Duarte Valério

Tuning of fractional PID controllers with Ziegler-Nichols-type rules

In this paper two sets of tuning rules for fractional PIDs are presented. These rules are quadratic and require the same plant time-response data used by the first Ziegler-Nichols tuning rule for (usual, integer) PIDs. Hence no model for the plant to control is needed--only an S-shaped step response is. Even if a model is known rules quickly provide a starting point for fine tuning. Results compare well with those obtained with rule-tuned integer PIDs.

Variable-order fractional derivatives and their numerical approximations

This paper addresses the different possible definitions of variable-order derivatives and their numerical approximations; both approximations based upon the definitions and approximations consisting of non-linear transfer functions (in particular combining existing approximations of constant-order fractional derivatives, such as the Crone approximation, with fuzzy logic) are considered. There are different possible configurations, implementing variable-order fractional derivatives both with and without memory of past values of the time-dependent differentiation order.

IDENTIFYING A TRANSFER FUNCTION FROM A FREQUENCY RESPONSE

In this paper, the classic Levy identification method is reviewed and reformulated using a complex representation. This new formulation addresses the well known bias of the classic method at low frequencies. The formulation is generic, coping with both integer order and fractional order transfer functions. A new algorithm based on a stacked matrix and its pseudoinverse is proposed to accommodate the data over a wide range of frequencies. Several simulation results are presented, together with a real system identification. This system is the Archimedes Wave Swing, a prototype of a device to convert the energy of sea waves into electricity.

Some pioneers of the applications of fractional calculus

In the last decades fractional calculus (FC) became an area of intensive research and development. This paper goes back and recalls important pioneers that started to apply FC to scientific and engineering problems during the nineteenth and twentieth centuries. Those we present are, in alphabetical order: Niels Abel, Kenneth and Robert Cole, Andrew Gemant, Andrey N. Gerasimov, Oliver Heaviside, Paul Lévy, Rashid Sh. Nigmatullin, Yuri N. Rabotnov, George Scott Blair.

Tuning-rules for fractional PID controllers

Abstract This paper presents several tuning rules for fractional PID controllers, similar to the first and the second sets of tuning rules proposed by Ziegler and Nichols for integer PIDs. Fractional PIDs so tuned perform better than integer PIDs; in particular, step-responses have roughly constant overshoots even when the gain of the plant varies.

Modelling and Control of a Wave Energy Converter

Abstract This work addresses an offshore oscillating water column for producing electricity from sea waves. It describes the modelling of this device and the study of control techniques that could improve energy extraction. Optimisation techniques applied improved the device performance for a wide number of sea states. A control strategy was developed with the objective of improving the quality of the energy absorbed by the device. This proved to be effective. In a later stage of this work, some experiments considering a variable pitch Wells turbine were performed with the objective of applying phase and amplitude control: it was possible to prove the possibility of obtaining a resonant response to a sinusoidal wave with a frequency different from the devices natural frequency.

Comparison of control strategies performance for a Wave Energy Converter

The Archimedes wave swing (AWS) is a a fully- submerged wave energy converter (WEC), that is to say, a device that converts the kinetic energy of sea waves into electricity. A first prototype of the AWS has already been built and tested. This paper presents simulation results of the performance of several control strategies applied to this device, including PID control, reactive control, phase and amplitude control, latching control, feedback linearisation control, internal model control, switching control, and combinations thereof. Linear, white-box nonlinear, and neural network models were employed. Significant (above threefold) increases in yearly energy production were found to be possible with properly designed control strategies.

Linear model identification of the Archimedes Wave Swing

This paper uses Levys identification method to build linear, second-order models for the Archimedes Wave Swing (AWS), an off-shore, fully-submerged, point absorber wave energy converter, expected to behave much like a mass-spring-damper system, though with relevant non-linearities. Since very few experimental data is available, data from an accurate non-linear simulator of the AWS was used. One of the identified models yields a satisfactory performance, and can now be used for the development of control strategies for the AWS.

Ziegler-Nichols Type Tuning Rules for Fractional PID Controllers

This paper presents two sets of tuning rules for fractional PIDs that rely solely on the same plant time-response data used by the first Ziegler-Nichols tuning rule for (usual, integer) PIDs. Thus no model for the plant to control is needed; only an S-shaped step response is. These rules are quadratic and their results compare well with those obtained with rule-tuned integer PIDs.Copyright

Rule-Based Fractional Control of an Irrigation Canal

In this paper a Simulink simulation of a four-pool irrigation canal extant in E¿vora, Portugal, is controlled using PID and fractional PID controllers, adjusted using an optimisation method and using tuning rules. Fractional control and rule-tuning emerge as the best options.