Discrete-Time Nonlinear Attitude Tracking Control of Spacecraft

Recent space programs require agile and large-angle attitude maneuvers for applications in various fields such as observational astronomy. To achieve agility and large-angle attitude maneuvers, it will be required to design an attitude control system that takes into account nonlinear motion because agile and large-angle rotational motion of a spacecraft in such missions represents a nonlinear system. Considerable research has been done about the nonlinear attitude tracking control of spacecraft, and these methods involve a continuous-time control framework. However, since a computer, which is a digital device, is employed as a spacecraft controller, the control method should have discrete-time control or sampled-data control framework. This chapter considers discrete-time nonlinear attitude tracking control problem of spacecraft. To this end, a Euler approximation system with respect to tracking error is first derived. Then, we design a discrete-time nonlinear attitude tracking controller so that the closed-loop system consisting of the Euler approximation system becomes input-to-state stable (ISS). Furthermore, the exact discrete-time system with a derived controller is indicated semiglobal practical asymptotic (SPA) stable. Finally, the effectiveness of proposed control method is verified by numerical simulations

Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

This paper presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its strength lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonlinear, its equivalent convex formulation is proposed utilizing state-dependent coefficient parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L₂-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H∞, and given nonlinear control for spacecraft attitude control and synchronization problems

Some applications of advanced nonlinear control techniques.

Jia Peng.Thesis (M.Phil.)--Chinese University of Hong Kong, 2005.Includes bibliographical references (leaves 85-87).Abstracts in English and Chinese.Abstract --- p.ivChapter 1 --- Introduction --- p.1Chapter 1.1 --- Overview of Output Regulation Problem --- p.2Chapter 1.2 --- Attitude Tracking Control of Rigid Spacecraft --- p.3Chapter 1.3 --- Overview of Continuous-time Nonlinear H∞ Control --- p.4Chapter 1.4 --- Overview of Discrete-time Nonlinear Hq∞ Control --- p.6Chapter 1.5 --- Flight Control in Windshears --- p.8Chapter 1.6 --- Nonlinear Benchmark System --- p.9Chapter 1.7 --- Outline of the Work --- p.11Chapter 2 --- Attitude Control and Asymptotic Disturbance Rejection of Rigid Spacecraft --- p.12Chapter 2.1 --- Model Description --- p.12Chapter 2.2 --- Problem Formulation --- p.16Chapter 2.3 --- Preliminaries of General Framework for Global Robust Output Regulation --- p.17Chapter 2.4 --- Application of Global Robust Output Regulation --- p.21Chapter 2.4.1 --- Case I: without unknown parameters --- p.21Chapter 2.4.2 --- Case II: with unknown parameters --- p.26Chapter 2.5 --- Simulation --- p.34Chapter 2.5.1 --- Case I: without unknown parameters --- p.34Chapter 2.5.2 --- Case II: with unknown parameters --- p.36Chapter 2.6 --- Conclusions --- p.38Chapter 3 --- Application of Approximation Continuous-time Nonlinear H∞ Control Law --- p.45Chapter 3.1 --- Preliminaries of Approximation Continuous-time Nonlinear Hq∞ Control Law --- p.45Chapter 3.2 --- Disturbance Attenuation of Flight Control System in Windshears --- p.50Chapter 3.2.1 --- Design of Control Law --- p.51Chapter 3.2.2 --- Computer Simulation --- p.56Chapter 3.3 --- Conclusions --- p.57Chapter 4 --- Application of Approximation Discrete-time Nonlinear H∞ Control Law --- p.65Chapter 4.1 --- Preliminaries of Approximation Discrete-time Nonlinear H∞ Control Law --- p.66Chapter 4.2 --- Explicit Expression of u --- p.69Chapter 4.3 --- Disturbance Attenuation of RTAC System --- p.73Chapter 4.4 --- Computer Simulation --- p.78Chapter 4.5 --- Conclusions --- p.80Chapter 5 --- Conclusions --- p.83Bibliography --- p.85A Programs --- p.88Vita --- p.11

Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

This paper presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito stochastic nonlinear systems and Lagrangian systems. Its strength lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonlinear, its equivalent convex formulation is proposed utilizing state-dependent coefficient parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L₂-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H∞, and given nonlinear control for spacecraft attitude control and synchronization problems

Drag-free and attitude control for the GOCE satellite

The paper concerns Drag-Free and Attitude Control of the European satellite Gravity field and steady-state Ocean Circulation Explorer (GOCE) during the science phase. Design has followed Embedded Model Control, where a spacecraft/environment discrete-time model becomes the realtime control core and is interfaced to actuators and sensors via tuneable feedback laws. Drag-free control implies cancelling non-gravitational forces and all torques, leaving the satellite to free fall subject only to gravity. In addition, for reasons of science, the spacecraft must be carefully aligned to the local orbital frame, retrieved from range and rate of a Global Positioning System receiver. Accurate drag-free and attitude control requires proportional and low-noise thrusting, which in turn raises the problem of propellant saving. Six-axis drag-free control is driven by accurate acceleration measurements provided by the mission payload. Their angular components must be combined with the star-tracker attitude so as to compensate accelerometer drift. Simulated results are presented and discusse