Integration of Soft Computing and Fractional Derivatives in Adaptive Control

Realizing that generality and uniformity of the usual Soft Computing (SC) structures exclude the application of plausible simplifications relevant in the case of whole problem classes resulted in the idea that a novel branch of soft computing could be developed by the use of which far simpler and more lucid uniform structures and procedures could be applied than in the traditional ones. Such a novel approach to computational cybernetics akin to SC was developed at Budapest Tech to control inaccurately and incompletely modelled dynamic systems under external disturbances. Hydraulic servo valve controlled differential cylinders as non-linear, strongly coupled multivariable electromechanical tools serve as excellent paradigms of such difficulties. Their control has to cope with the problem of instabilities due to the friction forces between the piston and the cylinder, as well as with uncertainties and variation of the hydrodynamic parameters that makes it unrealistic to develop an accurate static model for them. In this paper a combination of this novel method with the use of fractional derivatives is applied for the control of a hydraulic differential cylinder. Simulation results well exemplifying the conclusions are also presented

Adaptive Optimal Dynamic Control for Nonholonomic Systems

In this paper two different control methods are combined for controlling a typical nonholonomic device (a bicycle) the dynamic model and parameters of which are only approximately known. Most of such devices suffer from the problem that the time-derivatives of the coordinates of their location and orientation cannot independently be set so an arbitrarily prescribed trajectory cannot precisely be traced by them. For tackling this difficulty Optimal Control is proposed that can find acceptable compromise between the tracking error of the various coordinates. Further problem is that the solution proposed by the optimal controller cannot exactly be implemented in the lack of precise information on the dynamic model of the system. Based on the decoupled nature of the dynamic model of the longitudinal and lateral behavior of the engine special fixed point transformations are proposed to achieve adaptive tracking. These transformations were formerly successfully applied for the control of holonomic systems. It is the first time that the combined method is checked for various trajectories and dynamic model errors via simulation. It yielded promising results

Solution of The Inverse Kinematic Task of A Robot-Arm Based on A Quasi-Differential Fixed-Point Transformation Method

While the forward kinematic task of robots can be solved easily through homogenous transformation matrices, the inverse kinematic task leads to difficulties as the construction of the system becomes more complex. In this paper, a solution has been worked out for a three Degree-of-Freedom (DOF) robot-arm based on recent research, by the use of a novel, fixed-point transformation based technique

Robotkar inverz kinematikai feladatának megoldása „kvázidifferenciális” fixpont transzformációs módszerrel

Míg egy robotkar direkt kinematikai feladata általában homogén transzformációs mátrixok segítségé-vel egyszerűen megoldható, addig az inverz kinematikai feladat a rendszer felépítésétől függően rend-kívül bonyolulttá válhat. Jelen dolgozatban egy nemrégi kutatásra alapozva, fixpont transzformáción alapuló közelítő numerikus megoldás került kidolgozásra egy három szabadsági fokú robotkar inverz kinematikai feladatának megoldására

Modelling and Control of Freeway Traffic

This paper presents the most recent developments of the Simulator of Intelligent Transportation Systems (SITS). The SITS is based on a microscopic simulation approach to reproduce real traffic conditions in an urban or non-urban network. In order to analyse the quality of the microscopic traffic simulator SITS a benchmark test was performed. A dynamical analysis of several traffic phenomena, applying a new modelling formalism based on the embedding of statistics and Laplace transform, is then addressed. The paper presents also a new traffic control concept applied to a freeway traffic system

LPV-based quality interpretations on modeling and control of diabetes

In this study we introduce different novel interpretations in the case of Linear Parameter Varying (LPV) methodology, which are directly usable in modeling and control design in diabetes research. These novel interpretations are based on the parameter vectors of the LPV parameter space. The theoretical solutions are demonstrated on a simple, known Type 1 Diabetes Model used in intensive care

Törtrendű deriváltak integrálása nemlineáris rendszerek új lágy számítási eljárásokon alapuló adaptív szabályozásával = Integration of Fractional Order Derivatives in the Adaptive Control of Nonlinear Systems on the Basis of Novel Soft Computing Techniques

A projektben speciális, "Single Input - Single Output" rendszerekre hasonló háromszögeken alapuló adaptív fixpont transzformációs szabályozót dolgoztunk ki és alkalmaztunk nemlineáris paradigmákra (Ball-Beam System, polimerizációs reakció, hidraulikus munkahenger). A következő lépés e módszer robusztus változatának kidolgozása, majd "Multiple Input - Multiple Output" rendszerekre való kétféle általánosítása volt. A frakcionális deriváltak Caputo féle alakjából numerikus közelítéssel bevezettük a frakcionális derivált három paraméteres változatát és a "kezdeti érték" helyett a "kezdeti történet" fogalmát. Megmutattuk, hogy ez disszipatív és gerjedő rendszerek modellezésére is alkalmas. E deriváltat felhasználtuk egész rendű rendszerek szabályozásának javítására és hipotetikus frakcionális rendszerek modellezésére. Kimutattuk, hogy az általunk javasolt adaptív szabályozó e rendszerekre nehézség nélkül alkalmazható. Adaptív szabályozásunkat különféle egész és törtrendű rendszerek szabályozására alkalmaztuk szimulációval. Széles körű szimulációs vizsgálatokkal kimutattuk a legtipikusabb, Lyapunov függvényt használó adaptív módszerek hiányosságait. Végül ezek kiküszöbölésére kidolgoztuk a "Model Reference Adaptive Control" szabályozók új változatát, amely Lyapunov direkt módszere helyett robusztus fixpont transzformációval működik. | In the project special adaptive controllers were proposed for "Single Input - Single Output" systems. It applies similar triangles for formulating the control law. It was successfully applied for nonlinear paradigms as the Ball-Beam System, a polymerization reaction, and a hydraulic cylinder. In the next step the robust version of this method was elaborated, it was generalized for "Multiple Input - Multiple Output" systems in two different ways. Via numerically approximating Caputo's definition of fractional order (FO) systems a three parameters, finite memory generalization of the FO derivatives was proposed with the concept of the "preceding history" instaed of the "initial conditions". It was shown that it can be used for modeling stable dissipative and unstable systems, too. The new fractional derivative was utilized for improving the adaptive control elaborated for integer order systems, and for modeling the fractional order systems. It was shown that the fixed point transformations based control can easily be applied for the adaptive control of such hypothetical systems. Our method was applied for various integer and fractional order systems via simulations. The most important deficiencies of the most popular adaptive methods using Lyapunov's direct method were pointed out. To eliminate these deficiencies a novel approach was elaborated for the "Model Reference Adaptive Control" in which Lyapunov's method is replaced by robust fixed point transformation

Receding Horizon Control of Type 1 Diabetes Mellitus by Using Nonlinear Programming

Receding Horizon Controllers are one of the mostly used advanced control solutions in the industry. By utilizing their possibilities we are able to predict the possible future behavior of our system; moreover, we are able to intervene in its operation as well. In this paper we have investigated the possibilities of the design of a Receding Horizon Controller by using Nonlinear Programming. We have applied the developed solution in order to control Type 1 Diabetes Mellitus. The nonlinear optimization task was solved by the Generalized Reduced Gradient method. In order to investigate the performance of our solution two scenarios were examined. In the first scenario, we applied “soft” disturbance—namely, smaller amount of external carbohydrate—in order to be sure that the proposed method operates well and the solution that appeared through optimization is acceptable. In the second scenario, we have used “unfavorable” disturbance signal—a highly oscillating external excitation with cyclic peaks. We have found that the performance of the realized controller was satisfactory and it was able to keep the blood glucose level in the desired healthy range—by considering the restrictions for the usable control action