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Two cooperating manipulators with fractional controllers
Ferreira, Nuno M. F.; Machado, J. A. Tenreiro; Tar, József K.This paper analyzes the dynamic performance of two cooperative robot manipulators. It is studied the implementation of fractional-order algorithms in the position/force control of two cooperating robotic manipulators holding an object. The simulations reveal that fractional algorithms lead to performances superior to classical integer-order controllers.
Adaptive tackling of the swinging problem for a 2 DOF crane – payload system
Tar, József K.; Rudas, Imre J.; Bitó, János F.; Machado, J. A. Tenreiro; Kozłowski, Krzysztof R.The control of a crane carrying its payload by an elastic string corresponds to a task in which precise, indirect control of a subsystem dynamically coupled to a directly controllable subsystem is needed. This task is interesting since the coupled degree of freedom has little damping and it is apt to keep swinging accordingly. The traditional approaches apply the input shaping technology to assist the human ope...
Optimal approximation of fractional derivatives through discrete-time fractions...
Machado, J. A. Tenreiro; Galhano, Alexandra; Oliveira, Anabela; Tar, József K.This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.
Fixed point transformations in the adaptive control of fractional-order MIMO sy...
Tar, József K.; Rudas, Imre J.; Nádai, László; Kozłowski, Krzysztof R.; Machado, J. A. TenreiroThough the formal mathematical idea of introducing noninteger order derivatives can be traced from the 17th century in a letter by L’Hospital in which he asked Leibniz what the meaning of D n y if n = 1/2 would be in 1695 [1], it was better outlined only in the 19th century [2, 3, 4]. Due to the lack of clear physical interpretation their first applications in physics appeared only later, in the 20th century, i...
Application of robust fixed point transformations for technological operation o...
Tar, József K.; Rudas, Imre J.; Kozłowski, Krzysztof R.; Machado, J. A. TenreiroA robot’s drive has to exert appropriate driving forces that can keep its arm and end effector at the proper position, velocity and acceleration, and simultaneously has to compensate for the effects of the contact forces arising between the tool and the workpiece depending on the needs of the actual technological operation. Balancing the effects of a priori unknown external disturbance forces and the inaccuraci...
Approximating fractional derivatives through the generalized mean
Machado, J. A. Tenreiro; Galhano, Alexandra; Oliveira, Anabela; Tar, József K.This paper addresses the calculation of fractional order expressions through rational fractions. The article starts by analyzing the techniques adopted in the continuous to discrete time conversion. The problem is re-evaluated in an optimization perspective by tacking advantage of the degree of freedom provided by the generalized mean formula. The results demonstrate the superior performance of the new algorithm.
On the robustness of the slotine-Li and the FPT/SVD-based adaptive controllers
Tar, József K.; Rudas, Imre J.; Hermann, Gy.; Brito, J. F.; Machado, J. A. TenreiroA comparative study concerning the robustness of a novel, Fixed Point Transformations/Singular Value Decomposition (FPT/SVD)-based adaptive controller and the Slotine-Li (S&L) approach is given by numerical simulations using a three degree of freedom paradigm of typical Classical Mechanical systems, the cart + double pendulum. The effects of the imprecision of the available dynamical model, presence of dynamic ...
Electrical skin phenomena: a fractional calculus analysis
Machado, J. A. Tenreiro; Jesus, Isabel S.; Galhano, Alexandra; Cunha, J. Boaventura; Tar, József K.The internal impedance of a wire is the function of the frequency. In a conductor, where the conductivity is sufficiently high, the displacement current density can be neglected. In this case, the conduction current density is given by the product of the electric field and the conductance. One of the aspects of the high-frequency effects is the skin effect (SE). The fundamental problem with SE is it attenuates ...
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