Event-Triggered Control for a Three DoF Manipulator Robot

In the classical approach of Time-Triggered Control (TTC),  the control signal is updated  at  each  sampling  time  as  well  as  the  system  states  to  be  controlled,  which could imply a redundancy in the computational calculation as well as in the transfer of information in the regulation objective. On the other hand, the Event-Triggered Control (ETC) approach performs the same task in an asynchronous way, i.e,, it only updates the control signal when a performance requirement is violated and the states are updated at each sampling time. This reduces the amount of computational calculation without affecting the performance of the closed loop system. For this reason, in the present work the ETC is developed for the stabilization of a manipulator robot with three Degree of Freedom (DoF) in the joint space where a Lyapunov Control Function (LCF) is proposed to formulate the event function (e¯), which indicates whether or not  is required  the  control  signal  updating.  Simulation results show the reduction of the updates compared with a TTC

Semiglobal exponential input-to-state stability of sampled-data systems based on approximate discrete-time models

Several control design strategies for sampled-data systems are based on a discrete-time model. In general, the exact discrete-time model of a nonlinear system is difficult or impossible to obtain, and hence approximate discrete-time models may be employed. Most existing results provide conditions under which the stability of the approximate discrete-time model in closed-loop carries over to the stability of the (unknown) exact discrete-time model but only in a practical sense, meaning that trajectories of the closed-loop system are ensured to converge to a bounded region whose size can be made as small as desired by limiting the maximum sampling period. In addition, some sufficient conditions exist that ensure global exponential stability of an exact model based on an approximate model. However, these conditions may be rather stringent due to the global nature of the result. In this context, our main contribution consists in providing rather mild conditions to ensure semiglobal exponential input-to-state stability of the exact model via an approximate model. The enabling condition, which we name the Robust Equilibrium-Preserving Consistency (REPC) property, is obtained by transforming a previously existing consistency condition into a semiglobal and perturbation-admitting condition. As a second contribution, we show that every explicit and consistent Runge-Kutta model satisfies the REPC condition and hence control design based on such a Runge-Kutta model can be used to ensure semiglobal exponential input-to-state stability of the exact discrete-time model in closed loop.Comment: 10 page

Event-Triggered Control for a Three DoF Manipulator Robot

In the classical approach of Time-Triggered Control (TTC),  the control signal is updated  at  each  sampling  time  as  well  as  the  system  states  to  be  controlled,  which could imply a redundancy in the computational calculation as well as in the transfer of information in the regulation objective. On the other hand, the Event-Triggered Control (ETC) approach performs the same task in an asynchronous way, i.e,, it only updates the control signal when a performance requirement is violated and the states are updated at each sampling time. This reduces the amount of computational calculation without affecting the performance of the closed loop system. For this reason, in the present work the ETC is developed for the stabilization of a manipulator robot with three Degree of Freedom (DoF) in the joint space where a Lyapunov Control Function (LCF) is proposed to formulate the event function (e¯), which indicates whether or not  is required  the  control  signal  updating.  Simulation results show the reduction of the updates compared with a TTC

EASILY VERIFIABLE CONTROLLER DESIGN WITH APPLICATION TO AUTOMOTIVE POWERTRAINS

Bridging the gap between designed and implemented model-based controllers is a major challenge in the design cycle of industrial controllers. This gap is mainly created due to (i) digital implementation of controller software that introduces sampling and quantization imprecisions via analog-to-digital conversion (ADC), and (ii) uncertainties in the modeled plant’s dynamics, which directly propagate through the controller structure. The failure to identify and handle these implementation and model uncertainties results in undesirable controller performance and costly iterative loops for completing the controller verification and validation (V&V) process. This PhD dissertation develops a novel theoretical framework to design controllers that are robust to implementation imprecision and uncertainties within the models. The proposed control framework is generic and applicable to a wide range of nonlinear control systems. The final outcome from this study is an uncertainty/imprecisions adaptive, easily verifiable, and robust control theory framework that minimizes V&V iterations in the design of complex nonlinear control systems. The concept of sliding mode controls (SMC) is used in this study as the baseline to construct an easily verifiable model-based controller design framework. SMC is a robust and computationally efficient controller design technique for highly nonlinear systems, in the presence of model and external uncertainties. The SMC structure allows for further modification to improve the controller robustness against implementation imprecisions, and compensate for the uncertainties within the plant model. First, the conventional continuous-time SMC design is improved by: (i) developing a reduced-order controller based on a novel model order reduction technique. The reduced order SMC shows better performance, since it uses a balanced realization form of the plant model and reduces the destructive internal interaction among different states of the system. (ii) developing an uncertainty-adaptive SMC with improved robustness against implementation imprecisions. Second, the continuous-time SMC design is converted to a discrete-time SMC (DSMC). The baseline first order DSMC structure is improved by: (i) inclusion of the ADC imprecisions knowledge via a generic sampling and quantization uncertainty prediction mechanism which enables higher robustness against implementation imprecisions, (ii) deriving the adaptation laws via a Lyapunov stability analysis to overcome uncertainties within the plant model, and (iii) developing a second order adaptive DSMC with predicted ADC imprecisions, which provides faster and more robust performance under modeling and implementation imprecisions, in comparison with the first order DSMC. The developed control theories from this PhD dissertation have been evaluated in real-time for two automotive powertrain case studies, including highly nonlinear combustion engine, and linear DC motor control problems. Moreover, the DSMC with predicted ADC imprecisions is experimentally tested and verified on an electronic air throttle body testbed for model-based position tracking purpose

Stabilization of cascaded nonlinear systems under sampling and delays

Over the last decades, the methodologies of dynamical systems and control theory have been playing an increasingly relevant role in a lot of situations of practical interest. Though, a lot of theoretical problem still remain unsolved. Among all, the ones concerning stability and stabilization are of paramount importance. In order to stabilize a physical (or not) system, it is necessary to acquire and interpret heterogeneous information on its behavior in order to correctly intervene on it. In general, those information are not available through a continuous flow but are provided in a synchronous or asynchronous way. This issue has to be unavoidably taken into account for the design of the control action. In a very natural way, all those heterogeneities define an hybrid system characterized by both continuous and discrete dynamics. This thesis is contextualized in this framework and aimed at proposing new methodologies for the stabilization of sampled-data nonlinear systems with focus toward the stabilization of cascade dynamics. In doing so, we shall propose a small number of tools for constructing sampled-data feedback laws stabilizing the origin of sampled-data nonlinear systems admitting cascade interconnection representations. To this end, we shall investigate on the effect of sampling on the properties of the continuous-time system while enhancing design procedures requiring no extra assumptions over the sampled-data equivalent model. Finally, we shall show the way sampling positively affects nonlinear retarded dynamics affected by a fixed and known time-delay over the input signal by enforcing on the implicit cascade representation the sampling process induces onto the retarded system

Développement d'outils de calcul et de logiciels pour la réalisation et l'implantation de stratégies de commande non linéaires échantillonnées

Cette thèse concerne la conception de commandes échantillonnées pour les systèmes non-linéaires en temps continu. Les systèmes échantillonnés sont des éléments inhérents aux systèmes contrôlés par ordinateur, les systèmes hybrides ou les systèmes embarqués. La conception et le calcul des contrôleurs numériques appropriés sont des taches difficiles car ils contiennent des composants à la fois continu et en temps discret. Ce travail s'inscrit dans une activité de recherche menée par S. Monaco et D. Normand-Cyrot dans le domaine des systèmes échantillonnés non-linéaires. L'idée de base est de concevoir des contrôleurs digitaux qui permettent de récupérer certaines propriétés en temps continu qui sont généralement dégradées par l'échantillonnage. Tel est le cas de l'émulation lorsque les contrôleurs en temps continu sont mis en ouvre en utilisant des bloqueurs d'ordre zéro. Cette thèse apporte des contributions dans trois directions complémentaires. La première concerne les développements théoriques: une nouvelle conception de type backstepping digital" est proposée pour les systèmes en forme strict-feedback". Cette méthode est comparée à d'autres stratégies proposées dans la littérature. La deuxième contribution est le développement d'un logiciel pour la synthèse des contrôleurs et d'une boîte à outils" pour simuler (en Matlab) les systèmes échantillonnés non-linéaires et leurs contrôleurs. Cette boîte à outils inclut plusieurs algorithmes pour la synthèse de contrôleurs échantillonnés tels que: commande de type multi-échelle, reproduction entrée-sortie/Lyapunov, backstepping digital, etc. La troisième contribution concerne plusieurs études de cas menées pour mettre en évidence les performances des contrôleurs échantillonnés, calculés avec l'aide du logiciel. Des résultats expérimentaux et des simulations sont décrits pour divers exemples réels dans les domaines électriques et mécaniques.This thesis is concerned with the sampled-data control of non-linear continuous-time systems. Sampled-data systems are present in all computer controlled, hybrid or embedded systems. The design and computation of suitable digital controllers represent unavoidable tasks since both continuous and discrete-time components interact. The basic framework of this work takes part of a wide research activity performed by S. Monaco and D. Normand-Cyrot regarding non-linear sampled-data systems. The underlying idea is to design digital controllers that recover certain continuous-time properties that are usually degraded through sampling as it is the case when continuous-time controllers are implemented by means of zero-order holder devices (emulated control). This thesis brings contributions into three different directions. The first one regards theoretical developments: a new digital backstepping-like strategy design for strict-feedback systems is proposed. This method is compared with other strategies proposed in the literature. The second contribution is the development of a control designer and of a simulation toolbox (in Matlab) for non-linear sampled-data systems. This toolbox includes different digital design strategies such as: multi-rate control, input-output/Lyapunov matching, digital backstepping design, etc. The third contribution concerns several case studies conducted to highlight the performances of the sampled-data controller designs, computed by the means of the software toolbox. Experimental and simulation results are described for various real examples especially in the area of electrical and mechanical processes.PARIS11-SCD-Bib. électronique (914719901) / SudocSudocFranceF

Advanced tools for nonlinear sampled-data systems: analysis and control

It is shown that the formalism of asymptotic series expansions recently developed by the authors for computing the solutions of non autonomous differential equations, can be profitably employed to obtain the equivalent model to a nonlinear continuous system under generalized sampling procedures. Tools and insights for the design of sampled-data control systems are derived