Nonlinear Control and Analytical Mechanics: A Computational Approach (CD-Rom Included)(Control Engineering)

The features of the book include: integrated analytical mechanics and non-linear control; symbolic computing software tools for modelling and control system design; multiple levels of examples, ranging from simple, illustrative examples to true applications of professional interest. By simultaneously considering both mechanics and control we can achieve a fuller appreciation of the underlying geometric ideas and constructions that are common to both. Control theory has had a fruitful association with analytical mechanics from its birth in the late 19th century. That historical relationship has been reaffirmed during the past two decades with the emergence of a geometric theory for non-linear control systems closely linked to the modern geometric formulation of analytical mechanics. Not surprisingly, the shared evolution of these fields has paralleled the needs of technology. Today, mechanicians and control engineers are brought together in fields like space systems engineering, robotics, ground and sea vehicle design and biomechanics. Consequently, our integrated approach provides a rich set of models and control design examples that are of contemporary and practical interest. We emphasise symbolic computing because it is essential for working with non-linear, parameter-dependent systems and it is a relatively new tool for engineers. Symbolic computing does not replace numerical computing. It supplements and enhances it. Recognising the distinction between symbolic and numerical computing and how best to integrate them is a significance challenge. We will use symbolic computing for several purposes: basic mathematical operations (like implement a coordinate transformation or compute a Lie bracket), to build explicit mathematical models, to simplify models e.g. via Taylor linearisation or symmetry reduction), to generate numerical simulation code, to implement non-linear control constructions (such as compute inverse system or perform feedback linearisation), to generate numerical code for implementing controllers. In this work we will employ examples of various levels of complexity from simple examples that illustrate a theoretical point in a transparent way to examples with detailed models for which results are too complex to exhibit in print, but can nevertheless be manipulated using a computer. we will provide examples of the latter type using electronic media, specifically Mathematica notebooks.

Table of Contents:
Part I Introduction. Part 2 Preliminary concepts and tools: symbolic and numerical computation; Mathematica Basics. Part 3 Geometry: manifolds and flows; distributions; Lie groups. Part 4 Kinematics: kinematics of joints; kinematics of chains and trees. Part 5 Dynamics: Langarian systems; Poincare's equations; constraints and holonomy. Part 6 Linearisation and stability: Taylor linearisation; parameterised linear families; stability analysis. Part 7 Linear control systems. Part 8 Smooth non-linear control systems: state transformations; controllability; observability; exact feedback linearisation; input-output linearisation. Part 9 Variables structure control systems: adaptive control. Appendix: CD contents and software installation. Notes; bibliography; symbols and definitions.