Robust adaptive control of switched systems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2007.Includes bibliographical references (leaves 141-149).In this thesis, robust adaptive controllers are developed for classes of switched nonlinear systems. Switched systems are those governed by differential equations, which undergo vector field switching due to sudden changes in model characteristics. Such systems arise in many applications such as mechanical systems with contacts, electrical systems with switches, and thermal-fluidic systems with valves and phase changes. The presented controllers guarantee system stability, under typical adaptive control assumptions, for systems with piecewise differentiable bounded parameters and piecewise continuous disturbances without requiring a priori knowledge on such parameters or disturbances. The effect of plant variation and switching is reduced to piecewise continuous and impulsive inputs acting on a Bounded Input Bounded State (BIBS) stable closed loop system. This, in turn, provides a separation between the robust stability and robust performance control problems. The developed methodology provides clear guidelines for steady-state and transient performance optimization and allows for parameter scheduling and multiple model controller adjustment techniques to be utilized with no stability concerns. The results are illustrated for various systems including contact-based robotic manipulation and Atomic Force Microscope (AFM) based nano-manipulation.by Khalid El Rifai.Ph.D

Optimal sensor/actuator placement and switching schemes for control of flexible structures

The vibration control problem for flexible structures is examined within the context of overall controller performance and power reduction. First, the issue of optimal sensor and actuator placement is considered along with its associated control robustness aspects. Then the option of alternately activating subsets of the available devices is investigated. Such option is considered in order to better address the effects of spatiotemporally varying disturbances acting on a flexible structure while reducing the overall energy consumption. Towards the solution to the problem of optimal device placement, three different approaches are proposed. First, a computationally efficient scheme for the simultaneous placement of multiple devices is presented. The second approach proposes a strategy for the optimal placement of sensors and collocated sensor/actuator pairs, taking into account the influence of the spatial distribution of disturbances. The third approach provides a solution to the actuator location problem by incorporating considerations with respect to preferred spatial regions within the flexible structure. Then the second problem named above is considered. Activating a subset of the available and optimally placed actuators and sensors in a flexible structure provides enhanced performance with reduced energy consumption. Such approach of switching on and off different actuating devices, depending on their local-in-time authority, results in a hybrid system. Therefore the proposed work draws on existing results on hybrid systems and includes an additional degree of freedom, whereby both the actuating devices and the control signals allocated to them are switched in and out. To enable this switching an activation strategy, which insures also that stability-under-switching is guaranteed, is required. Three different strategies are considered for such actuators allocation: first a cost-to-go index is considered, then a cost function based on the mechanical energy of the flexible structure and finally a performance index based on the maximum deviation of the transverse displacement. A flexible aluminum plate was chosen to validate and test the proposed approaches. The set up utilized four pairs of collocated piezoceramic patches that serve to provide sensing and actuating capabilities. Extensive numerical simulations were performed for both the placement strategies and the switching policies proposed, in order to predict the behavior of the flexible plate and provide the optimal actuator and sensor locations that were to be affixed on the flexible structure. Finally, to complete the validation process a sequence of experimental tests were performed. The objective of these tests was to compare the performance of the proposed hybrid control system to traditional non switched control schemes. In order to provide a repeatable perturbation, four of the piezoceramic patches were allocated to simulate a spatiotemporally varying disturbance, while the remaining four patches were used as sensors and controlling actuators. The experimental results showed a significant performance improvement for the switched controller over the traditional controller. Moreover the switched controller exhibited improved robustness towards spatiotemporally varying disturbances while the traditional controller showed a significant loss of controller performance. The improvement achieved in vibration control problems could be extended to a wider range of applications. In particular, although this study was concentrated on a rectangular thin plate, the proposed strategies can be applied to emph{any} structure and more generally to any plant whose dynamics can be represented by a second order linear system. For example, by removing the restriction of spatially fixed actuators and sensors, the proposed theory can be applied to the problem of unmanned vehicles control

Modeling and Model-Based Control Of Multi-Mode Combustion Engines for Closed-Loop SI/HCCI Mode Transitions with Cam Switching Strategies.

Homogeneous charge compression ignition (HCCI) combustion has been investigated by many researchers as a way to improve gasoline engine fuel economy through highly dilute unthrottled operation while maintaining acceptable tailpipe emissions. A major concern for successful implementation of HCCI is that it's feasible operating region is limited to a subset of the full engine regime, which necessitates mode transitions between HCCI and traditional spark ignition (SI) combustion when the HCCI region is entered/exited. The goal of this dissertation is to develop a methodology for control-oriented modeling and model-based feedback control during such SI/HCCI mode transitions. The model-based feedback control approach is sought as an alternative to those in the SI/HCCI transition literature, which predominantly employ open-loop experimentally derived actuator sequences for generation of control input trajectories. A model-based feedback approach has advantages both for calibration simplicity and controller generality, in that open-loop sequences do not have to be tuned, and that use of nonlinear model-based calculations and online measurements allows the controller to inherently generalize across multiple operating points and compensate for case-by-case disturbances. In the dissertation, a low-order mean value modeling approach for multi-mode SI/HCCI combustion that is tractable for control design is described, and controllers for both the SI to HCCI (SI-HCCI) and HCCI to SI (HCCI-SI) transition are developed based on the modeling approach. The model is shown to fit a wide range of steady-state actuator sweep data containing conditions pertinent to SI/HCCI mode transitions, and is extended to capture transient SI-HCCI transition data through using an augmented residual gas temperature parameter. The mode transition controllers are experimentally shown to carry out SI-HCCI and HCCI-SI transitions in several operating conditions with minimal tuning, though the validation in the SI-HCCI direction is more extensive. The model-based control architecture is also equipped with an online parameter updating routine, to attenuate error in model-based calculations and improve robustness to engine aging and cylinder to cylinder variability. Experimental examples at multiple operating conditions illustrate the ability of the parameter update routine to improve controller performance by using transient data to tune the model parameters for enhanced accuracy during SI-HCCI mode transitions.PhDMechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/113351/1/pgoz_1.pd

A stability-theory perspective to synchronisation of heterogeneous networks

Dans ce mémoire, nous faisons une présentation de nos recherches dans le domaine de la synchronisation des systèmes dynamiques interconnectés en réseau. Une des originalités de nos travaux est qu'ils portent sur les réseaux hétérogènes, c'est à dire, des systèmes à dynamiques diverses. Au centre du cadre d'analyse que nous proposons, nous introduisons le concept de dynamique émergente. Il s'agit d'une dynamique "moyennée'' propre au réseau lui-même. Sous l'hypothèse qu'il existe un attracteur pour cette dynamique, nous montrons que le problème de synchronisation se divise en deux problèmes duaux : la stabilité de l'attracteur et la convergence des trajectoires de chaque système vers celles générées par la dynamique émergente. Nous étudions aussi le cas particulier des oscillateurs de Stuart-Landau

Dynamical Systems

Complex systems are pervasive in many areas of science integrated in our daily lives. Examples include financial markets, highway transportation networks, telecommunication networks, world and country economies, social networks, immunological systems, living organisms, computational systems and electrical and mechanical structures. Complex systems are often composed of a large number of interconnected and interacting entities, exhibiting much richer global scale dynamics than the properties and behavior of individual entities. Complex systems are studied in many areas of natural sciences, social sciences, engineering and mathematical sciences. This special issue therefore intends to contribute towards the dissemination of the multifaceted concepts in accepted use by the scientific community. We hope readers enjoy this pertinent selection of papers which represents relevant examples of the state of the art in present day research. [...