Path-tracking of a tractor-trailer vehicle along rectilinear and circular paths: A Lyapunov-based approach

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ESP for Suppression of Jackknifing in an Articulated Bus

The Electronic Stability Program (ESP) is becoming increasingly popular in vehicles as a means to prevent spin-out and lane departure accidents, and is nowadays a standard feature in most cars. From 2012 the ESP will also be a standard feature in buses. As a first step, this thesis is dedicated to implementing an ESP for an articulated bus in simulation using Matlab/Simulink. The core of the ESP is a yaw rate controller that calculates a moment about the center of gravity of the front part of the bus to stabilize it. Integrated in the ESP are also an Anti-lock Braking System (ABS) and an Anti-Spin Regulation (ASR) system, which are model-based controllers that produce the brake pressures needed to achieve the desired moment. For the articulated bus it is clear that the fact that the bus consists of two parts makes the problem of stabilizing the bus more difficult. Furthermore, for articulated vehicles it is known that the risk of having the vehicle folding, known as jackknifing, during cornering is a major problem. However, the ESP is found to stabilize the bus for a large number of maneuvers and loading configurations, as well as suppressing jackknifing

On Observer-Based Control of Nonlinear Systems

Filtering and reconstruction of signals play a fundamental role in modern signal processing, telecommunications, and control theory and are used in numerous applications. The feedback principle is an important concept in control theory. Many different control strategies are based on the assumption that all internal states of the control object are available for feedback. In most cases, however, only a few of the states or some functions of the states can be measured. This circumstance raises the need for techniques, which makes it possible not only to estimate states, but also to derive control laws that guarantee stability when using the estimated states instead of the true ones. For linear systems, the separation principle assures stability for the use of converging state estimates in a stabilizing state feedback control law. In general, however, the combination of separately designed state observers and state feedback controllers does not preserve performance, robustness, or even stability of each of the separate designs. In this thesis, the problems of observer design and observer-based control for nonlinear systems are addressed. The deterministic continuous-time systems have been in focus. Stability analysis related to the Positive Real Lemma with relevance for output feedback control is presented. Separation results for a class of nonholonomic nonlinear systems, where the combination of independently designed observers and state-feedback controllers assures stability in the output tracking problem are shown. In addition, a generalization to the observer-backstepping method where the controller is designed with respect to estimated states, taking into account the effects of the estimation errors, is presented. Velocity observers with application to ship dynamics and mechanical manipulators are also presented

THE SYNTHESIS OF STEERING RULES FOR STABILIZING ROAD TRAIN REVERSE MOTION TO SOLVE THE TASK OF REACHING A SET GOAL

Mathematical models of a road train are developed to study both its direct and reverse motion. The laws for the automatic steering system turning vehicle steering wheels to achieve the required trailer direction when moving reverse are synthesized. A road train with a hitching unit on the tractor truck rear axle directly schematic constructions (an “on-axle hitching” model) are used. The kind of kinematic mathematic model for describing a road train moving reverse at low speeds without wheels side slipping is satisfactory. In this condition its motion is defined by geometry only independent from masses, momentums and friction forces. The steering laws are synthesized with the help of alpha-stabilizing approach, according to Lyapunov’s direct method using fuzzy logics mathematical tool and a solution method depending on the Riccati equation state (SDRE). The task of reaching a set goal has been solved by calculating the folding angle when the target belongs to the calculated path for the case of curvilinear motion and via calculating the matching tractor truck and trailer orientation angles for direct motion. The received results have been rendered as phase portraits in the Maple environment and meshes in Meshlab, simulated in Unity 3D and with a robotic installation getting control information generated automaticall

Exponential Stabilization of Driftless Nonlinear Control Systems

This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form, xdot = X1(x)u1 + .... + Xm(x)um, x ∈ ℝ^n Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a non-standard dilation. Even though the approximation can be given a coordinate-free interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the closed-loop system. The stability achieved is called p-exponential stability. The closed-loop system is stable and the equilibrium point is exponentially attractive. This extended notion of exponential stability is required since the feedback, and hence the closed-loop system, is not Lipschitz. However, it is shown that the convergence rate of a Lipschitz closed-loop driftless system cannot be bounded by an exponential envelope. The synthesis methods generate feedbacks which are smooth on ℝ^n \ {0}. The solutions of the closed-loop system are proven to be unique in this case. In addition, the control inputs for many driftless systems are velocities. For this class of systems it is more appropriate for the control law to specify actuator forces instead of velocities. We have extended the kinematic velocity controllers to controllers which command forces and still p-exponentially stabilize the system. Perhaps the ultimate justification of the methods proposed in this thesis are the experimental results. The experiments demonstrate the superior convergence performance of the p-exponential stabilizers versus traditional smooth feedbacks. The experiments also highlight the importance of transformation conditioning in the feedbacks. Other design issues, such as scaling the measured states to eliminate hunting, are discussed. The methods in this thesis bring the practical control of strongly nonlinear systems one step closer

Flat systems, equivalence and trajectory generation

Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft