European Journal of Control (2011)4:394–396 © 2011 EUCA Discussion on: “State Feedback Fuzzy Adaptive Control for Active Shimmy Damping”g Marcello Bonfè Dipartimento di Ingegneria, Università di Ferrara, Via Saragat 1, 44122 Ferrara, Italy The paper by Pouly et al addresses modeling and control design for a classical physical system, an elastic rotating wheel with a vertical steering axis, which can be found in many vehicles characterized by critical safety issues, aircrafts and motorcycles above all Because of safety requirements, prediction and mitigation of violent oscillating phenomena, typically exhibited by such wheels, are fundamental problems for many mechanical and control engineers working on aerospace or automotive applications Despite the fact that undesirable shimmy (or wobble) behaviour of elastic wheels, either pulled like in aircraft Nose Landing Gears (NLG) or pushed like in motorcycles, has been observed and studied since the very first days of tyre production, final words on modeling and control of this behaviour have yet to be said This remark applies to both theoretical and technological aspects, since the replacement of traditional passive stabilisers for NLGs or motorbike steering axes with semi-active or active systems is currently difficult, even if state-of-the-art mechatronic components are used Therefore, the aim of this discussion paper is to highlight the key points, in the paper by Pouly et al., that could be of interest for further investigation by the same authors and by other research groups working on similar topics The rest of the paper presents the points of discussion following the sequential order in which fundamental steps of any control project are typically addressed: modeling, control design, realisation E-mail: marcello.bonfe@unife.it Modeling The oscillation of an elastic wheel, rotating in contact with the ground, around the additional degree of freedom provided by a steering axis is generally called shimmy Wheel shimmy is also called wobble among cyclists and motorcyclists ([1], [2]) Scientific reports on this phenomenon have been presented since 1941 (see the introduction of [3] and [4], or the sidebars of [2]) Mathematical models of steering wheels, in any context, highlight nonlinear effects mainly due to the elasticity of the tyre Even simpler models, with few degrees of freedom and point contact (between wheel and ground) assumption, reveal complicated and chaotic behaviour On the other hand, such models may be used as a starting point for feedback linearisation control design [5] In fact, Pouly et al adopted a similar control approach, but extended the design with fuzzy adaptation mechanisms and Sliding Mode control, in order to compensate modeling uncertainties Of course, recent advances in mathematical analysis of wheel shimmy behaviour should be considered for future works In particular, there are two interesting facts that arise from a review of publications related to this topic The first one is the explanation of shimmy in terms of energy transfer from the contact force between the tyre and the ground to the vibrational modes of the steering mechanism ([6], [7]) The other one is the relevance of memory effects of the tyre, namely the fact that lateral forces in the system depend on the tyre contact point positions, determined by the wheel leading edge positions in the past Taking these effects into account leads to Delay Differential Equations (DDE), as shown in [3], [4], [8] Stability analysis of these time-delayed models reveals Hopf bifurcations, which are typical of other classes of systems with 395 Discussion on: “Fuzzy Adaptive Shimmy Control” analogous traveling-wave solutions [9] Similar results are obtained in [7], by using a different modeling approach A final, yet important, issue that must be addressed is the validation of mathematical analysis by means of experiments or, at least, multi-body software simulations Strong efforts in this direction are reported in [10], [11] and [4], from which interested researchers may obtain useful practical suggestions Control Design As previously mentioned, feedback linearisation of a class of shimmy-prone physical systems is possible, as reported in the paper under discussion and other previous works [5] A drawback of this approach is that it relies on full-state measurement, which is not always available in practice, especially when cost minimisation or, conversely, maximum reliability and physical redundancy of sensors are essential requirements In fact, Pouly et al have also investigated other control design methods, that can be realised by feeding back a subset of the state vector [12] Interestingly, a similar method (i.e based on H∞ control theory) has been applied in [13] to steering control of a motorcyle Other control design approaches, that can be readily implemented using semi-active mechanical dampers or purely mechanical compensation networks (based on springs, dampers and inerters), are reported in [14] and [15] Reviewing the latter references and considering the remarks of [6], it seems that stabilisation of steering wheels by means of a novel control design method, called Interconnection and Damping Assignment PassivityBased Control (IDA-PBC) [16], is worth for investigation It is important to remark that the class of physical systems addressed by Pouly et al requires careful analysis of physical energy dissipation, already included in the system under study, and its relationship with the stability properties of an IDA-PBC design, as pointed out in [17] Finally, issues related to the presence of time delays [3] resemble those typically addressed by control design methods developed for robotic teleoperation [18] Therefore, results obtained in this context would be of interest also for the research on active shimmy damping Realisation The last point of discussion is related to the physical realisation of steering wheel stabilising systems Needless to say, reliability is a primary issue in both aerospace and automotive domains For this reason, passive or semiactive solutions are currently preferred by aircraft and motorcycle manufacturers On the other hand, technological progress is unstoppable, so that it is expected that electro-hydraulic actuators suitable for active shimmy damping will soon be available ([19], [20]) To conclude this discussion, it is useful to remark that the introduction of steering control systems for aircraft NLGs would not modify dramatically the current behavior of human pilots Intuitive and comfortable interaction with the driver is instead a mandatory feature for systems designed to be installed on cars or motorcycles, as accurately described in [21] and [22] References Cossalter V Motorcycle Dynamics Lulu, Second ed., 2006 Limebeer D, Sharp R “Bicycles, motorcycles, and models” IEEE Control Syst Magazine 2006; 26: 34–61 Takács D, Stépán G “Comparison of time delayed tyre models” In Proc of 9th IFAC 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S, Limebeer D, Sharp R, Smith M “Control of motorcycle steering instabilities” IEEE Control Syst Magazine 2006; 26: 78–88 396 16 Ortega R, Spong M, Gómez-Estern F, Blankenstein G “Stabilization of underactuated mechanical systems via interconnection and damping assignment” IEEE Trans Autom Control 2002; 47: 1218–1233 17 Gómez-Estern F, van der Schaft A “Physical damping in IDA-PBC controlled underactuated mechanical systems” Eur J Control 2004; 10: 451–468 18 Nuño E, Basañez L, Ortega R “Passivity-based control for bilateral teleoperation: A tutorial” Automatica, 47: 485– 495 19 Wijekoon T, Empringham L, Wheeler P “Dual-output motor control unit for an electromechanically actuated nose landing gear” In Proc of 35th Annual Conf of IEEE Industrial Electronics, pp 2563–2568, November 2009 Discussion on: “Fuzzy Adaptive Shimmy Control” 20 Sateesh B, Maiti D “Closed-loop active vibration control of a typical nose landing gear with torsional MR fluid based damper” Structural Engineering and Mechanics, vol 31, January 2009 Techno Press 21 Canudas De Wit C, Bechart H, Claeys X, Dolcini P, Martinez Molina J “Fun-To-Drive By Feedback” Eur J Control 2005; 11: 353–383 22 Seiniger P, Schröter K, Gail J "Perspectives for motorcycle stability control systems" Accident Analysis and Prevention (In Press) Corrected Proof, 2011 ... for robotic teleoperation [18] Therefore, results obtained in this context would be of interest also for the research on active shimmy damping Realisation The last point of discussion is related... unstoppable, so that it is expected that electro-hydraulic actuators suitable for active shimmy damping will soon be available ([19], [20]) To conclude this discussion, it is useful to remark that the introduction... IDA-PBC controlled underactuated mechanical systems” Eur J Control 2004; 10: 451–468 18 Nuño E, Basañez L, Ortega R “Passivity-based control for bilateral teleoperation: A tutorial” Automatica,