José Sá da Costa

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.

Modeling of Flexible Beams for Robotic Manipulators

This work treats the problem of modeling robotic manipulators withstructural flexibility. A mathematical model of a planarmanipulator with a single flexible link is developed. This modelis capable of reproducing nonlinear dynamic effects, such as thebeam stiffening due to the centrifugal forces induced by therotation of the joints, giving it the capability to predictreliable dynamic behaviors for a wide range of applications. Onthe other hand, the model complexity is reduced, in order to keepit amenable for analysis and controller design. The models foundin current literature for control design of flexible manipulatorarms present dynamic limitations for the sake of real timeimplementation in a control scheme. These limitations are theresult of premature linearizations in the formulation of thedynamics equations. In this paper, these common linearizations arepresented and their dynamic limitations uncovered. An alternativereliable model is then presented. The model is founded on twobasic assumptions: inextensibility of the neutral fiber, andmoderate rotations of the cross sections in order to account forthe foreshortening of the beam due to bending. Simulation andexperimental results show that the proposed model has the closestdynamic behavior to the real beam.

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.

Predictive control based on neural network models with I/O feedback linearization

This paper presents an approach for the constrained non-linear predictive control problem based on the input-output feedback linearization (IOFL) of a general non-linear system modelled by a discrete-time affine neural network model. Using the resulting linear system in the formulation of the original non-linear predictive control problem enables to restate the optimization problem as the minimization of a quadratic function, which solution can be found using reliable and fast quadratic programming (QP) routines. However, the presence of a non-linear feedback linearizing controller maps the original linear input constraints onto non-linear and state dependent constraints on the controller output, which invalidates a direct application of QP routines. In order to cope with this problem and still be able to use QP routines, an approximate method is proposed which simultaneously guarantees a feasible solution without constraints violation over the complete prediction horizon within a finite number of steps, ...

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.

Robust stability of feedback linearised systems modelled with neural networks: dealing with uncertainty

Abstract This paper presents a systematic procedure to analyse the stability robustness to modelling errors when a neural network model is integrated in an approximate feedback linearisation control scheme. The propagation through the control loop of the structured uncertainty from the neural network model parameters enables the construction of a polytopic uncertainty description for the overall linear closed-loop system. By using computationally efficient algorithms the solution of a set of linear matrix inequalities provides a Lyapunov function for the uncertain system, therefore proving robust stability of the overall control system. A nonlinear multivariable water vessel system is chosen as the case study for the application of this control strategy.

Constrained Nonlinear Predictive Control Based on Input-Output Linearization Using a Neural Network

Abstract Affine neural network models can be used as good aproximators of the dynamics of a nonlinear process, and are easily included in a input-output feedback linearization (IOFL) scheme. This paper proposes a new solution for solving a constrained optimization problem using IOFL imbedded in a predictive control scheme. The linearization of the nonlinear feedback law over the entire prediction horizon, enables an optimal solution to be found by solving a general quadratic programming problem. The procedure here presented also guarantees convergenceto a feasible solution without constraint violation.

Multi-agent Platform and Toolbox for Fault Tolerant Networked Control Systems

Industrial distributed networked control systems use different communication networks to exchange different critical levels of information. Real-time control, fault diagnosis (FDI) and Fault Tolerant Networked Control (FTNC) systems demand one of the more stringent data exchange in the communication networks of these networked control systems (NCS). When dealing with large-scale complex NCS, designing FTNC systems is a very difficult task due to the large number of sensors and actuators spatially distributed and network connected. To solve this issue, a FTNC platform and toolbox are presented in this paper using simple and verifiable principles coming mainly from a decentralized design based on causal modelling partitioning of the NCS and distributed computing using multi-agent systems paradigm, allowing the use of agents with well established FTC methodologies or new ones developed taking into account the NCS specificities. The multi-agent platform and toolbox for FTNC systems have been built in Matlab/Simulink environment, which is in our days the scientific benchmark for this kind of research. Although the tests have been performed with a simple case, the results are promising and this approach is expected to succeed with more complex processes.