ISEP – DEE – Comunicações em eventos científicos
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Browsing ISEP – DEE – Comunicações em eventos científicos by Subject "Adaptive control"
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- Adaptive Controller for Systems of Fractional Dynamics Based on Robust Fixed Point TransformationsPublication . Tar, J. K.; Rudas, I. J.; Bitó, J. F.; Tenreiro Machado, J. A.; Kozlowski, K.In this paper a discrete time approximation of Caputo’s fractional order derivatives is used for modeling the dynamic behavior of hypothetical fractional order systems the appropriate responses of which that can directly be manipulated by some physical agents are some fractional order time-derivatives of their state variables. A possible generalization of the concept of “initial conditions” of the integer order systems is proposed as “preceding history” for fractional order ones. It is shown that the number of the independent data characteristic to the “preceding history” can be made independent of the order of derivation. It is shown that the discrete time approximation proposed makes it possible to interpret the order of derivation in a higher range than in the case of the original integral form of Caputo’s definition. By providing a simple analysis of the so obtained time-sequences it is shown that by manipulating the order of differentiation in this model both dissipative and unstable behavior can be modeled. The dissipative casecorresponds to the presence of unmodeled internal degrees of freedom that are dynamically coupled to the directly controlled ones but cannot directly be controlled. The unstable case seems to be appropriate for modeling the behavior of systems coupled to some directly unmodeled exciting environment. For this purpose very simple mathematical estimations can be applied. The paradigm controlled is a fractional order Φ6 type Van der Pol oscillator that already obtained certain attention in the literature. It is shown that the simple fixed point transformations based adaptive control elaborated for integer order systems can be applied without any modification for fractional order ones.
- Adaptive nonlinear vibration control based on causal time-invariant green functions and on a novel branch of soft computingPublication . Tar, József K.; Rudas, Imre J.; Bitó, János F.; Tenreiro Machado, J. A.In this paper a simple nonlinear, adaptive approach inspired by the fractional derivatives based CRONE control is presented for vibration damping. Its key idea is replacement of the fractional derivatives with the mathematically less restricted concept of time-invariant Green functions. Instead of the traditional PID feedback terms it applies positive definite weighted moving average of the square of the error plus a nonlinear term making the error converge to zero. In this way simple kinematic design of the desired damping becomes possible. The adaptive part of the controller guarantees the realization of this kinematic design without making it necessary to the designer to have an accurate and complete dynamic model of the system to be controlled or to design sophisticated linear controller. The applicability of the approach is illustrated via simulations for a paradigm consisting of a pair of coupled damper linear oscillators under external excitation. One of the oscillators is not modeled by the controller. The adaptive loop successively maps the observed system behavior to the desired one without exerting any effort to identify the reasons of the differences. The approach was found be useful for solving vibration damping problems with unmodeled and uncontrolled internal degrees of freedom.
- An adaptive robot control for thecnological operations based on uniform structures and reduced number of free parametersPublication . Tar, József K.; Tenreiro Machado, J. A.; Rudas, Imre J.; Bitó, János F.Grinding and polishing are typical application paradigms in which efficient control is needed for approximately and partially known multivariable, nonlinear, strongly coupled mechanical systems (robots) under strong dynamic interaction with an unmodeled environment. A novel adaptive approach to this problem using uniform structures and procedures as well as a passive compliant component as an essential part of the control was recently invented. The method seems to overcome the limitations of the classic approaches as limited speed of motion and supposed separability in the operational space supposing free directions for force/torque components and for free components of translation in their orthogonal sub-spaces. Like Soft Computing, instead developing the formally exact analytical model of the robot, its environment and the dynamic interaction between them the proposed method uses uniform structures but these are derived from the Euler-Lagrange equations considered in a general and formal level of abstraction. In contrast to the general approach fit to a quite wide class of problems, these structures are rather fit to a far narrower task of modeling and control of mechanical devices. This results in a drastic reduction in the number of tunable parameters, fast tuning for those parameters for which no a priori linguistic rules are available and uses simple fuzzy rules for tuning other parameters for which at least qualitative a priori known tuning are known. The proposed technique also is free from "scaling problems" so characteristic to the classic ones. The method is proved and illustrated via simulation in the case of a 3 DOF SCARA arm used for polishing a convex surface as an application paradigm.
- Evasion of Instabilities Caused by Neglected Subsystems and Saturations in the Control of a Cart of Asynchronous Electric DrivesPublication . Tar, József K.; Ráti, Csaba; Rudas, Imre J.; Bitó, János F.; Tenreiro Machado, J. A.The task of solving the adaptive control of a partially and imprecisely modeled electrical vehicle driven by three omnidirectional wheels together with the torque and/or power limits of their electric driving motors is considered. Thevehicle is very roughly modeled as a rigid body while the a part of the burden carried by it through elastic connection is completely neglected in the controller’s model. Instead parameter estimation techniques a simple, kinematically designed, PID– type trajectory tracking is formulated that is implemented via robust fixed point transformations. It is shown that if the nominal trajectory does not significantly excite the vehicle– burden connection precise and stable control can be achieved by the adaptivity, while the pure PID–type control may considerably excite this degree of freedom and can be corrupted by achieving either the torque or the power limits of the motors. The motors are supposed to be voltage controlled asynchronous drives with constant frequency excitation. Our statement is substantiated by numerical simulations. The main advantage of the proposed control is that it operates with local basin of attraction developed for convergent iterative Cauchy sequences that is easy to design by setting only a few parameters. Its disadvantage is that it cannot guarantee global stability therefore its application must be preceded by numerical tests. Its use may be especially useful in applications in industrial workshops when modeling the dynamics of the coupled subsystem technically is very difficult, e.g. when it is a tank partially containing heavy liquid.
- Possible Adaptive Control by Tangent Hyperbolic Fixed Point Transformations Used for Controlling the Φ6-Type Van der Pol OscillatorPublication . Tar, József K.; Bitó, János F.; Rudas, Imre J.; Kozłowski, Krzysztof R.; Tenreiro Machado, J. A.In this paper a further step towards a novel approach to adaptive nonlinear control developed at Budapest Tech in the past few years is reported. Its main advantage in comparison with the complicated Lyapunov function based techniques is that its fundament is some simple geometric consideration allowing to formulate the control task as a Fixed Point Problem for the solution of which various Contractive Mappings can be created that generate Iterative Cauchy Sequences for Single Input - Single Output (SISO) systems. These sequences can converge to the fixed points that are the solutions of the control tasks. Recently alternative potential solutions were proposed and sketched by the use of special functions built up of the “response function” of the excited system under control. These functions have almost constant values apart from a finite region in which they have a “wrinkle” in the vicinity of the desired solution that is the “proper” fixed point of these functions. It was shown that at one of their sides these fixed points were repulsive, while at the opposite side they were attractive. It was shown, too, that at the repulsive side another, so called “false” fixed points were present that were globally attractive, with the exception of the basins of attraction of the “proper” ones. This structure seemed to be advantageous because no divergences could occur in the iterations, the convergence to the “false” values could easily be detected, and by using some ancillary tricks in the most of the cases the solutions could be kicked from the wrong fixed points into the basins of attraction of the “proper ones”. It was expected that via adding simple rules to the application of these transformations good adaptive control can be developed. However, due to certain specialties of these functions practical problems arose. In the present paper novel transformations are presented that seem to evade these difficulties. Their applicability is illustrated via simulations in the adaptive control of the popular nonlinear paradigm, the Φ6 Van der Pol oscillator.
- Simple Adaptive Dynamical Control of Vehicles Driven by Omnidirectional WheelsPublication . Tar, J. K.; Rudas, I. J.; Nagy, I.; Kozłowski, K. R.; Tenreiro Machado, J. A.Precise control of Automatic Guided Vehicles (AGVs) navigating between the aisles of manufacturing systems by the use of local markers is an important task. On the basis of the geometric model of the workspace and the vehicles and that of the sensor uncertainties precise trajectories were recently generated along which the vehicle safely can move. In order to achieve precise trajectory tracking the effects of the system’s dynamical uncertainties (modeling errors and possible external perturbations) have to be compensated. In the present paper a simple, fixed point transformations based adaptive control is proposed for this purpose. The proposed method is tested via simulation for a vehicle of triangular shape, driven by three omnidirectional wheels. The method is also able to monitor and evade the conditions that may lead to turning over the vehicle.