Academic literature on the topic 'Transverse feedback linearization'

In this article, we develop and assess a novel approach for the control of underactuated planar bipeds that is based on velocity decomposition. The new controller employs heuristic rules that mimic the functionality of transverse linearization feedback control and that can be layered on top of a conventional hybrid zero dynamics (HZD)-based controller. The heuristics sought to retain HZD-based control’s simplicity and enhance disturbance rejection for practical implementation on realistic biped robots. The proposed control strategy implements a feedback on the time rate of change of the decomposed uncontrolled velocity and is compared with conventional HZD-based control and transverse linearization feedback control for both vanishing and non-vanishing disturbances. Simulation studies with a point-foot, three-link biped show that the proposed method has nearly identical performance to transverse linearization feedback control and outperforms conventional HZD-based control. For the non-vanishing case, the velocity decomposition-enhanced controller outperforms HZD-based control, but takes fewer steps on average before failure than transverse linearization feedback control when walking on uneven terrain without visual perception of the ground. The findings were validated experimentally on a planar, five-link biped robot for eight different uneven terrains. The velocity decomposition-enhanced controller outperformed HZD-based control while maintaining a relatively low specific energetic cost of transport (~0.45). The biped robot “blindly” traversed uneven terrains with changes in terrain height accumulating to 5% of its leg length using the stand-alone low-level controller.

This work presents a path-following controller for a unicycle robot. The main contribution of this paper is to demonstrate the restriction of transverse feedback linearization (TFL) to obtuse angles on piecewise linear paths. This restriction is experimentally demonstrated on a Kobuki mobile robot, where it is possible to observe, as a result of the limitation of the TFL, the convergence to another domain of attraction.

Direct drive wave energy conversion systems have been identified as a potentially major contributor to the world’s energy demands, forecasting shares of up to 25 % of the energy mix. Anders Hagnestål conducts research at the Royal Institute of Technology where a novel linear transverse flux permanent magnet generator is developed. This concept machine is particularly well-suited for the pertaining operating conditions in marine environments, producing large forces at low speeds with outstandingly low resistive losses. However, it exhibits severe magnetic saturation and draws unsymmetrical phase currents at nominal operation. In addition, it possesses a low power factor. All in all, this places stern requirements on the power electronic system and control algorithms. The aim of this thesis has been to design a functioning power conditioning system that connects the machine to the electric grid. For this purpose, a three-phase two-level voltage source converter is proposed to be back-to-back connected with two-level single-phase voltage source converters (active rectifiers) interfacing each and every machine phase. It is shown that the intermediate DC link can be maintained at a constant voltage with restricted ripple while feeding power at unity power factor to the grid by appropriately sizing the DC capacitor and adopting a feedback linearization control scheme. The phase currents can be controlled effectively by means of a cascaded gain-scheduled PID controller. By including a low-pass filter the iron losses in the machine may be suppressed even at lower switching frequencies. A constrained cost optimization indicates that the converter consequently can reach 99.1 % efficiency. Finally, with this thesis as a background, it is suggested that the thermal stresses on the selected semiconductor modules and the iron losses of the machine are evaluated to further improve the design. If higher efficiency of the active rectifiers is strived for, more complex converter topologies could be considered.
Direktdrivna vågenergiomvandlingssystem har utpekats som en potentiellt starkt bidragande resurs för att tillgodose världens efterfrågan på energi med andelar på uppemot 25 % av energimixen förutspådda. Anders Hagnestål bedriver forskning och utveckling av en ny typ av linjär permanentmagnetiserad transversalflödesmaskin vid Kungliga Tekniska Högskolan. Konceptmaskinen är särskilt väl lämpad för de rådande marina förhållandena genom att kunna producera stora krafter vid låga hastigheter med utomordentligt låga resistiva förluster. Maskinen går emellertid i kraftig magnetisk mättnad och drar asymmetriska strömmar vid nominell drift. Dessutom är effektfaktorn låg i jämförelse med standardmaskiner. Alltsomallt inför detta hårda krav på det effektelektroniska systemet och kontrollalgoritmerna. Målet med detta examensarbete har varit att designa ett funktionellt effektkonditioneringssystem som sammanfogar maskinen med det angränsande elektriska nätet. För att åstadkomma detta föreslås att en tvånivås-trefasomriktare kopplas rygg-mot-rygg till tvånivås-enfasomvandlare (aktiva likriktare) som i sin tur är kopplade till varje maskinfas. Med den här konfigurationen visas det att spänningen på den mellanliggande DC-länken kan hållas konstant med begränsat rippel, alltmedan effekt tillförs nätet vid effektfaktor ett genom att dimensionera DC-kondensatorn på rätt sätt och använda en kontrollag baserad på exakt linjärisering. Maskinens fasströmmar kan kontrolleras effektivt med hjälp av en kaskadkopplad PID-regulator med schemalagda förstärkningsfaktorer. Genom att inkludera ett lågpassfilter förväntas det att järnförlusterna i maskinen kan begränsas även vid lägre switchfrekvenser. Genom att lösa ett kostnadsoptimeringsproblem visas det att den resulterande aktiva likriktaren kan uppnå en verkningsgrad på 99.1 %. Slutligen, med det här examensarbetet som grund, föreslås det att den termiska stressen på de valda halvledarkomponentsmodulerna och järnförlusterna i maskinen utvärderas för att ytterligare förbättra designen. Om högre verkningsgrad eftersträvas hos de aktiva likriktarna kan mer komplicerade omvandlartopologier övervägas.

De nombreux problèmes de contrôle se ramènent à imposer que la sortie du système suive un signal donné, tout en rejetant les effets de perturbations. Dans ce vaste contexte de problématiques traitées principalement en temps continu, l’utilisation de techniques de contrôle reposant sur l’inversion est bien connue. Cependant, la présence incontournable de capteurs et d’actionneurs numériques nécessite une conception ad hoc en temps discret. Plus précisément, il s’agit de contrôler des systèmes dits échantillonnés, dont les mesures sont acquises à des instants échantillonnés dans le temps et pour lesquels les variables de commande sont maintenues constantes sur un intervalle de temps donné, la période d’échantillonnage. Dans ce domaine des systèmes échantillonnés, des systèmes supposés en temps continu à déphasage minimal, perdent cette propriété sous échantillonnage; le système en temps discret équivalent n’est plus à déphasage minimal. L’objet de cette thèse est d’établir des résultats constructifs, procédures et algorithmes permettant de réduire les effets dus à l’inversion dans le contexte échantillonné. Une première contribution propose une procédure d’inversion stable pour une classe de systèmes à déphasage non minimal multi-input multi-output (MIMO). L’approche repose sur le linéarisé tangent du système et une factorisation de la dynamique des zéros dont une partie seulement est à déphasage minimal. Les contributions suivantes concernent la commande prédictive (MPC) et la linéarisation transverse par bouclage (TFL), deux stratégies de commande concernées par la pertede la propriété de déphasage minimal sous échantillonnage. Concernant la commande prédictive deux problématiques utilisant des techniques de discrétisation à échelles de temps multiques sont étudiées pour des objectifs de prédiction puis de planification de trajectoire. Les solutions développées sont validées sur plusieurs exemples allant de la conduite et poursuite de systèmes admettant des formes chainées jusqu’au maintien des quasi Halo orbites du système terre-lune. Concernant la linéarisation transverse par bouclage, deux solutions préservant l’invariance dessous espaces caractérisant les objectifs de contrôle sont proposées. L’une repose sur des techniques d’échantillonnage simple et, quoique solution approchée, est très simple de calcul et présente des performances bien supérieures à une implantation classique par bloqueur d’ordre zéro. La deuxième solution, proposée au sens exact, fait appel à des techniques d’échantillonnage multiple et propose aussi des solutions par bouclage statique dans des cas ou seul un bouclage dynamique résout le problème en temps continu. Les deux approches sont validées sur des exemples académiques et appliquées à la résolution de problèmes de poursuite de trajectoires pour des robots mobiles ou déstabilisation d’orbites périodiques pour des systèmes mécaniques sous actionnés
Several well studied control problems reduce to asking the output of a given process to track a desired signal while rejecting effects of undesired perturbations. In the rich body of knowledge dealing with problems of this type in continuous-time, the use of partial inversion-based controllers (i.e controllers that cancel part of the dynamics in the sense of rendering it unobservable) and their effectiveness is well established. Nowadays, however, sensing and actuation is done through digital devices so necessitating a suitable control design. In this setting, the control engineer works with systems referred to as sampled-data systems where measures of the output are available only at sporadic discrete-time instants while the control is piecewise constant over a fixed time interval. In this sampled-data context, systems that are originally minimum phase in continuous-time, and because of sampling and holding, may lose this property. The general argument of this thesis contributes to establishing constructive results, procedures and algorithms to the purpose of mitigating the issues caused by sampled-data design under partial inversion-based controllers. Since partial inversion-based controllers typically cancel the zero dynamics, the central idea is to mitigate the loss of the minimum-phase property. A first contribution in this direction stands in proposing a procedure for stable partial inversion for a class of continuous-time non-minimum phase Multi-Input Multi-Output systems. The procedure proposed, generalizing a previous result, works over the linear tangent model of a system factorizing a sub-set of the zero dynamics known to be minimum-phase a priori. This preliminary result is at the basis of control strategies which are herein proposed for model predictive control and digital transverse feedback linearization. Both control strategies under sampling are affected by the above-mentioned pathology linked to the loss of the minimum-phase property. In particular, for model predictive control, two solutions based on multi-rate sampling techniques, employed at the prediction, or the trajectory planning level are proposed and compared. Their validity is established through several case studies ranging from steering and tracking in systems admitting chained forms to quasi Halo orbits station-keeping for space-crafts in the Earth-Moon system. Concerning transverse feedback linearization, two sampled-data solutions preserving the in-variant subset specifying the control objectives are proposed. The former is based on single-rate sampling and, albeit approximate in nature, is computationally simple and outperforms zero-order holding of the continuous-time design. The later, an exact solution based on multi-rate sampling, improves upon the former solution and provides, in special cases, static state feedback solutions even when the problem is only solvable via dynamic feedback in continuous-time. Both solutions are validated over academic case studies as well as in solving path following for mobile robots and periodic orbits stabilization for underactuated mechanical systems

In this thesis we study the problem of stabilizing smooth embedded submanifolds in the state space of smooth, nonlinear, autonomous, deterministic control-affine systems. Our motivation stems from a realization that important applications, such as path following and synchronization, are best understood in the set stabilization framework. Instead of directly attacking the above set stabilization problem, we seek feedback equivalence of the given control system to a normal form that facilitates control design. The process of putting a control system into the normal form of this thesis is called transverse feedback linearization. When feasible, transverse feedback linearization allows for a decomposition of the nonlinear system into a “transverse” and a “tangential” subsystem relative to the goal submanifold. The dynamics of the transverse subsystem determine whether or not the system’s state approaches the submanifold. To ease controller design, we ask that the transverse subsystem be linear time-invariant and controllable. The dynamics of the tangential subsystem determine the motion on the submanifold. The main problem considered in this work, the local transverse feedback linearization problem (LTFLP), asks: when is such a decomposition possible near a point of the goal submanifold? This problem can equivalently be viewed as that of finding a system output with a well-defined relative degree, whose zero dynamics manifold coincides with the goal submanifold. As such, LTFLP can be thought of as the inverse problem to input-output feedback linearization. We present checkable, necessary and sufficient conditions for the existence of a local coordinate and feedback transformation that puts the given system into the desired normal form. A key ingredient used in the analysis is the new notion of transverse controllability indices of a control system with respect to a set. When the goal submanifold is diffeomorphic to Euclidean space, we present sufficient conditions for feedback equivalence in a tubular neighbourhood of it. These results are used to develop a technique for solving the path following problem. When applied to this problem, transverse feedback linearization decomposes controller design into two separate stages: transversal control design and tangential control design. The transversal control inputs are used to stabilize the path, and effectively generate virtual constraints forcing the system’s output to move along the path. The tangential inputs are used to control the motion along the path. A useful feature of this twostage approach is that the motion on the set can be controlled independently of the set stabilizing control law. The effectiveness of the proposed approach is demonstrated experimentally on a magnetically levitated positioning system. Furthermore, the first satisfactory solution to a problem of longstanding interest, path following for the planar/vertical take-off and landing aircraft model to the unit circle, is presented. This solution, developed in collaboration with Luca Consolini and Mario Tosques at the University of Parma, is made possible by taking a set stabilization point of view.