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

All-propulsion design of the drag-free and attitude control of the European satellite GOCE

This paper concerns the drag-free and attitude control (DFAC) of the European Gravity field and steady-state Ocean Circulation Explorer satellite (GOCE), during the science phase. GOCE aims to determine the Earth's gravity field with high accuracy and spatial resolution, through complementary space techniques such as gravity gradiometry and precise orbit determination. Both techniques rely on accurate attitude and drag-free control, especially in the gradiometer measurement bandwidth (5-100mHz), where non-gravitational forces must be counteracted down to micronewton, and spacecraft attitude must track the local orbital reference frame with micro-radian accuracy. DFAC aims to enable the gravity gradiometer to operate so as to determine the Earth's gravity field especially in the so-called measurement bandwidth (5-100mHz), making use of ion and micro-thruster actuators. The DFAC unit has been designed entirely on a simplified discrete-time model (Embedded Model) derived from the fine dynamics of the spacecraft and its environment; the relevant control algorithms are implemented and tuned around the Embedded Model, which is the core of the control unit. The DFAC has been tested against uncertainties in spacecraft and environment and its code has been the preliminary model for final code development. The DFAC assumes an all-propulsion command authority, partly abandoned by the actual GOCE control system because of electric micro-propulsion not being fully developed. Since all-propulsion authority is expected to be imperative for future scientific and observation missions, design and simulated results are believed to be of interest to the space communit

Embedded Model Control calls for disturbance modeling and rejection

Robust control design is mainly devoted to guaranteeing the closed-loop stability of a model-based control law in the presence of parametric uncertainties. The control law is usually a static feedback law which is derived from a (nonlinear) model using different methodologies. From this standpoint, stability can only be guaranteed by introducing some ignorance coefficients and restricting the feedback control effort with respect to the model-based design. Embedded Model Control shows that, the model-based control law must and can be kept intact in the case of uncertainty, if, under certain conditions, the controllable dynamics is complemented by suitable disturbance dynamics capable of real-time encoding the different uncertainties affecting the ‘embedded model', i.e. the model which is both the design source and the core of the control unit. To be real-time updated the disturbance state is driven by an unpredictable input vector, the noise, which can only be estimated from the model error. The uncertainty-based (or plant-based) design concerns the noise estimator, so as to prevent the model error from conveying uncertainty components (parametric, cross-coupling, neglected dynamics) which are command-dependent and thus prone to destabilizing the controlled plant, into the embedded model. Separation of the components in the low and high frequency domain by the noise estimator itself allows stability recovery and guarantee, and the rejection of low frequency uncertainty components. Two simple case studies endowed with simulated and experimental runs will help to understand the key assets of the methodolog

Robust control stability using the error loop

The paper briefly formulates the error loop as a tool for designing robust stability control systems in front of structured and unstructured uncertainties. The error loop indicates that a tool for accommodating such uncertainties is the noise estimator, which is the unique feedback channel from plant to control. It is shown that the causality constraint preventing perfect cancellation of causal uncertainties (unknown disturbance), makes also control law to play a role, offering a further degree of freedom. Employing asymptotic expansions of the closed-loop transfer functions, simple, explicit design formulae derive from stability inequalities: they relate closed-loop eigenvalues to model parameter and requirements. A simple example is provided from a ball and beam plan

The four-tank benchmark: a simple solution by embedded model control

The four-tank benchmark is a multivariate and nonlinear control problem which has been widely studied in the literature. Two pairs of tanks in series are supplied by two pumps. Under certain configurations, the Embedded Model Control approach provides a simple decoupled solution by separately controlling the two output tank levels and treating the input flow as a partly unknown disturbance. Neglected dynamics in a form of unknown delays both in sensors and actuator dynamics is considered. The core of the control unit is a discrete-time embedded model consisting of unknown disturbance dynamics and partly known nonlinear interactions. The embedded model is driven by the plant command and by a feedback vector which is retrieved from the model error. The feedback is capable of keeping updated the unknown disturbance prediction, ready to be cancelled by the control law. The control gains are tuned using two sets of closed-loop eigenvalues in order to trade-off between disturbance rejection and robust stability. Simulated runs under different tank interactions prove design effectiveness

A NEW APPROACH TO DISCRETE-EVENT DYNAMIC SYSTEM THEORY

The paper presents an original formulation of discrete-event dynamic systems (DEDS) strictly consistent with the Kalman definition of dynamic systems. The paper starts with a clear definition of event as a pair (occurrence time, fact), where the time is a real number and the fact is an element of a set with algebraic properties. The introduction of the concept of event sequences and of suitable operations over their set allows to formulate DEDS as causal operators transforming input e\'ent sequences into output event sequences. The definition of a state for such operator allows to give a state representation of the input-output relation. The state representation is a state equation as in the standard continuous or discrete-time systems, and allows to compute the free and the forced responses of the system. The paper terminates by providing the elementary stability defmitions and the state equations of linear and time-invariant DEDS