A Sampled-Data Form of Incremental Nonlinear Dynamic Inversion for Spacecraft Attitude Control

This paper presents a sampled–data form of the recently reformulated incremental nonlinear dynamic inversion (INDI) applied for robust spacecraft attitude control. INDI is a combined model– and sensor–based approach mostly applied for attitude control that only requires an accurate control effectiveness model and measurements of the state and some of its derivatives. This results in a reduced dependency on exact knowledge of system dynamics which is known as a major disadvantage of model–based nonlinear dynamic inversion controllers. However, most of the INDI derivations proposed in the literature assume a very high sampling rate of the system and its controller while also not explicitly considering the available sampling time of the digital control computer. Neglecting the sampling time and its effect in the controller derivations can lead to stability and performance issues of the resulting closed–loop nonlinear system. Therefore, our objective is to bridge this gap between continuous–time, highly sampled INDI formulations and their discrete, lowly sampled counterparts in the context of spacecraft attitude control where low sampling rates are common. Our sampled–data reformulation allows explicit consideration of the sampling time via an approximate sampled–data model in normal form widely known in the literature. The resulting sampled–data INDI control is still robust up to a certain sampling time since it remains only sensitive to parametric uncertainties. Simulation experiments for this particular problem demonstrate the bridge considered between INDI formulations which allows for low sampling control rates

Time-optimal reorientation for rigid satellite with reaction wheels

This article introduces a time-optimal reorientation manoeuvre controller with saturation constraints on both reaction wheels’ torques and angular momentum. The proposed control scheme consists of two parts. The first part is an open-loop time-minimum reorientation trajectory generated by the Legendre pseudospectral method. Actuator dynamics, saturations on control torques and angular momentums of reaction wheels are taken into account in generating the open-loop optimal trajectory. The second part is a closed-loop tracking control law to track the optimised reference trajectory based on attitude error dynamics with reaction wheel dynamics. Numerical simulations show that reaction wheel dynamics play an important role in attitude manoeuvres. The proposed controller performs better for rest-to-rest reorientation manoeuvre than other existing methods

Optimal control problems solved via swarm intelligence

Questa tesi descrive come risolvere problemi di controllo ottimo tramite swarm in telligence. Grande enfasi viene posta circa la formulazione del problema di controllo ottimo, in particolare riguardo a punti fondamentali come l’identificazione delle incognite, la trascrizione numerica e la scelta del risolutore per la programmazione non lineare. L’algoritmo Particle Swarm Optimization viene preso in considerazione e la maggior parte dei problemi proposti sono risolti utilizzando una formulazione differential flatness. Quando viene usato l’approccio di dinamica inversa, il problema di ottimo relativo ai parametri di trascrizione è risolto assumendo che le traiettorie da identificare siano approssimate con curve B-splines. La tecnica Inverse-dynamics Particle Swarm Optimization, che viene impiegata nella maggior parte delle applicazioni numeriche di questa tesi, è una combinazione del Particle Swarm e della formulazione differential flatness. La tesi investiga anche altre opportunità di risolvere problemi di controllo ottimo tramite swarm intelligence, per esempio usando un approccio di dinamica diretta e imponendo a priori le condizioni necessarie di ottimalitá alla legge di controllo. Per tutti i problemi proposti, i risultati sono analizzati e confrontati con altri lavori in letteratura. Questa tesi mostra quindi the algoritmi metaeuristici possono essere usati per risolvere problemi di controllo ottimo, ma soluzioni ottime o quasi-ottime possono essere ottenute al variare della formulazione del problema.This thesis deals with solving optimal control problems via swarm intelligence. Great emphasis is given to the formulation of the optimal control problem regarding fundamental issues such as unknowns identification, numerical transcription and choice of the nonlinear programming solver. The Particle Swarm Optimization is taken into account, and most of the proposed problems are solved using a differential flatness formulation. When the inverse-dynamics approach is used, the transcribed parameter optimization problem is solved assuming that the unknown trajectories are approximated with B-spline curves. The Inverse-dynamics Particle Swarm Optimization technique, which is employed in the majority of the numerical applications in this work, is a combination of Particle Swarm and differential flatness formulation. This thesis also investigates other opportunities to solve optimal control problems with swarm intelligence, for instance using a direct dynamics approach and imposing a-priori the necessary optimality conditions to the control policy. For all the proposed problems, results are analyzed and compared with other works in the literature. This thesis shows that metaheuristic algorithms can be used to solve optimal control problems, but near-optimal or optimal solutions can be attained depending on the problem formulation