2011 (Volume 21)
Regular design equations for the continuous reduced-order Kalman filter
(Universität Erlangen-Nürnberg, Germany)
Reduced-order Kalman filters yield an optimal state estimate for linear dynamical systems, where parts of the output are not corrupted by noise. The design of such filters can either be carried out in the time domain or in the frequency domain. Different from the full-order case where all measurements are noisy, the design equations of the reduced-order filter are not regular. This is due to the rank deficient measurement covariance matrix and it can cause problems when using standard software for the solution of the Riccati equations in the time domain. In the frequency domain the spectral factorization of the non-regular polynomial matrix equation does not cause problems. However, the known proof of optimality of the factorization result also requires a regular measurement covariance matrix. This paper presents regular (reduced-order) design equations for reduced-order Kalman filters in the time and in the frequency domains for linear continuous-time systems. They allow to use standard software for the design of the filter, to formulate the conditions for the stability of the filter and they also prove that the existing frequency domain solutions obtained by spectral factorization of a non-regular polynomial matrix equation are indeed optimal.
keywords: optimal estimation, polynomials, multivariable systems, continuous-time systems
Parametric optimization of neutral linear system with two delays with P-controller
(AGH University of Science and Technology, Krakow, Poland)
In the paper the problem of parametric optimization of a linear neutral system with two delays accomplished with respect to the integral quadratic performance index is formulated and solved. A method of computing the value of performance index relies on determining such a Lyapunov functional defined on the state space that its value for the initial state is equal to that of performance index. In the paper the form of Lyapunov functional is assumed and a method of computing its coefficients is given. An example illustrating the application of the theory discussed is presented. It concerns a system with the P-controller designed to control a plant with two delays both retarded and neutral type. For such a system the value of the considered performance index is determined.
keywords: parametric optimization, Lyapunov functional, time delay system, neutral system
Optimal control problem for infinite variables hyperbolic systems with time lags
|G.M. Bahaa and M.M. Tharwat|
(Beni-Suef University, Beni-Suef, Egypt)
In this paper, by using the theorems of [Lions (1971) and Lions, Magenes (1972)], the optimal control problem for distributed hyperbolic systems, involving second order operator with an infinite number of variables, in which constant lags appear both in the state equations and in the boundary conditions is considered. The ptimality conditions for Neumann boundary conditions are obtained and the set of inequalities that characterize these conditions is formulated. Also, several mathematical examples for derived optimality conditions are presented. Finally, we consider an optimal distributed control problem for (n × n)-infinite variables hyperbolic systems.
keywords: optimal control, hyperbolic system, time delays, distributed control problems, Neumann conditions, existence and uniqueness of solutions, second order operator with an infinite number of variables
Application of agent cooperation by means of DES supervision to manufacturing system
(Slovak Academy of Sciences, Bratislava, Slovakia)
The supervision of complex manufacturing systems is handled in this paper. Production lines of manufacturing systems are understood here to be hybrid agents. Such an agent expresses continuous material flow together with a set of imperative discrete operations. In other words, the hybrid agent makes a cooperation of continuous and discrete event devices possible. The results are applied to complex continuous manufacturing system. First Order Hybrid Petri Nets (FOHPN) are utilized in order to model the elementary autonomous hybrid agents. The cooperation of hybrid agents is based on the DES (discrete-event systems) control theory. It is realized by means of DES supervision methods and the agent negotiation is based on place/transition Petri nets (P/T PN). The proposed approach is illustrated in details on the cooperation of hybrid production lines in the real complex manufacturing systems recycling waste plastics into plastic bags. The usefulness and applicability of the approach consists especially in the fact that the procedures in analytical terms can be employed. In such a way the approach turns lucid also in complicated cases.
keywords: agents, control, cooperation, discrete-event systems, continuous systems, hybrid Petri nets, supervisor, synthesis
Comparison between two approaches to modeling microsatellite DNA repeats: infinite dimensional model and its n-dimensional approximation
(Silesian University of Technology, Gliwice, Poland)
Two approaches to modeling microsatellite DNA repeats are considered. The former is an infinite dimensional system based on the theory of branching random walks which dynamic properties are characterized using Laplace transforms and Laplace asymptotic techniques. The latter is an n-dimensional approximation where microsatellite DNA repeats model is the example of a chain system. Both models were the subject of many numerical calculations using the MATLAB software. The results allow us to evaluate the asymptotic behavior and determine the effect of the system parameters on the run of the solution and the state variables.
keywords: infinite-dimensional systems, asymptotic stability, chain systems, microsatellites DNA repeats, polymerase slippage
Dynamic decoupling of left-invertible MIMO LTI plants
(West Pomeranian University of Technology, Szczecin, Poland)
In the paper problems with dynamic decoupling of the left-invertible multi-input multioutput dynamic (MIMO) linear time invariant (LTI) plants are considered. It is presented an universal and efficient algorithm for synthesis of control system for proper, square, right and left invertible plants which can be both unstable and/or on-minimumphase.
keywords: dynamic decoupling, left-invertible, pole assignment, polynomial matrix equations
FPGA implementation of DPWM utility/DG interfaced solar (PV) power converter for green home power supply
|S.N. Singh and S. Mishra|
(National Institute of Technology, Jamshedpur, India)
In this paper, utility/DG interfaced DPWM solar (PV) power converter (SPC) has been proposed and developed to meet the growing green energy demand of household applications in a developing country like India. The use of new software based direct PWM strategy (DPWM) in the inverter circuit has resulted in to produce a very near sine-wave, most suitable for various home loads. Simulated results of proposed PWM output wave form and computation of its harmonics content in terms of THD value (upto 5% or even less) using MATLAB software has been reflected in the proposed scheme. The features like an intelligent control action to prevent battery from overcharge or undercharge, higher efficiency (> 90%), generation of grid quality green electricity, sustainability of solar renewable energy sources, cost effective hardware realization with FPGA based VLSI embedded system, shows the superiority of the proposed scheme over conventional power supply systems.
keywords: direct pulse width modulation (DPWM), total harmonic distortion (THD), field SMF: sealed maintenance, free programmable gate array (FPGA)