Existence of Solutions to a Class of Nonlinear Convergent Chattering-free Sliding Mode Control Systems

Sliding mode control is a nonlinear control technique, which is robust against some classes of uncertainties and disturbances. However, this control produces chattering which can cause instability due to unmodeled dynamics and can also cause damage to actuators or the plant. There are essentially two ways to counter the chattering phenomenon. One way is to use higher order sliding mode, and the other way is to add a boundary layer around the switching surface and use continuous control inside the boundary. The problem with the first method is that the derivative of a certain state variable is not available for measurement, and therefore methods have to be used to observe that variable. In the second method, it is important that the trajectories inside the boundary layer do not try to come outside the boundary after entering the boundary layer. Control laws producing chattering-free sliding mode using a boundary layer have been proposed and the existence of solutions to the system using these control laws are presente

Pedestrian Dynamics: Mathematical Theory and Evacuation Control

Homeland security, transportation, and city planning depend upon well-designed evacuation routes. You can’t wait until the day of to realize your plan won’t work. Designing successful evacuation plans requires an in-depth understanding of models and control designs for the problems of traffic flow, construction and road closures, and the intangible human factors. Pedestrian Dynamics: Mathematical Theory and Evacuation Control clearly delineates the derivation of mathematical models for pedestrian dynamics and how to use them to design feedback controls for evacuations. The book includes: * Mathematical models derived from basic principles * Mathematical analysis of the model * Details of past work * MATLAB® code * 65 figures and 400 equations Unlike most works on traffic flow, this book examines the development of optimal methods to effectively control and improve pedestrian traffic flow. The work of a leading expert, it examines the differential equations applied to conservation laws encountered in the study of pedestrian dynamics and evacuation control problem. The author presents new pedestrian traffic models for multi-directional flow in two dimensions. He considers a range of control models in various simulations, including relaxed models and those concerned with direction and magnitude velocity commands. He also addresses questions of time, cost, and scalability. The book clearly demonstrates what the future challenges are and provides the tools to meet them

Modeling, Analysis and Control of Fuzzy Systems

For the development of the field of fuzzy control systems, techniques for modeling fuzzy systems need to be developed, which makes analysis of the system and the design of control laws systematic. In this paper, a new model of fuzzy systems is proposed which is a variation of “Tagaki and Sugeno\u27s fuzzy model”. Analysis of this model in terms of stability, controllability, observability etc. Is much simpler. It also makes model-based control design easier, while retaining the derivations of connections of fuzzy blocks for piecewise continuous polynomial membership functions. Although the model is easier to analyze, it can represent highly nonlinear dynamics

Integral Action for Chattering Reduction and Error Convergence in Sliding Mode Control

Sliding mode control is a standard approach to tackle the parametric and modeling uncertainities of a non-linear system. However, the robust control obtained by using sliding mode has a price, which is the high frequency chattering encountered during the digital implementation of the control. The idea of introducing a boundary layer around the switching surface and approximating a continuous control inside it has been extended for different kinds of systems. The systems should be analyzed to ascertain which continuous law is appropriate within the boundary layer. In this paper the effect of various continuous control approximations within the boundary layer to chattering and error convergence in different systems is studied

Feedback Control Design and Stability Analysis of One Dimensional Evacuation System

This paper presents design of nonlinear feedback controllers for two different models representing evacuation dynamics in one dimension. The models presented here are based on the laws of conservation of mass and momentum. The first model is the classical one equation model for a traffic flow based on conservation of mass with a prescribed relationship between density and velocity. The other model is a two equation model in which the velocity is independent of the density. This model is based on conservation of mass and momentum. The equations of motion in both cases are described by nonlinear partial differential equations. We address the feedback control problem for both models. The objective is to synthesize a nonlinear distributed feedback controller that guarantees stability of a closed loop system. The problem of control and stability is formulated directly in the framework of partial differential equations. Sufficient conditions for Lyapunov stability for distributed control are derived

Study of Driver’s Behavior Using Physiological Signals

Introduction According to National Transportation Safety Board (NTSB) 58% of roadway crashes are safety related. Factors such as fatigue and drowsiness causes significance decline in driver’s abilities of perception, recognition and vehicle control. Exposes driver’s to a higher level of risk while driving with these conditions. Being awake for 18 hours is equivalent to a Blood Alcohol Concentration (BAC) of 0.08%

Incident Management in Intelligent Transportation Systems

Since the conception of Intelligent Transportation Systems (ITS) in the 1980s, many transportation researchers have also worked on the development of incident management models and integrated systems for real-time operations. ITS created the required infrastructure for collecting, processing, and managing real-time traffic data that can be used to develop on-line incident management strategies. This book provides the reader with a broad picture of the overall incident management process in the context of ITS along with a quick review of the models and systems developed by numerous researchers worldwide. This book is a direct result of the long-term incident management research efforts at the Virginia Tech Center for Transportation Research. The initial work was performed under work order #DTFH71-DP86-VA-20 given to VDOT by FHWA. In addition to this initial contract, the FHWA Intelligent Transportation Systems Research Center of Excellence (RCE) program and VDOT sponsored different parts of the research described here

Mobile Robotic Car Design

This book enables hobbyists to build their own robotic car, about 1/10th the size of a standard vehicle, for under $1000 -- and learn the mechanical and electrical theory and design secrets behind it. * Step-by-step instructions for building the vehicle, from theory and design to hardware and software implementation * Discussions on mathematical modeling, control design theory, sensors, servos, motors, controllers, and environmental sensing * Printed circuit board files for the car can be downloaded for free from accompanying websit

Modeling and Control of Electromagnetic Brakes for Enhanced Braking Capabilities for Automated Highway Systems

In automatic highway systems, a faster response and a robust braking system are crucial part of the overall automatic control of the vehicle. This paper describes electromagnetic brakes as a supplementary system for regular brakes. This system provides better time for emergency situations, and in general keeps the friction brake working longer and safer. A modified mathematical model for electromagnetic brakes is proposed to describe their static characteristics (angular speed versus brake torque). The performance of the modified mathematical model is better than the other three models available in the literature. To control the brakes, a robust sliding mode controller is designed to maintain the wheel slip at a given value. Simulations show that the controller designed is capable of controlling the vehicle with parameter deviations and disturbances

Vehicle Merging Control Design for an Automated Highway System

The merging process in an automated highway system (AHS) is divided into a speed adjustment stage and a lane merging stage. Three important parameters, namely acceptability, availability and pursuability, are analyzed to characterize the AHS lane gap features for the ideal, smooth and safe merging of the ramp vehicles. Three control guidance laws, namely linear, optimal and parabolic speed profiles, are developed to describe the desired behaviors of the merging vehicle based on the merging quality and safety. The desired states of the merging vehicle are generated through the outer loop by specified control guidance law. The tracking errors compared with desired states are eliminated by the proper design of controllers in the inner loop. Both longitudinal and lateral controllers are designed using sliding mode control theory that can handle the nonlinear and model uncertainties of the vehicle dynamics. The simulation results show encouraging results