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- Application of fractional calculus in the system modelling and controlPublication . Tenreiro Machado, J. A.; Barbosa, Ramiro; Silva, Manuel; Figueiredo, Lino; Jesus, Isabel S.; Galhano, AlexandraFractional Calculus (FC) goes back to the beginning of the theory of differential calculus. Nevertheless, the application of FC just emerged in the last two decades, due to the progress in the area of chaos that revealed subtle relationships with the FC concepts. In the field of dynamical systems theory some work has been carried out but the proposed models and algorithms are still in a preliminary stage of establishment. Having these ideas in mind, the paper discusses a FC perspective in the study of the dynamics and control of several systems.
- A new method for approximating fractional derivatives: application in non-linear controlPublication . Tenreiro Machado, J. A.; Galhano, AlexandraThe theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.
- Fractional control of two arms working in cooperationPublication . Ferreira, N. M. Fonseca; Tenreiro Machado, J. A.; Galhano, Alexandra; Cunha, J. BoaventuraThis paper analyzes the performance of two cooperative robot manipulators. It is studied the implementation of fractional-order algorithms in the position/force control of two robots holding an object. The experiments reveal that fractional algorithms lead to performances superior to classical integer-order controllers.
- Fractional-order position/force robot controlPublication . Ferreira, N. M. Fonseca; Tenreiro Machado, J. A.; Galhano, Alexandra; Cunha, J. BoaventuraIn this paper it is studied the implementation of fractional-order algorithms in position/force control of two cooperating robotic manipulaotrs. The performance and system robustness are analyzed in the time and frequency domains. The effect of backlash and flexibility at the robot joints is also investigated.
- Approximating fractional derivatives in the perspective of system controlPublication . Machado, J. A. Tenreiro; Galhano, AlexandraThe theory of fractional calculus goes back to the beginning of the theory of differential calculus, but its application received attention only recently. In the area of automatic control some work was developed, but the proposed algorithms are still in a research stage. This paper discusses a novel method, with two degrees of freedom, for the design of fractional discrete-time derivatives. The performance of several approximations of fractional derivatives is investigated in the perspective of nonlinear system control.