Enhanced LFR-toolbox for MATLAB and LFT-based gain scheduling

We describe recent developments and enhancements of the LFR-Toolbox for MATLAB for building LFT-based uncertainty models and for LFT-based gain scheduling. A major development is the new LFT-object definition supporting a large class of uncertainty descriptions: continuous- and discrete-time uncertain models, regular and singular parametric expressions, more general uncertainty blocks (nonlinear, time-varying, etc.). By associating names to uncertainty blocks the reusability of generated LFT-models and the user friendliness of manipulation of LFR-descriptions have been highly increased. Significant enhancements of the computational efficiency and of numerical accuracy have been achieved by employing efficient and numerically robust Fortran implementations of order reduction tools via mex-function interfaces. The new enhancements in conjunction with improved symbolical preprocessing lead generally to a faster generation of LFT-models with significantly lower orders. Scheduled gains can be viewed as LFT-objects. Two techniques for designing such gains are presented. Analysis tools are also considered

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations

Cross Entropy-based Analysis of Spacecraft Control Systems

Space missions increasingly require sophisticated guidance, navigation and control algorithms, the development of which is reliant on verification and validation (V&V) techniques to ensure mission safety and success. A crucial element of V&V is the assessment of control system robust performance in the presence of uncertainty. In addition to estimating average performance under uncertainty, it is critical to determine the worst case performance. Industrial V&V approaches typically employ mu-analysis in the early control design stages, and Monte Carlo simulations on high-fidelity full engineering simulators at advanced stages of the design cycle. While highly capable, such techniques present a critical gap between pessimistic worst case estimates found using analytical methods, and the optimistic outlook often presented by Monte Carlo runs. Conservative worst case estimates are problematic because they can demand a controller redesign procedure, which is not justified if the poor performance is unlikely to occur. Gaining insight into the probability associated with the worst case performance is valuable in bridging this gap. It should be noted that due to the complexity of industrial-scale systems, V&V techniques are required to be capable of efficiently analysing non-linear models in the presence of significant uncertainty. As well, they must be computationally tractable. It is desirable that such techniques demand little engineering effort before each analysis, to be applied widely in industrial systems. Motivated by these factors, this thesis proposes and develops an efficient algorithm, based on the cross entropy simulation method. The proposed algorithm efficiently estimates the probabilities associated with various performance levels, from nominal performance up to degraded performance values, resulting in a curve of probabilities associated with various performance values. Such a curve is termed the probability profile of performance (PPoP), and is introduced as a tool that offers insight into a control system's performance, principally the probability associated with the worst case performance. The cross entropy-based robust performance analysis is implemented here on various industrial systems in European Space Agency-funded research projects. The implementation on autonomous rendezvous and docking models for the Mars Sample Return mission constitutes the core of the thesis. The proposed technique is implemented on high-fidelity models of the Vega launcher, as well as on a generic long coasting launcher upper stage. In summary, this thesis (a) develops an algorithm based on the cross entropy simulation method to estimate the probability associated with the worst case, (b) proposes the cross entropy-based PPoP tool to gain insight into system performance, (c) presents results of the robust performance analysis of three space industry systems using the proposed technique in conjunction with existing methods, and (d) proposes an integrated template for conducting robust performance analysis of linearised aerospace systems

Development of Robust Control Techniques towards Damage Identification

Robust control techniques have enabled engineers to create uncertain models which are able to describe any differences between the model and experimental system with uncertainties defined as a combination of exogenous inputs and plant perturbations. Subsequently, robust model validation techniques arose to provide a guarantee that the uncertain model is able to recreate all observed experimental data. As a result, the complete model set is robust to any model inaccuracies or external noise. At the same time, the technique of model-based identification was developed in the robust control framework to identify the dynamics resulting from unmodeled or under-modeled components in mechanical systems. The approach controls the nominal model in order to minimize the error between its response and that of the experimentally identified system. The resulting controller estimates the difference in dynamics between the model and actual system, also known as the unmodeled dynamics. In this work, a damage identification technique is developed which combines model validation and model-based identification for robust control relevant structural health monitoring. The method will both detect the presence of damage and identify the local change in dynamics due to the damage in a robust control framework. As a result, the damage detection will be robust to mismodeling and noise. Additionally, the identified damage dynamics will be defined with an uncertainty bound which will serve the dual purpose of a definition for robust control and a quality estimation of the nominal damage dynamics. The new technique is demonstrated experimentally on a rotordynamic test rig. First, feasibility of the method is verified by the identification of a fully-open seeded crack in a non-rotating shaft. Finally, the precision of the method is demonstrated through identification of a breathing crack in a rotating shaft

Development of Robust Control Techniques towards Damage Identification

Robust control techniques have enabled engineers to create uncertain models which are able to describe any differences between the model and experimental system with uncertainties defined as a combination of exogenous inputs and plant perturbations. Subsequently, robust model validation techniques arose to provide a guarantee that the uncertain model is able to recreate all observed experimental data. As a result, the complete model set is robust to any model inaccuracies or external noise. At the same time, the technique of model-based identification was developed in the robust control framework to identify the dynamics resulting from unmodeled or under-modeled components in mechanical systems. The approach controls the nominal model in order to minimize the error between its response and that of the experimentally identified system. The resulting controller estimates the difference in dynamics between the model and actual system, also known as the unmodeled dynamics. In this work, a damage identification technique is developed which combines model validation and model-based identification for robust control relevant structural health monitoring. The method will both detect the presence of damage and identify the local change in dynamics due to the damage in a robust control framework. As a result, the damage detection will be robust to mismodeling and noise. Additionally, the identified damage dynamics will be defined with an uncertainty bound which will serve the dual purpose of a definition for robust control and a quality estimation of the nominal damage dynamics. The new technique is demonstrated experimentally on a rotordynamic test rig. First, feasibility of the method is verified by the identification of a fully-open seeded crack in a non-rotating shaft. Finally, the precision of the method is demonstrated through identification of a breathing crack in a rotating shaft

Development of Robust Control Techniques towards Damage Identification

Robust control techniques have enabled engineers to create uncertain models which are able to describe any differences between the model and experimental system with uncertainties defined as a combination of exogenous inputs and plant perturbations. Subsequently, robust model validation techniques arose to provide a guarantee that the uncertain model is able to recreate all observed experimental data. As a result, the complete model set is robust to any model inaccuracies or external noise. At the same time, the technique of model-based identification was developed in the robust control framework to identify the dynamics resulting from unmodeled or under-modeled components in mechanical systems. The approach controls the nominal model in order to minimize the error between its response and that of the experimentally identified system. The resulting controller estimates the difference in dynamics between the model and actual system, also known as the unmodeled dynamics. In this work, a damage identification technique is developed which combines model validation and model-based identification for robust control relevant structural health monitoring. The method will both detect the presence of damage and identify the local change in dynamics due to the damage in a robust control framework. As a result, the damage detection will be robust to mismodeling and noise. Additionally, the identified damage dynamics will be defined with an uncertainty bound which will serve the dual purpose of a definition for robust control and a quality estimation of the nominal damage dynamics. The new technique is demonstrated experimentally on a rotordynamic test rig. First, feasibility of the method is verified by the identification of a fully-open seeded crack in a non-rotating shaft. Finally, the precision of the method is demonstrated through identification of a breathing crack in a rotating shaft