Nonlinear backstepping design for the underactuated TORA system

The nonlinear feedback cascade model of the underactuated translational oscillators with rotating actuator is obtained through a collocated partial feedback linearization and a global change of coordinates. A nonlinear controller is designed with the backsteping technology, which treats the state variables as virtual control inputs to design the virtual controllers step by step. The system stability is proved with the Lyapunov stability theorem. The simulation results show the system under any initial states can be asymptotically stabilized to the origin and the controller has a good control performance

PD control for global stabilization of an n-TORA system

This paper concerns a global stabilization problem for an n-TORA (Translational Oscillator with a Rotational Actuator) system which consists of n carts connected to the fixed walls and each other by n+1 linear springs with each cart having an eccentric rotational proof-mass actuator moving in the horizontal plane. First, this paper derives the motion equation of the n-TORA system. Then, by using Lyapunov stability theory and physical properties of mechanical parameters of the n-TORA system, this paper proves that the global stabilization of the n-TORA system can be achieved by the PD control of the angle of the rotational proof-mass of each TORA. This paper presents numerical simulation results for 2- and 3-TORA systems to validate the result of the global stabilization

Control of the TORA System through the IDA-PBC without Explicit Solution of Matching Equations

This paper presents the control of a translational oscillator with a rotational actuator (TORA) system, in full gravity, through the interconnection and damping assignment passivity-based control (IDA-PBC). The sought goal is to control the underactuated TORA system while reducing the complexity in solving the partial differential equations coming out from the so-called matching equations, which arise from the IDA-PBC. The performance of the designed controller is illustrated through numerical simulations

A Constructive Methodology for the IDA-PBC of Underactuated 2-DoF Mechanical Systems with Explicit Solution of PDEs

This paper presents a passivity-based control strategy dealing with underactuated two-degree-of-freedom (2-DoF) mechanical systems. Such a methodology, which is based on the interconnection and damping assignment passivity-based control (IDA-PBC), rooted within the port-controlled Hamiltonian framework, can be applied to a very large class of underactuated 2-DoF mechanical systems. The main contribution, compared to the previous literature, is that the new methodology does not involve the resolution of any partial differential equation, since explicit solutions are given, while no singularities depending on generalised momenta are introduced by the controller. The proposed strategy is applied to two case studies: a) the stabilisation of a translational oscillator with a rotational actuator (TORA) system; b) the gait generation for an underactuated compass-like biped robot. The performances of the presented solution are evaluated through numerical simulations

Nonlinear control of feedforward systems with bounded signals

Published versio

Dynamical Analysis and Stabilizing Control of Inclined Rotational Translational Actuator Systems

Rotational translational actuator (RTAC) system, whose motions occur in horizontal planes, is a benchmark for studying of control techniques. This paper presents dynamical analysis and stabilizing control design for the RTAC system on a slope. Based on Lagrange equations, dynamics of the inclined RTAC system is achieved by selecting cart position and rotor angle as the general coordinates and torque acting on the rotor as general force. The analysis of equilibriums and their controllability yields that controllability of equilibriums depends on inclining direction of the inclined RTAC system. To stabilize the system to its controllable equilibriums, a proper control Lyapunov function including system energy, which is used to show the passivity property of the system, is designed. Consequently, a stabilizing controller is achieved directly based on the second Lyapunov stability theorem. Finally, numerical simulations are performed to verify the correctness and feasibility of our dynamical analysis and control design

Investigation of feedforward neural networks and its applications to some nonlinear control problems.

Ng Chi-fai.Thesis submitted in: December 2000.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 69-73).Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiList of Figures --- p.viiiList of Tables --- p.ixChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation and Objectives --- p.1Chapter 1.2 --- Principles of Feedforward Neural Network Approximation --- p.1Chapter 1.3 --- Contribution of The Thesis --- p.5Chapter 1.4 --- Outline of The Thesis --- p.5Chapter 2 --- Feedforward Neural Networks: An Approximator for Nonlinear Control Law --- p.8Chapter 2.1 --- Optimization Methods Applied in Feedforward Neural Network Approximation --- p.8Chapter 2.2 --- Example in Supervised Learning --- p.10Chapter 2.2.1 --- Problem Description --- p.10Chapter 2.2.2 --- Neural Network Configuration and Training --- p.12Chapter 2.2.3 --- Simulation Result --- p.13Chapter 3 --- Neural Based Approximation of Center Manifold Equations --- p.19Chapter 3.1 --- Solving Center Manifold Equations by Feedforward Neural Network Approx- imation --- p.19Chapter 3.2 --- Example --- p.21Chapter 3.2.1 --- Problem Description --- p.21Chapter 3.2.2 --- Simulation Result --- p.24Chapter 3.2.3 --- Discussion --- p.24Chapter 4 --- Connection of Center Manifold Equations to Output Regulation Problem --- p.29Chapter 4.1 --- Output Regulation Theory --- p.29Chapter 4.2 --- Reduction of Regulator Equation into Center Manifold Equations --- p.31Chapter 5 --- Application to the Control Design of Ball and Beam System --- p.34Chapter 5.1 --- Problem Description --- p.34Chapter 5.2 --- Neural Approximation Solution of Center Manifold Equations --- p.37Chapter 5.3 --- Simulation Results --- p.38Chapter 5.4 --- Discussion --- p.45Chapter 6 --- Neural Based Disturbance Rejection of Nonlinear Benchmark Problem (TORA System) --- p.48Chapter 6.1 --- Problem Description --- p.48Chapter 6.2 --- Neural based Approximation of the Center Manifold Equations of TORA System --- p.51Chapter 6.3 --- Simulation Results --- p.53Chapter 6.4 --- Discussion --- p.59Chapter 7 --- Conclusion --- p.62Chapter 7.1 --- Future Works --- p.63Chapter A --- Center Manifold Theory --- p.64Chapter B --- Relation between Center Manifold Equation and Output Regulation Prob- lem --- p.66Biography --- p.68References --- p.6

The output regulation problem : a convergent dynamics approach

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