Fractional-order control: A new approach for industrial applications

This Special Issue collects a few original papers that present recent ideas and results focused on industrial applications of noninteger-order controllers, frequently named fractional-order controllers, as opposed to conventional integer-order ones. Namely, they are based on differential or integral operators of non-integer order. Without the intention to be an exhaustive presentation of current problems and innovative solutions in this specific field, the special issue aims at giving a feeling of what the fractional-order control paradigm can do, by the associated benefits and improvements, with respect to integer-order control. Namely, the selected applications-oriented contributions show that fractionalorder control can be effectively applied to different engineering problems, as testified by the included experiments and by the simulation studies, which are in turn obtained by models that are representative of a genuine application. The general idea is that fractional-order controllers can be beneficial to industrial processes, automotive systems, mechatronics, robotic systems, unmanned vehicles, and many other services and systems where robust but easy-to-implement control is required. However, the intention here is not to persuade academicians, researchers and practitioners of the control engineering community of the superiority of fractional-order controllers in all conditions, such as a panacea or an ultimate key to the success in a practical control problem. Nevertheless, an alternative point of view is provided: fractional-order controllers are felt as a possible and powerful tool that is still not well explored by the community. The historical result by Bode in designing feedback amplifiers reinforces this convincement. Namely, he recognized the increased robustness to gain and load variations that can be obtained by a non-integer integrator in the ideal open-loop transfer function. These considerations should foster the implementation of analogue (and digital) fractional-order controllers, especially if these controllers achieve a better trade-off between dynamic performance and robust stability than the controllers usually employed in industrial loops, in which disturbances, uncertainties, parametric variations, delays, hardware limitations, etc., are source of inefficiencies. One main advantage is that the realization schemes of fractional-order controllers may offer a relatively simple solution as compared to other more complex and expensive integerorder ones, with higher computational requirements and sensitivity to hardware limitations. Taking into account these premises, even unfamiliar industrial control engineers and industrially related researchers should get a basic message that discloses the benefits of controllers based on practical tools derived from the theory of fractional calculus, fractional differentiation and fractional/non-integer-order control. To this aim, the Special Issue puts care to the realization of control techniques and implementation details. The papers propose new solutions for a step forward of the research in the field and may suggest new investigations. Namely, as most of the attentive researchers in this field, we believe that many challenges are open as well as many results can be achieved by exploiting the flexibility of fractional-order controllers. To this aim, contributions of researchers not specifically working in fractional-order systems and fractional-order control is also important, as testified by the explosion of interests, conferences and scientific papers in fractional calculus and control. More specifically, it is likely that a massive amount of research could have a great impact on model-based control applied to engineering and real-world problems. The five papers in this Special Issue show the results achieved by applying fractional-order controllers to industrial processes, automotive systems, smart structures. All the considered architectures share the idea of applying non-integer-order elements in the control functions, as opposed to integer-order elements such as in the standard PID controllers. In the following, we summarize the main contributions of the selected papers. The first paper “Robust fractional-order controller for an EAF electrode position system” by Vicente Feliu and Raul Rivas-Perez is on the position control of the electrodes of an industrial electric arc furnace. The electrode position system has a complex, nonlinear, and time-varying dynamics. However, robust control is necessary to reduce the plant energy consumption and its effect on environmental pollution and, at the same time, to increase the efficiency and safety of the furnace. To this aim, simple dynamic models are useful for control design. The model identified from real-time field data shows large parameter variations due to the system operation range. Moreover, the plant is subject to measured and random unmeasured disturbances. The proposed controller employs dynamic inversion and a fractional proportionalintegral transfer function that includes an integration of non-integer order. Only three parameters require tuning. The synthesized controller significantly improves the performance and robustness obtained by standard PI and PID controllers and is compared to other types of fractional-order controllers. Disturbance rejection and low sensitivity to inaccurate dynamic inversion are shown. The simple structure of the controller, which has three parameters as the industrial PID, and the efficiency of the design procedure are a key aspect of the proposed fractional control technique. As remarked by the authors, other robust control methods may provide similar results at the cost of much more parameters to tune and more time necessary in the design procedure. The second paper “Development of a fractional order based MIMO controller for high dynamic engine testbeds” by Patrick Lanusse, Dominique Nelson Gruel, Abderrahim Lamara, Antoine Lesobre, Xiaoqing Wang, Yann Chamaillard, Alain Oustaloup, comes from an explicit cooperation between two academic partners and industry, namely a testbed manufacturer for vehicle engines. The paper illustrates how to profitably apply the CRONE (French acronym of “Commande Robuste d′Ordre Non Entier”) methodology to control a high dynamic engine testbed which is coupled to a spark-ignition engine. Since the testbed is a highly nonlinear MIMO system, a properly designed, model-based robust MIMO control system realizes fractional control based on the CRONE approach, which employs fractional differentiation. The methodology can be automated for a fast and easy industrial implementation and includes system identification, robust MIMO controller design and simplified realization, and finally the assessment of experimental results. A main advantage of the proposed approach is that decoupling is achieved. The third paper “Fractional Robust PID Control of a Solar Furnace” by Manuel Beschi, Fabrizio Padula, Antonio Visioli, describes how to cope with variations of the working point of solar furnace plants, which represent an industrial sustainable solution to generate heat for domestic and industrial purposes. In particular, the solar furnaces nonlinear model is linearized at different operating points so that a family of linearized models is obtained depending on the temperature. The authors design a fractional-order proportional-integral-derivative controller that achieves an invariant loop phase margin in a neighbourhood of the nominal process. To this aim, they apply an approach based on a generalized iso-damping property, namely the controller is designed by solving a constrained optimization aimed at minimizing the maximum sensitivity. Moreover, gain scheduling allows them to take into account the plant parametric variations, namely the temperature operating range. The fourth paper “CRONE control based anti-icing/deicing system for wind turbine blades” by Jocelyn Sabatier, Patrick Lanusse, Benjamin Feytout, Serge Gracia, illustrates another application of the CRONE control methodology. Since wind turbines are often located in cold areas, it is important both to prevent blade icing and to deice the blade after a rest time. The presented anti-icing/deicing system is based on the application of strips made by an electrically conductive polymer paint on the critical parts of the blades. Heat is produced by current circulation that is determined by the potential difference between the strips’ opposite edges and can be controlled with flexibility. However, the strips’ thermal behaviour depends on many parameters. Then a blade thermal dynamic model is experimentally identified by considering several operating conditions, on which basis a robust CRONE controller is designed. Control is made possible by an electronic dimmer that supplies the paint strips on the basis of temperature measurements by sensors located on the blade. Experimental results on real blades show the efficiency of the method even in the presence of perturbations like location of sensors, blade rotation speed, thickness of the paint strip. The fifth paper “Fractional-order integral resonant control of collocated smart structures” by Daniel Feliu-Talegon, Andres San-Millan, Vicente Feliu, regards vibration control in smart structures employing strain gauges and piezoelectric actuators to achieve active vibration damping. The proposed fractional-order integral controller increases robustness with respect to previously proposed, relevant and wellknown, integer-order controllers. Namely, the last are subject to poor stability margins, although they provide insensitivity to spill over and guarantee closed-loop stability when changes occur in the plant parameters. In particular, the fractional-order controller better removes the smart structure vibration if the mass of the payload at the tip changes because the phase margin is maintained approximately constant. Moreover, the controller guarantees damping for all vibration modes as well as robustness to gain changes. To conclude this Editorial, we wish to thank the Editor-in-Chief, Prof. Andreas Kugi, for his support, and the designated Associate Editors and the Reviewers for the time and work spent in the review process.