Non-linear Control for Underactuated Mechanical Systems [Paperback]

This book deals with the application of modern control theory to some important underactuated mechanical systems, from the inverted pendulum to the helicopter model. It will help readers gain experience in the modelling of mechanical systems and familiarize with new control methods for non-linear systems.

1 Introduction.- 1.1 Motivation.- 1.2 Outline of the book.- 1.2.1 Energy-based control approaches for several underactuated mechanical systems.- 1.2.2 The hovercraft model, the PVTOL aircraft and the helicopter.- 2 Theoretical preliminaries.- 2.1 Lyapunov stability.- 2.2 Lyapunov direct method.- 2.3 Passivity and dissipativity.- 2.4 Stabilization.- 2.5 Non-holonomic systems.- 2.6 Underactuated systems.- 2.7 Homoclinic orbit.- 3 The cart-pole system.- 3.1 Introduction.- 3.2 Model derivation.- 3.2.1 System model using Newtons second law.- 3.2.2 Euler-Lagranges equations.- 3.3 Passivity of the inverted pendulum.- 3.4 Controllability of the linearized model.- 3.5 Stabilizing control law.- 3.5.1 The homoclinic orbit.- 3.5.2 Stabilization around the homoclinic orbit.- 3.5.3 Domain of attraction.- 3.3 Stability analysis.- 3.4 Simulation results.- 3.5 Experimental results.- 3.6 Conclusions.- 4 A convey-crane system.- 4.1 Introduction.- 4.2 Model.- 4.3 Passivity of the system.- 4.4 Damping oscillations control law.- 4.5 Asymptotic stability analysis.- 4.6 Simulation results.- 4.7 Concluding remarks.- 5 The pendubot system.- 5.1 Introduction.- 5.2 System dynamics.- 5.2.1 Equations of motion via Euler-Lagrange formulation.- 5.3 Passivity of the pendubot.- 5.4 Linearization of the system.- 5.5 Control law for the top position.- 5.5.1 The homoclinic orbit.- 5.5.2 Stabilization around the homoclinic orbit.- 5.6 Stability analysis.- 5.7 Simulation results.- 5.8 Experimental results.- 5.9 Conclusions.- 6 The Furuta pendulum.- 6.1 Introduction.- 6.2 Modeling of the system.- 6.2.1 Energy of the system.- 6.2.2 Euler-Lagrange dynamic equations.- 6.3.3 Passivity prol³ƒ