Algebraic robust control of a closed circuit heating-cooling system with a heat exchanger and internal loop delays

This study demonstrates the use of a simple algebraic controller design for a cooling-heating plant with a through-flow air-water heat exchanger that evinces long internal delays with respect to the robustness to plant model uncertainties and variable ambient temperature conditions during the season. The advantage of the proposed design method consists in that the delays are not approximated but fully considered. Moreover, the reduction of sensitivity to model parameters’ variations yields the better applicability regardless modeling errors or environmental fluctuations. The infinite-dimensional mathematical model of the plant has been obtained by using anisochronic modeling principles. The key tool for the design is the ring special of quasipolynomial meromorphic functions (RQM). The Two-Feedback-Controllers (TFC) rather than the simple negative control feedback loop is utilized, which enables to solve the reference tracking and disturbance rejection independently and more efficiently. The eventual controller is then tuned such that robust stability and robust performance requirements are fulfilled. The tuning procedure is supported by a performance optimization idea. Since the originally obtained controller is of the infinite-dimensional nature, a possible way how to substitute it by a simplified finite-dimensional one is proposed for engineering practice. The functionality of both the controllers is compared and verified by simulations as well as by real measurements which prove a very good performance. © 2016 Elsevier LtdEuropean Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376

The revision and extension of the R-MS ring for time delay systems

This paper is aimed at reviewing the ring of retarded quasipolynomial meromorphic functions (R-MS) that was recently introduced as a convenient control design tool for linear, time-invariant time delay systems (TDS). It has been found by the authors that the original definition does not constitute a ring and has some essential deficiencies, and hence it could not be used for an algebraic control design without a thorough reformulation which i.e. extends the usability to neutral TDS and to those with distributed delays. This contribution summarizes the original definition of RMS, simply highlights its deficiencies via examples, and suggests a possible new extended definition. Hence, the new ring of quasipolynomial meromorphic functions (R-QM) is established to avoid confusion. The paper also investigates and introduces selected algebraic properties supported by some illustrative examples and concisely outlines its use in controller design.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19

Determination of the modal parameters on the thin flat structures

This paper presents the investigation of modal parameters using the different approaches. The object of the examination is the simple structure such as flat rectangle plate is. Before starting the measurement, there have been calculated natural frequencies of the plate by analytical approach. Subsequently, the experiment part is performed. The appropriate measuring apparatus has to be applicated for the experimental analysis. First, there are evaluated modal parameters of the specimen, the so-called “frequency sweep” is used as the input signal for excitation. After that, the experimental harmonic analysis is performed according the obtained eigen frequencies from the modal analysis. In the final stage, the data from simulations and experimental measurement are compared

Robust control of continuous stirred tank reactor with jacket cooling

Continuous Stirred-Tank Reactors (CSTR) belong to basic technological equipment frequently used in the the production of various types of chemicals. These systems are quite complex with many nonlinearities. So, the conventional linear control with fixed parameters can be questionable or unacceptable. The solution should be found in so-called “non-traditional” control approaches like Adaptive, Robust, Fuzzy or Artificial Intelligent methods. One way is the utilization of selftuning adaptive schemes but computations are quite difficult, clumsy and time-consuming. This paper brings an alternative principle called robust approach. This approach considers a linear system with parametric uncertainty which covers a family of all feasible plants. Then a controller with fix parameters is designed so that for all possible plants the acceptable control behavior is obtained. The two degree of freedom (2DOF) structure for the control law was chosen. All calculation and simulations of mathematical models and control responses was performed in the Matlab and Simulink environment. Copyright © 2019, AIDIC Servizi S.r.l

Gridding discretization-based multiple stability switching delay search algorithm: The movement of a human being on a controlled swaying bow

Delay represents a significant phenomenon in the dynamics of many human-related systems - including biological ones. It has i.a. a decisive impact on system stability, and the study of this influence is often mathematically demanding. This paper presents a computationally simple numerical gridding algorithm for the determination of stability margin delay values in multiple-delay linear systems. The characteristic quasi-polynomial - the roots of which decide about stability - is subjected to iterative discretization by means of pre-warped bilinear transformation. Then, a linear and a quadratic interpolation are applied to obtain the associated characteristic polynomial with integer powers. The roots of the associated characteristic polynomial are closely related to the estimation of roots of the original characteristic quasi-polynomial which agrees with the system's eigenvalues. Since the stability border is crossed by the leading one, the switching root locus is enhanced using the Regula Falsi interpolation method. Our methodology is implemented on - and verified by - a numerical bio-cybernetic example of the stabilization of a human-being's movement on a controlled swaying bow. The advantage of the proposed novel algorithm lies in the possibility of the rapid computation of polynomial zeros by means of standard programs for technical computing; in the low level of mathematical knowledge required; and, in the sufficiently high precision of the roots loci estimation. The relationship to the direct search QuasiPolynomial (mapping) Rootfinder algorithm and computational complexity are discussed as well. This algorithm is also applicable for systems with non-commensurate delays. © 2017 Pekař et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.CZ.1.05/2.1.00/19.0376, ERDF, European Regional Development FundMinistry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)]; European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376

Two degrees-of-freedom hybrid adaptive approach with pole-placement method used for control of isothermal chemical reactor

Continuous Stirred-Tank Reactors (CSTR) are technological plants often used in the chemical or biochemical industry for the production of various types of chemicals. These systems are very complex from the control point-of-view - mainly because of their nonlinearity. Controlling such processes by means of conventional methods that use controllers with fixed parameters; often produces bad - or even, unacceptable results. This is the right field for so-called "modern" control methods like Robust, Predictive, and Adaptive Control. The control method used in this work is a hybrid adaptive control where the originally nonlinear system is represented by the external linear model whose parameters are recursively identified during the control phase. The pole-placement method with a spectral factorization and two degrees-of-freedom (2DOF) control configuration used in the control synthesis in order satisfy the basic control requirements, for instance: stability, reference signal tracking and disturbance attenuation. Moreover, the resulting controller obtained from the polynomial synthesis is easily programmable and be implemented in control computers. All of the proposed methods were tested by simulations on a mathematical model of an isothermal CSTR, with a complex reaction inside. The results so obtained, demonstrate the applicability of this control method for these kinds of processes. The team used the MATLAB simulation program in this research. Copyright © 2017, AIDIC Servizi S.r.l.CZ.1.05/2.1.00/03.0089, ERDF, European Regional Development Fund; MOE, Ministry of Educatio