the nucleation and nuclei growth. This approach leads to the so called micro/macro models (the second generation models). The capacity of internal heat source appearing in the equation concerning the macro scale (solidification and cooling of domain considered) results from the phenomena proceeding in the micro scale (nuclei growth). The function fS can be defined as a product of nuclei density N and single grain volume V (a linear model of crystallization) and this approach is applied in the paper presented. The problem discussed consists in the simultaneous identification of two parameters determining a course of solidification. In particular it is assumed that nuclei density N (micro scale) and volumetric specific heat of metal (macro scale) are unknown. Formulated in this way inverse problem is solved using the least squares criterion and gradient methods. The additional information which allows to identify the unknown parameters results from knowledge of cooling curves at the selected set of points from solidifying metal domain. On the stage of numerical realization the boundary element method is used. In the final part of the paper the examples of computations are presented.

In the paper, a solution to the problem of elastic deformation of thin-walled shell structures with complex shapes within the theory of geometrically non-linear shells has been presented. It is a modification of the Newton-Raphson method. In a variational formulation, the problem is based on a Lagrange’s functional for increments of displacements. The method has been applied to investigations of a harmonic drive, in particular to analysis of the stress state in the flexspline with a variable curvature as well as bearings of the generator. For verification of the obtained results, a more adequate FEM model calculated by ANSYS has been used.

Macroscopic coefficients together with a Darcy law are obtained for porous piezoelectric medium with random, not necessarily ergodic, distribution of pores in which a two-ionic electrolyte flows. Peculiarities of stochastic porosity are indicated.