Numerical Treatment of Non-Linear singular pertubation problems

Magister Scientiae - MScThis thesis deals with the design and implementation of some novel numerical methods for non-linear singular pertubations problems (NSPPs). It provide a survey of asymptotic and numerical methods for some NSPPs in the past decade. By considering two test problems, rigorous asymptotic analysis is carried out. Based on this analysis, suitable numerical methods are designed, analyzed and implemented in order to have some relevant results of physical importance. Since the asymptotic analysis provides only qualitative information, the focus is more on the numerical analysis of the problem which provides the quantitative information.South Afric

Singular Perturbations and Time-Scale Methods in Control Theory: Survey 1976-1982

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryJoint Services Electronics Program / N00014-79-C-0424U.S. Air Force / AFOSR 78-363

Modeling and Robust Control of Two Collaborative Robot Manipulators Handling a Flexibile Object

Robots are often used in industry to handle flexible objects, such as frames, beams, thin plates, rubber tubes, leather goods and composite materials. Moving long flexible objects in a desired path and also precise positioning and orienting the objects need a collaborative action between two robot arms. Most of the earlier studies have dealt with manipulation of rigid objects and only a few have focused on the collaborative manipulators handling flexible objects. Such studies on handling of flexible objects generally used finite element method or assumed mode method for deriving the dynamic model of the flexible objects. These approximation methods require more number of sensors to feedback the vibration measurements or require an observer. Unlike in the earlier studies, this thesis concerns with development of a dynamic model of the flexible object in partial differential equation (PDE) form and design of a robust control strategy for collaborative manipulation of the flexible objects by two rigid robot arms. Two planar rigid manipulators each with three links and revolute joints handling a flexible object is considered during the model development. Kinematic and dynamic equations of the flexible object are derived without using any approximation techniques. The resulting dynamic equation of the flexible object together with the manipulator dynamic equations form the combined dynamic model of the system. The developed complete system of dynamic equations is described by the PDE’s having rigid as well as flexible parameters coupled together. Such a coupled system must be controlled without using any form of approximation techniques and this is accomplished using the singular perturbation approach. By utilizing this technique, slow and fast subsystems are identified in two different time scales and controller is designed for each subsystem. The key issue in developing a control algorithm is that, it should be robust against uncertain parameters of the manipulators and the flexible object and it should also achieve the exponential convergence. Hence, for the slow subsystem, sliding mode control algorithm is developed and for the fast subsystem, a simple feedback control algorithm is designed. In general, usage of singular perturbation technique necessitates exponential stability of the slow and fast subsystems, which is evaluated by satisfying the Tikhnov’s theorem. Hence, the exponential stability analysis for both the subsystems is performed. Simulation results are presented to validate the composite control scheme. As a further consideration in the improvement of control law for the slow subsystem, two modified control algorithms are suggested. The first one focused on the avoidance of velocity signal measurement which is useful to eliminate the need of velocity sensors and the second controller aims at avoiding the complex regressor in the control law. The capability of those controllers is illustrated through simulation studies. The extension of earlier analysis has been carried out by developing the complete system of dynamic equations in joint space

Modeling and Robust Control of Two Collaborative Robot Manipulators Handling a Flexibile Object

Robots are often used in industry to handle flexible objects, such as frames, beams, thin plates, rubber tubes, leather goods and composite materials. Moving long flexible objects in a desired path and also precise positioning and orienting the objects need a collaborative action between two robot arms. Most of the earlier studies have dealt with manipulation of rigid objects and only a few have focused on the collaborative manipulators handling flexible objects. Such studies on handling of flexible objects generally used finite element method or assumed mode method for deriving the dynamic model of the flexible objects. These approximation methods require more number of sensors to feedback the vibration measurements or require an observer. Unlike in the earlier studies, this thesis concerns with development of a dynamic model of the flexible object in partial differential equation (PDE) form and design of a robust control strategy for collaborative manipulation of the flexible objects by two rigid robot arms. Two planar rigid manipulators each with three links and revolute joints handling a flexible object is considered during the model development. Kinematic and dynamic equations of the flexible object are derived without using any approximation techniques. The resulting dynamic equation of the flexible object together with the manipulator dynamic equations form the combined dynamic model of the system. The developed complete system of dynamic equations is described by the PDE’s having rigid as well as flexible parameters coupled together. Such a coupled system must be controlled without using any form of approximation techniques and this is accomplished using the singular perturbation approach. By utilizing this technique, slow and fast subsystems are identified in two different time scales and controller is designed for each subsystem. The key issue in developing a control algorithm is that, it should be robust against uncertain parameters of the manipulators and the flexible object and it should also achieve the exponential convergence. Hence, for the slow subsystem, sliding mode control algorithm is developed and for the fast subsystem, a simple feedback control algorithm is designed. In general, usage of singular perturbation technique necessitates exponential stability of the slow and fast subsystems, which is evaluated by satisfying the Tikhnov’s theorem. Hence, the exponential stability analysis for both the subsystems is performed. Simulation results are presented to validate the composite control scheme. As a further consideration in the improvement of control law for the slow subsystem, two modified control algorithms are suggested. The first one focused on the avoidance of velocity signal measurement which is useful to eliminate the need of velocity sensors and the second controller aims at avoiding the complex regressor in the control law. The capability of those controllers is illustrated through simulation studies. The extension of earlier analysis has been carried out by developing the complete system of dynamic equations in joint space

Advanced Strategies for Robot Manipulators

Amongst the robotic systems, robot manipulators have proven themselves to be of increasing importance and are widely adopted to substitute for human in repetitive and/or hazardous tasks. Modern manipulators are designed complicatedly and need to do more precise, crucial and critical tasks. So, the simple traditional control methods cannot be efficient, and advanced control strategies with considering special constraints are needed to establish. In spite of the fact that groundbreaking researches have been carried out in this realm until now, there are still many novel aspects which have to be explored

Robust Hybrid Systems for Control, Learning, and Optimization in Networked Dynamical Systems

The deployment of advanced real-time control and optimization strategies in socially-integratedengineering systems could significantly improve our quality of life whilecreating jobs and economic opportunity. However, in cyber-physical systems such assmart grids, transportation networks, healthcare, and robotic systems, there still existseveral challenges that prevent the implementation of intelligent control strategies.These challenges include the existence of limited communication networks, dynamicand stochastic environments, multiple decision makers interacting with the system,and complex hybrid dynamics emerging from the feedback interconnection of physicalprocesses and computational devices.In this dissertation, we study the problem of designing robust control and optimizationalgorithms for cyber-physical systems using the framework of hybrid dynamicalsystems. We propose different theoretical frameworks for the design and analysis offeedback mechanisms that optimize the performance of dynamical systems without requiringan explicit characterization of their mathematical model, i.e., in a model-freeway. The closed-loop system that emerges of the interconnection of the plant with thefeedback mechanism describes, in general, a set-valued hybrid dynamical system. Thesetypes of systems combine continuous-time and discrete-time dynamics, and they usuallylack the uniqueness of solutions property. The framework of set-valued hybriddynamical systems allows us to study many complex dynamical systems that emerge indifferent engineering applications, such as networked multi-agent systems with switching graphs, non-smooth mechanical systems, dynamic pricing mechanisms in transportationsystems, autonomous robots with logic-based controllers, etc. We proposea step-by-step approach to the design of different types of discrete-time, continuous-time,hybrid, and stochastic controllers for different types of applications, extendingand generalizing different results in the literature in the area of extremum seeking control,sampled-data extremization, robust synchronization, and stochastic learning innetworked systems. Our theoretical results are illustrated via different simulations andnumerical examples

Aeronautical engineering: A continuing bibliography with indexes (supplement 227)

This bibliography lists 418 reports, articles, and other documents introduced into the NASA scientific and technical information system in May, 1988