Hybrid Systems and Control With Fractional Dynamics (I): Modeling and Analysis

No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give additional flexibility and help to the system designer. It is part I of two companion papers and introduces the fundamentals of fractional-order hybrid systems, in particular, modeling and stability analysis of two kinds of such systems, i.e., fractional-order switching and reset control systems. Some examples are given to illustrate the applicability and effectiveness of the developed theory. Part II will focus on fractional-order hybrid control.Comment: 2014 International Conference on Fractional Differentiation and its Application, Ital

Hybrid Systems and Control With Fractional Dynamics (II): Control

No mixed research of hybrid and fractional-order systems into a cohesive and multifaceted whole can be found in the literature. This paper focuses on such a synergistic approach of the theories of both branches, which is believed to give additional flexibility and help the system designer. It is part II of two companion papers and focuses on fractional-order hybrid control. Specifically, two types of such techniques are reviewed, including robust control of switching systems and different strategies of reset control. Simulations and experimental results are given to show the effectiveness of the proposed strategies. Part I will introduce the fundamentals of fractional-order hybrid systems, in particular, modelling and stability of two kinds of such systems, i.e., fractional-order switching and reset control systems.Comment: 2014 International Conference on Fractional Differentiation and its Application, Ital

Basic Properties and Stability of Fractional-Order Reset Control Systems

Reset control is introduced to overcome limitations of linear control. A reset controller includes a linear controller which resets some of states to zero when their input is zero or certain non-zero values. This paper studies the application of the fractional-order Clegg integrator (FCI) and compares its performance with both the commonly used first order reset element (FORE) and traditional Clegg integrator (CI). Moreover, stability of reset control systems is generalized for the fractional-order case. Two examples are given to illustrate the application of the stability theorem.Comment: The 12th European Control Conference (ECC13), Switzerland, 201

Practical application of digital fractional-order controller to temperature control

Príspevok sa zaoberá praktickým návrhom a aplikáciou èíslicového regulátora neceloèíselného rádu na riadenie teploty iarièa. V príspevku je ïalej uvedený matematický popis regulátorov a regulovaných sústav neceloèíselného rádu. Pre pouitie èíslicových regulátorov neceloèíselného rádu je uvedený prísluný algoritmus. Vlastnosti regulaèného obvodu s regulátorom neceloèíselného rádu sú porovnané s regulaèným obvodom s klasickým regulátorom celoèíselného rádu a dosiahnuté výsledky sú uvedené a diskutované v závere príspevku