A comparative study of sliding mode control and time-optimal control

Abstract

A comparative study of sliding mode control and time-optimal control for spacecraft attitude control using thrusters is presented. The on-off type thrusters are assumed to be attitude control actuators. Application of time-optimal control theory to the kinematic and dynamic equations of motion leads to a nonlinear two-point boundary value problem. The solution can be computed by iterative numerical methods, but typically, the computing method is not compatible with real-time computing constraints. In this paper, sliding mode control is used for the input of PWPF (Pulse Width and Pulse Frequency) modulator thrusters. The settling times are minimized by tuning the gains of sliding mode control. The sliding mode control is derived using modified Rodrigues parameters. We also derive the upper bound of sliding function for inertia uncertainty and external disturbances. Disturbance accommodating sliding mode control with PWPF is derived to minimize the settling time with inertia uncertainty and external disturbance. Simulation results show that the settling times are shorter than the ones of the sliding mode control with PWPF. INTRODUCTION Spacecraft attitude control for large-angle slewing maneuvers poses a difficult problem, including: the nonlinear characteristics of the governing equation, modeling uncertainty and unexpected external disturbances. Usually, for rapid and coarse attitude maneuvers, on-off type thrusters have been used. Control algorithms can be divided into open-loop systems and closed-loop systems. Application of Graduate Student, Department of Aerospace Engineering, Texas A&M University, College Station, Texas, 77843, Student Member AIAA t Assistant Professor, Department of Aerospace Engineering, Texas A&M University, College Station, Texas, 77843, Senior Member AIAA t Copyright ©1998 The American Institute of Aeronautics and Astronautics, Inc. All rights reserved time-optimal control theory to the kinematic and dynamic equations of motions leads to a nonlinear two-point boundary value problem. Time-optimal control for spacecraft attitude maneuvers is different from the eigenaxis rotation. The solution can be computed by iterative numerical methods, but the computing method is not compatible with real-time computing constraint. Also, it is sensitive with respect to modeling errors and external disturbances. Sliding mode (variable structure) control provides robustness with respect to modeling errors and is an effective method for handling the nonlinear characteristics for attitude control. Vadali presented an optimal sliding manifold using error quaternions. In his paper, two types of actuators, i.e., thrusters and reaction wheels, are used for the spacecraft maneuver. In this paper, the sliding mode control using modified Rodrigues parameters are combined with a PWPF (Pulse Width Pulse Frequency) modulator. The PWPF modulator drives a thruster valve with an on-off pulse sequence having a nearly linear duty cycle with the input amplitude. The settling tune is minimised by tuning the gains in the sliding mode control using standard optimization techniques. One of the drawbacks of sliding mode control is the chattering problem due to disturbance and modeling imprecision. For spacecraft attitude control, chattering may excite the higher frequencies of the spacecraft. Chattering can be settled by smoothing the control input using boundary layer or bandwidth-limited sliding mode control, which was presented by Dwyer and Kirn. However, a globally suitable boundary layer thickness cannot be easily determined. Moreover, for spacecraft attitude control it may be difficult to predict the external disturbances acting on body. When bounded unmodeled external torques are added, the closed-loop system is no longer globally asymptotically stable since a steady-state error is present. The error can be minimized by increasing the correction control gain or decreasing the thickness of the boundary layer in sliding mode control. In this paper we de-