Robust stability of thermal control systems with uncertain parameters: The graphical analysis examples

This paper is intended to present the investigation of robust stability for integer order or fractional order feedback control loops affected by parametric uncertainty and time-delay(s) with special emphasis on the thermal control systems. The applied graphical method is based on the numerical calculations of the value sets and the zero exclusion condition. Three robust stability examples inspired by control of the real-world thermal processes are used for demonstration of the technique applicability. Namely, the work deals with the analysis of a shell-and-tube heat exchanger which was identified as the (integer order) time-delay model with parametric uncertainty, a heat transfer process modeled as the fractional order time-delay plant with parametric uncertainty, and a heating–cooling system with a heat exchanger described by the anisochronic model with internal delays and parametric uncertainty. © 2017 Elsevier LtdEuropean Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303 (MSMT-7778/2014)

Systems Structure and Control

The title of the book System, Structure and Control encompasses broad field of theory and applications of many different control approaches applied on different classes of dynamic systems. Output and state feedback control include among others robust control, optimal control or intelligent control methods such as fuzzy or neural network approach, dynamic systems are e.g. linear or nonlinear with or without time delay, fixed or uncertain, onedimensional or multidimensional. The applications cover all branches of human activities including any kind of industry, economics, biology, social sciences etc

Delay-Independent Stability Analysis of Linear Time-Delay Systems Based on Frequency

This paper studies strong delay-independent stability of linear time-invariant systems. It is known that delay-independent stability of time-delay systems is equivalent to some frequency-dependent linear matrix inequalities. To reduce or eliminate conservatism of stability criteria, the frequency domain is discretized into several sub-intervals, and piecewise constant Lyapunov matrices are employed to analyze the frequency-dependent stability condition. Applying the generalized Kalman–Yakubovich–Popov lemma, new necessary and sufficient criteria are then obtained for strong delay-independent stability of systems with a single delay. The effectiveness of the proposed method is illustrated by a numerical example

Robust stability of fractional order polynomials with complicated uncertainty structure

The main aim of this article is to present a graphical approach to robust stability analysis for families of fractional order (quasi-)polynomials with complicated uncertainty structure. More specifically, the work emphasizes the multilinear, polynomial and general structures of uncertainty and, moreover, the retarded quasi-polynomials with parametric uncertainty are studied. Since the families with these complex uncertainty structures suffer from the lack of analytical tools, their robust stability is investigated by numerical calculation and depiction of the value sets and subsequent application of the zero exclusion condition. © 2017 Matusu 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.European Regional Development Fund under the project CEBIA-Tech Instrumentation [CZ.1.05/ 2.1.00/19.0376]; Ministry of Education, Youth and Sports of the Czech Republic within the National Sustainability Programme [LO1303, MSMT-7778/2014

STABILITY AND PERFORMANCE OF NETWORKED CONTROL SYSTEMS

Network control systems (NCSs), as one of the most active research areas, are arousing comprehensive concerns along with the rapid development of network. This dissertation mainly discusses the stability and performance of NCSs into the following two parts. In the first part, a new approach is proposed to reduce the data transmitted in networked control systems (NCSs) via model reduction method. Up to our best knowledge, we are the first to propose this new approach in the scientific and engineering society. The "unimportant" information of system states vector is truncated by balanced truncation method (BTM) before sending to the networked controller via network based on the balance property of the remote controlled plant controllability and observability. Then, the exponential stability condition of the truncated NCSs is derived via linear matrix inequality (LMI) forms. This method of data truncation can usually reduce the time delay and further improve the performance of the NCSs. In addition, all the above results are extended to the switched NCSs. The second part presents a new robust sliding mode control (SMC) method for general uncertain time-varying delay stochastic systems with structural uncertainties and the Brownian noise (Wiener process). The key features of the proposed method are to apply singular value decomposition (SVD) to all structural uncertainties, to introduce adjustable parameters for control design along with the SMC method, and new Lyapunov-type functional. Then, a less-conservative condition for robust stability and a new robust controller for the general uncertain stochastic systems are derived via linear matrix inequality (LMI) forms. The system states are able to reach the SMC switching surface as guaranteed in probability 1 by the proposed control rule. Furthermore, the novel Lyapunov-type functional for the uncertain stochastic systems is used to design a new robust control for the general case where the derivative of time-varying delay can be any bounded value (e.g., greater than one). It is theoretically proved that the conservatism of the proposed method is less than the previous methods. All theoretical proofs are presented in the dissertation. The simulations validate the correctness of the theoretical results and have better performance than the existing results