Pulse-width predictive control for LTV systems with application to spacecraft rendezvous

Abstract

This work presents a model predictive controller (MPC) that is able to handle linear time-varying (LTV) plants with PWM control. The MPC is based on a planner that employs a PAM or impulsive approximation as a hot-start and then uses explicit linearization around successive PWM solutions for rapidly improving the solution by means of linear programming. As an example, the problem of rendezvous of spacecraft for eccentric target orbits is considered. The problem is modeled by the LTV Tschauner-Hempel equations, whose transition matrix is explicit; this is exploited by the algorithm for rapid convergence. The efficacy of the method is shown in a simulation study.

A flatness-based predictive controller for six-degrees of freedom spacecraft rendezvous

“…Possible future research lines include the following. First, it will be of great interest to consider on/off thrusters as it is done in [10]. This will cause continuous coupling between translational and rotational motion since the vehicle will be spinning when the thrusters are fired.…”

“…This transition matrix is computed by means of its fundamental matrix and inverse without need of numerical integration. In this work, following [10] (note that the axes are not the same as in this work), the Yamanaka-Ankersen state transition matrix is expressed by means of the eccentric anomaly E,…”

“…Typically, the rendezvous problem has been widely studied just considering orbit control making the assumption that translational and rotational motions are decoupled. This problem has been usually tackled by means of direct transcription methods which transform the optimal control problem into a discrete optimization problem as in [6,7,8,9,10] among others. The main advantage of these methods, against indirect ones, is that several kinds of constraints can be easily added to the problem such as approach corridors through the docking axis (V-bar or R-bar guidance), way-points, thrust direction inhibition, obstacle avoidance or fault-tolerant trajectories.…”

A three-step decomposition method for solving the minimum-fuel geostationary station keeping of satellites equipped with electric propulsion

“…In order to counteract uncertainties affecting the control law, the use of Model Predictive Control algorithms is proposed in [29,30]. To deal with on-off models of thrusts, the references [31,32] use the Pulse Width Modulation technique to generate rectangular profiles from a continuous one. [18] has formulated a method based on differential inclusion, and a first avenue for the use of decomposition methods to solve the problem is given in [19].…”

Integer Programming for Optimal Control of Geostationary Station Keeping of Low-Thrust Satellites

“…For this kind of approaches integrating the satellite dynamic, the state and the control variables are discretised to produce a non linear programming problem and get an optimal open loop control. To deal with onoff models of the thrusts, rectangular profiles may be generated from a continuous one with the Pulse Width Modulation technique (see Vazquez et al (2015) and the references therein). Losa et al (2005) has formulated a method based on differential inclusion and Losa et al (2006) and Gazzino et al (2016) have implemented a decomposition technique.…”