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- On the Fractional PID Control of a Laboratory Servo SystemPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.; Jesus, Isabel S.In this paper are investigated several types of fractional-order PID controllers in the velocity control of a servo system. The fractional controller is more flexible and gives the possibility of adjusting carefully the dynamical properties of a control system. The servo system is controlled by using a real-time digital control system based on MATLAB/Simulink. Results are compared with those obtained from classical PID controllers. Experimental responses are presented and analyzed, showing the effectiveness of the proposed fractional-order algorithms.
- Some Applications of Fractional Calculus in EngineeringPublication . Tenreiro Machado, J. A.; Silva, Manuel; Barbosa, Ramiro; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria G.; 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 FC in the study of system dynamics and control. In this perspective, this paper investigates the use of FC in the fields of controller tuning, legged robots, redundant robots, heat diffusion, and digital circuit synthesis.
- Fractional describing function analysis of systems with backlash and impact phenomenaPublication . Barbosa, Ramiro; Tenreiro Machado, J. A.This paper analyses the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional-order dynamics is illustrated using the Nyquist plot and the results are compared with those of standard models.
- Performance of fractional PID algorithms controlling nonlinear systems with saturation and backlash phenomenaPublication . Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Galhano, AlexandraThe development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.
- Fractional modelling of the electrical conduction in nacl electrolytePublication . Jesus, Isabel S.; Tenreiro Machado, J. A.; Barbosa, RamiroThe fractional calculus (FC) constitutes a mathematical tool that presently is being applied in many emerging scientific areas, such as electricity, magnetism, mechanics, fluid dynamics and medicine. This paper describes the use of an electrolytic process for developing fractional order capacitors. The study includes several experiments for measuring the electrical impedance of the devices. The results are analyzed through the frequency response revealing capacitances of fractional order.
- Applications of fractional calculus in electrical and computer engineeringPublication . Tenreiro Machado, J. A.; Silva, Manuel; Barbosa, Ramiro; Jesus, Isabel S.; Reis, Cecília; Marcos, Maria da Graça; M. Afonso, Luís; Lima, Miguel F. M.; Pires, E. J. Solteiro; Ferreira, N. M. FonsecaFractional 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. This article illustrates several applications of fractional calculus in science and engineering. It has been recognized the advantageous use of this mathematical tool in the modeling and control of many dynamical systems. In this perspective, this paper investigates the use of FC in the fields of controller tuning, electrical systems, digital circuit synthesis, evolutionary computing, redundant robots, legged robots, robotic manipulators, nonlinear friction and financial modeling.
- Effect of fractional orders in the velocity control of a servo systemPublication . Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Jesus, Isabel S.The application of fractional-order PID controllers is now an active field of research. This article investigates the effect of fractional (derivative and integral) orders upon system's performance in the velocity control of a servo system. The servo system consists of a digital servomechanism and an open-architecture software environment for real-time control experiments using MATLAB/Simulink tools. Experimental responses are presented and analyzed, showing the effectiveness of fractional controllers. Comparison with classical PID controllers is also investigated.
- Discretization of complex-order algorithms for control applicationsPublication . Barbosa, Ramiro S.; Machado, J. A. Tenreiro; Silva, Manuel F.In this article we describe several methods for the discretization of the differintegral operator sa, where α = u + jv is a complex value. The concept of the conjugated-order differintegral is also introduced, which enables the use of complex-order differintegrals while still producing real-valued time responses and transfer functions. The performance of the resulting approximations is analysed in both the time and frequency domains. Several results are presented that demonstrate its utility in control system design.
- Using fractional derivatives for the joint ontrol of hexapod robotsPublication . Silva, Manuel F.; Machado, J. A. Tenreiro; Barbosa, Ramiro S.This article studies several Fractional Order Control algorithms used for joint control of a hexapod robot. Both Padé and series approximations to the fractional derivative are considered for the control algorithm. The walking performance is evaluated through two indices: The mean absolute density of energy used per unit distance travelled, and the control effort. A set of simulation experiments reveals the influence of the different approximations upon the proposed indices. The results show that the fractional proportional and derivative algorithm, implemented using the Padé approximation with a small number of terms, gives the best results.
- 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.
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