Pavel Navrátil

PPSA: A Tool for Suboptimal Control of Time Delay Systems: Revision and Open Tasks

During the development of algebraic controller design in a special ring for time delay systems (TDSs) a problem of a suitable free controller parameters setting appeared. The first author of this contribution recently suggested a natural idea of placing the dominant characteristic numbers (poles) and zeros of the infinite-dimensional feedback control system on the basis of the desired overshoot for a simple finite-dimensional matching model and shifting of the rest of the spectrum. However, the original procedure called the Pole-Placement Shifting based controller tuning Algorithm (PPSA) was not developed and described entirely well. The aim of this paper is to revise the idea of the PPSA and suggest a possible ways how to improve or extend the algorithm. A concise illustrative example is attached to clarify the procedure for the reader as well.

One of possible approaches to control of multivariable control loop

Abstract This paper deals with description of one of possible approaches to control of MIMO control loops with utilisation of the so called binding members and correction members. The designed method of control combinations classical way to ensure of autonomy of control loop via binding members and the use of the method of SISO branched control loops with measurement of dominant disturbance variables to ensure of invariance of control loop by means of correction members. Simulation verification of this method was carried out for three-variable control loop of a steam turbine.

THE WAY OF DISTRICT HEATING OUTPUT CONTROL BY MEANS OF HYDROTHERMAL POWER SYSTEMS – THREE MODIFICATIONS

Abstract District Heating Systems (DHS) are being developed in large cities in accordance with their growth. The DHS are formed by enlarging networks of heat distribution to consumers and at the same time they interconnect the heat sources gradually built. DHS is used in larger cities of some European countries e.g. in Germany, France, Denmark, Finland, Sweden, Austria, Czech Republic, Poland and others. Production technology of heat by means of combined production of power and heat (CHP) is an important way to increasing of thermal efficiency of closed thermal loop. The paper shows the system access to the control of extensive DHS -controlled plant. It concerns automatic control of technological string :production, transport + distribution, consumption” of extensive district heating and that is the contribution of this paper. Control by means of advanced control algorithms is a tool (up to now neglect) for decreasing consumption of energy and increasing the level of environment protection. The paper deals with brief description of three modifications of the way of control of hot-water piping heat output at simultaneous operation of qualitative and also quantitative parts of control.

Polynomial Approximation of Quasipolynomials Based on Digital Filter Design Principles

This contribution is aimed at a possible procedure approximating quasipolynomials by polynomials. Quasipolynomials appear in linear time-delay systems description as a natural consequence of the use of the Laplace transform. Due to their infinite root spectra, control system analysis and synthesis based on such quasipolynomial models are usually mathematically heavy. In the light of this fact, there is a natural research endeavor to design a sufficiently accurate yet simple engineeringly acceptable method that approximates them by polynomials preserving basic spectral information. In this paper, such a procedure is presented based on some ideas of discrete-time (digital) filters designing without excessive math. Namely, the particular quasipolynomial is subjected to iterative discretization by means of the bilinear transformation first; consequently, linear and quadratic interpolations are applied to obtain integer powers of the approximating polynomial. Since dominant roots play a decisive role in the spectrum, interpolations are made in their very neighborhood. A simulation example proofs the algorithm efficiency.

Some Recent Results on Direct Delay-Dependent Stability Analysis: Review and Open Problems

This contribution focuses an overview of selected results on time-delay systems stability analysis in the delay space, recently published in outstanding high-impacted journals and top conferences and meetings. A numerical gridding algorithm solving this problem designed by the first author is included as well. The theoretical background and a concise literature overview are followed by the list of practical and software applications. Unsolved tasks and open problems stemming from the analysis of presented methods and results concisely conclude the paper. The reader is supposed to use this survey to follow some of the presented techniques in his/her own research or engineering practice.

Spectral Abscissa Minimization when Algebraic Control of Unstable LTI-TDS

Abstract Optimal pole assignment minimizing the spectral abscissa when algebraic control of linear time-invariant time delay systems (LTI-TDS) is focused in this paper. We concentrate on algebraic controller design approach in the R MS ring resulting in delayed controllers as well. In the case of unstable delayed plants, the use a simple feedback loop results in a characteristic quasipolynomial instead of polynomial is obtained which means that the closed loop has an infinite spectrum. Thus, it is not possible to place all feedback poles to the prescribed positions exactly by a finite number of free controller parameters. The pole placement problem is translated to the minimization of the spectral abscissa which is a nonsmooth nonconvex function of free parameters in many cases. We initially solve the problem via standard quasi-continuous shifting algorithm followed by a comparative utilization of three iterative optimization algorithms; namely, Nelder-Mead algorithm, Extended Gradient Sampling Algorithm and Self-Organizing Migration Algorithm. Simulation control of an unstable LTI-TDS - the roller skater on the swaying bow - serves as an illustrative example for the algebraic control with the spectral abscissa minimization.