Regulation of magnetically actuated satellites using model predictive control with disturbance modelling

The problem of magnetic attitude regulation of low Earth orbiting satellites is addressed using model predictive control. This paper considers extending the current literature within this area by combining a standard predictive controller with a suitable disturbance model. For low Earth orbiting satellites the disturbances due to the external environment are very significant and consideration of these torques within the control law is imperative to obtain the best possible controller performance. In order to obtain an estimate of the external disturbance, a state estimator of varying complexity is used. This estimator initially assumes that the disturbances acting on the satellite remain constant with time, but this assumption is then improved to assume harmonic variation of the disturbance. Simulations show that inclusion of a feed-forward element to the control offers notable performance benefits. Interestingly, increasing the complexity of the disturbance model seems to offer little improvement in performance and a simple constant disturbance model provides a suitable solution to the problem while maintaining simplicity of the state estimator

Attitude control of magnetically actuated satellites with an uneven inertia distribution

This paper addresses magnetic attitude control of a satellite with one axis of inertia significantly lower than that of the other two. With onboard resources often limited, this paper considers the development of an effective control strategy that remains easy to implement. Often used in this type of application, the classical ‘torque-projection’ approach is shown to be unsuitable for satellites with an uneven inertia distribution. To tackle the weaknesses in this approach a new ‘weighted’ PD approach is proposed, with the control torque determined through minimization of a simple cost function. Through a similar philosophy, a feed-forward compensator is designed to supplement the feedback control and improve the disturbance rejection characteristics of the controller. Floquet analysis is used to verify stability of the control strategy for the nominal case and satellites with uncertainties. Simulations carried out on a high fidelity model demonstrate the effectiveness of the proposed control law and the significant performance benefits offered over existing approaches

PD control of magnetically actuated satellites with uneven inertia distribution

This paper considers PD attitude control of magnetically actuated satellites where one axis of inertia is considerably lower than that of the other two. The classic ‘torque-projection’ method of implementing the control is unsuitable for this configuration as the nature of the torque projection controller places little significance on the low inertia axis. This paper proposes a modification to the PD approach by determining the dipole moments through minimisation of a performance index rather than projection onto the magnetic field orthogonal. This allows fairer consideration of the low inertia axis and leads to improved performance of the feedback control. This approach is taken further by introducing an element of feed-forward control to improve the disturbance rejection properties of the system. In a similar way the required feed-forward compensation is determined through minimisation of an appropriate performance index. Combination of the feed-forward and feedback control successfully regulates the satellite attitude when assessed using a high fidelity simulation model. Overall this paper presents a systematic approach to the design of an effective and easy to implement attitude control system for a satellite with an uneven inertia distribution

Model predictive control of low Earth-orbiting satellites using magnetic actuation

This paper presents a model predictive control approach for regulating the attitude of magnetically actuated satellites. Unlike other contributions in this area, a predictive control approach is developed which guarantees closed-loop stability of satellite configurations with unstable open-loop pitch dynamics. With the pitch axis being unstable, two magnetic dipoles are used exclusively for regulation of this axis. This allows the dynamics to be treated as a linear time-invariant system, and a simple proportional–derivative (PD) scheme is implemented. A model predictive controller is designed to regulate the lateral dynamics, with a Lyapunov function derived to guarantee asymptotic stability of the closed-loop system. The regulation of the lateral dynamics is achieved with a singe dipole moment, with a novel reformulation of the lateral dynamics also providing an explicit link between the two controllers. Simulations demonstrate the effectiveness and stability of the proposed algorithm when applied to the European Space Agency’s GOCE satellite

Model predictive control of low earth orbiting spacecraft with magneto-torquers

The problem of attitude control using magnetic torque rods is addressed, in order to demonstrate predictive control as a suitable and effective technique of magnetic attitude control. The study addresses the key issues of magnetic field modeling, controller stability and implementation. Two controller designs are implemented, the first adopting an MPC approach with a constant magnetic field assumption, while the second method includes the true variation of the magnetic field within the control law. Both methods demonstrate significantly improved performance over PD control with the inclusion of the true magnetic field variation leading to the best results. Controller stability is considered with and without terminal penalty within the cost function. Floquet analysis demonstrates both methods to be stable, however the terminal penalty based method leads to a more stable controller

Regulation of Magnetically Actuated Satellites using Model Predictive Control with Disturbance Modelling

The problem of magnetic attitude regulation of low Earth orbiting satellites is addressed using model predictive control. This paper considers extending the current literature within this area by combining a standard predictive controller with a suitable disturbance model. For low Earth orbiting satellites the disturbances due to the external environment are very significant and consideration of these torques within the control law is imperative to obtain the best possible controller performance. In order to obtain an estimate of the external disturbance, a state estimator of varying complexity is used. This estimator initially assumes that the disturbances acting on the satellite remain constant with time, but this assumption is then improved to assume harmonic variation of the disturbance. Simulations show that inclusion of a feed-forward element to the control offers notable performance benefits. Interestingly, increasing the complexity of the disturbance model seems to offer little improvement in performance and a simple constant disturbance model provides a suitable solution to the problem while maintaining simplicity of the state estimator

Model predictive control of low earth orbiting spacecraft with magneto-torquers

The problem of attitude control using magnetic torque rods is addressed, in order to demonstrate predictive control as a suitable and effective technique of magnetic attitude control. The study addresses the key issues of magnetic field modeling, controller stability and implementation. Two controller designs are implemented, the first adopting an MPC approach with a constant magnetic field assumption, while the second method includes the true variation of the magnetic field within the control law. Both methods demonstrate significantly improved performance over PD control with the inclusion of the true magnetic field variation leading to the best results. Controller stability is considered with and without terminal penalty within the cost function. Floquet analysis demonstrates both methods to be stable, however the terminal penalty based method leads to a more stable controller

Surgical Success judged by two criteria IOP≤16, not on ocular hypotensive treatment and ≤21mmHg at different follow up intervals.

<p>Surgical Success judged by two criteria IOP≤16, not on ocular hypotensive treatment and ≤21mmHg at different follow up intervals.</p

Referral, Inclusion and Exclusion criteria.

<p>Referral, Inclusion and Exclusion criteria.</p

Flow diagram of recruitment and follow-up.

<p>Flow diagram of recruitment and follow-up.</p