Fractional Order Modeling and Control of a Flexible Satellite

Researchers have engrossed fractional-order modeling because of its ability to capture phenomena that are nearly impossible to describe owing to its long-term memory and inherited properties. Motivated by the research in fractional modeling, a fractional-order prototype for a flexible satellite whose dynamics are governed by fractional differential equations is proposed for the first time. These relations are derived using fractional attitude dynamic description of rigid body simultaneously coupled with the fractional Lagrange equation that governs the vibration of the appendages. Two attitude controls are designed in the presence of the faults and uncertainties of the system. The first is the fractional-order feedback linearization controller, in which the stability of the internal dynamics of the system is proved. The second is the fractional-order sliding mode control, whose asymptotic stability is demonstrated using the quadratic Lyapunov function. Several nonlinear simulations are implemented to analyze the performance of the proposed controllers.

Virtual Calibration of CO2 and Pollutant Emissions of a High-Performance PHEV using Model-in-the-Loop Methodology

The study analyses the calibration process of a newly developed high-performance plug-in hybrid electric passenger car powertrain. The complexity of modern powertrains and the more and more restrictive regulations regarding pollutant emissions are the primary challenges for the calibration of a vehicle’s powertrain. In addition, the managers of OEM need to know as earlier as possible if the vehicle under development will meet the target technical features (emission included). This leads to the necessity for advanced calibration methodologies, in order to keep the development of the powertrain robust, time and cost effective. The suggested solution is the virtual calibration, that allows the tuning of control functions of a powertrain before having it built. The aim of this study is to calibrate virtually the hybrid control unit functions in order to optimize the pollutant emissions and the fuel consumption. Starting from the model of the conventional vehicle, the powertrain is then hybridized and integrated with emissions and aftertreatments models. After its validation, the hybrid control unit strategies are optimized using the Model-in-the-Loop testing methodology. The calibration activities will proceed thanks to the implementation of a Hardware-in-the-Loop environment, that will allow to test and calibrate the Engine and Transmission control units effectively, besides in a time and cost saving manner.

Optimal Control and Lyapunov exponents

Il presente lavoro è suddiviso in due parti. Nella prima sono presentate la teoria degli esponenti di Lyapunov e la teoria del Controllo Ottimo da un punto di vista geometrico. Sono riportati i risultati principali di queste due teorie e vengono abbozzate le dimostrazioni dei teoremi più importanti. Nella seconda parte, usando queste due teorie, abbiamo provato a trovare una stima per gli esponenti di Lyapunov estremali associati ai sistemi dinamici lineari switched sul gruppo di Lie SL2(R). Abbiamo preso in considerazione solo il caso di un sistema generato da due matrici A,B ∈ sl2(R) che generano l’intera algebra di Lie. Abbiamo suddiviso il problema in alcuni possibili casi a seconda della posizione nello spazio tridimensionale sl2(R) del segmento di estremi A e B rispetto al cono delle matrici nilpotenti. Per ognuno di questi casi, abbiamo trovato una candidata soluzione ottimale. Riformuleremo il problema originale di trovare una stima per gli esponenti di Lyapunov in un problema di Controllo Ottimo. Dopodiché, applichiamo il Principio del massimo di Pontryagin e troveremo un controllo e la corrispondente traiettoria che soddisfa tale Principio.

Development of a Predictive Control Function for a Plug-in Hybrid Electric Vehicle with Electrically-heated Catalyst

This master thesis work is focused on the development of a predictive EHC control function for a diesel plug-in hybrid electric vehicle equipped with a EURO 7 compliant exhaust aftertreatment system (EATS), with the purpose of showing the advantages provided by the implementation of a predictive control strategy with respect to a rule-based one. A preliminary step will be the definition of an accurate powertrain and EATS physical model, starting from already existing and validated applications. Then, a rule-based control strategy managing the torque split between the electric motor (EM) and the internal combustion engine (ICE) will be developed and calibrated, with the main target of limiting tailpipe NOx emission by taking into account EM and ICE operating conditions together with EATS conversion efficiency. The information available from vehicle connectivity will be used to reconstruct the future driving scenario, also referred to as electronic horizon (eHorizon), and in particular to predict ICE first start. Based on this knowledge, an EATS pre-heating phase can be planned to avoid low pollutant conversion efficiencies, thus preventing high NOx emission due to engine cold start. Consequently, the final NOx emission over the complete driving cycle will be strongly reduced, allowing to comply with the limits potentially set by the incoming EURO 7 regulation. Moreover, given the same NOx emission target, the gain achieved thanks to the implementation of an EHC predictive control function will allow to consider a simplified EATS layout, thus reducing the related manufacturing cost. The promising results achieved in terms of NOx emission reduction show the effectiveness of the application of a predictive control strategy focused on EATS thermal management and highlight the potential of a complete integration and parallel development of involved vehicle physical systems, control software and connectivity data management.