Browsing by Author "Ferreira, Isabel M."
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- Algorithmic music composition: a surveyPublication . Ferreira, Isabel M.; Tenreiro Machado, J. A.This paper surveys some of the methods used for algorithmic composition and their evolution during the last decades. Algorithmic composition was motivated by the natural need to assist and to develop the process of music creation. Techniques and applications of algorithmic composition are broad spectrum, ranging from methods that produce entire works with no human intervention, up to methods were both composer and computer work closely together in real-time. Common algorithms used for music composition are based in stochastic, deterministic, chaotic and artificial intelligence methods.
- Describing function analysis of mechanical systems with nonlinear friction and backlash phenomenaPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.; Ferreira, Isabel M.This paper analyses the dynamical properties of systems with nonlinear friction and backlash phenomena based on the describing function method. The dynamics is illustrated using the Nyquist and Bode plots and the results are compared with those of standards models.
- Design of Digital Fractional-Order Integrators and Differentiators by Least SquaresPublication . Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Ferreira, Isabel M.In this paper we develop a method for obtaining digital rational approximations (IIR filters) to fractional-order operators of type sα, where α ∈ . The proposed method is based on the least-squares (LS) minimization between the impulse responses of the digital fractional-order integrator/differentiator and of the rational-fraction approximation. The results reveal that the LS approach gives similar or superior approximations in comparison with other methods. The effectiveness of the method is demonstrated both in the time and frequency domains through an illustrative example.
- Dynamics of the fractional-order Van der Pol oscillatorPublication . Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Ferreira, Isabel M.; Tar, József K.In this paper we propose a modified version of the classical unforced Van der Pol oscillator that occurs when introducing a fractional-order time derivative in the state space equations that describes its dynamics. The resulting fractional-order Van der Pol oscillator is analyzed in the time and frequency domains, for several values of order's fractional derivative and, consequentlly, of the total system order. It is shown that the system can exhibit different output behavior depending on the total system order. Several numerical simulations and performances indices illustrate the fractional dynamics.
- A fractional calculus perspective of PID tuningPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.; Ferreira, Isabel M.This paper gives an interpretation of the classical PID controller tuning based on the fractional calculus theory. The PID parameters are calculated according with the specifications of an elementary system whose open-loop transfer function is a fractional order integrator (FOI). The performances of the two systems are compared and illustrated through the frequency and time responses.
- Least-squares design of digital fractional-order operatorsPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.; Ferreira, Isabel M.In this paper we develop a method for obtaining digital rational approximations to fractional-order operators of type s^y, where y e R. The proposed method is based on the least-squares (LS) minimization between the impulse response of the fractional Euler/Tustin operators and the digital rational-fraction approximation. We make a comparison with other approaches and the results reveal that the LS method gives superior approximations. The effectiveness of the method is demonstrated both in the time and frequency domains through an illustrative example.
- PID controller tuning using fractional calculus conceptsPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.; Ferreira, Isabel M.In this paper, we present a new approach for tuning PID controllers. The proposed method is based on the application of basic fractional calculus concepts. In fact, the controller specifications include the desired gain crossover frequency and the slope at that frequency (which is equivalent to prescribing a specific phase margin) of a fractional-order integrator inserted in the forward path of unit feedback control system. The PID parameters are obtained by minimizing the integral of square error (ISE) between the step responses of the actual closed-loop system (with the fractional-order integrator) and that of the actual closed-loop system with the PID controller. The obtained closed-loop system is robust to gain variations with step responses exhibiting an iso-damping property. Simulation examples are given to illustrate the effectiveness and applicability of the proposed scheme.
- Pole-zero approximations of digital fractional-order integrators and differentiators using signal modeling techniquesPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.; Ferreira, Isabel M.A novel strategy to the development of digital pole-zero approximations to fractional-order integrators and differentiators is presented here. The scheme is based in the signal modeling techniques applied to deterministic signals, namely the Padé, the Prony and the Shanks methods. It is shown that the illustrated algorithms yield good results both in the time and the frequency domains. Moreover, they are capable to give superior approximations than other existent approaches, namely the widely used CFE method. Several examples are given that demonstrate the effectiveness of the proposed techniques.
- Tuning of PID Controllers Based on Bode’s Ideal Transfer FunctionPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.; Ferreira, Isabel M.This paper presents a new strategy for tuning PID controllers based on a fractional reference model. The model is represented as an ideal closed-loop system whose open-loop is given by the Bode’s ideal transfer function. The PID controller parameters are determined by the minimization of the integral square error (ISE) between the time responses of the desired fractional reference model and of the system with the PID controller. The resulting closed-loop system (with the PID controller) has the desirable feature of being robust to gain variations with step responses exhibiting an iso-damping property. Several examples are presented that demonstrate the effectiveness and validity of the proposed methodology.