Robustness and performance tradeoffs in control design for flexible structures

The design of control laws for the Caltech flexible structure experiment using a nominal design model with varying levels of uncertainty is considered. A brief overview of the structured singular value (µ) H∞ control design, and µ-synthesis design techniques is presented. Tradeoffs associated with uncertainty modeling of flexible structures are discussed. A series of controllers are synthesized based on different uncertainty descriptions. It is shown that an improper selection of nominal and uncertainty models may lead to unstable or poor-performing controllers on the actual system. In contrast, if descriptions of uncertainty are overly conservative, performance of the closed-loop system may be severely limited. Experimental results on control laws synthesized for different uncertainty levels on the Caltech structure are presented

Dynamic output feedback sliding-mode control using pole placement and linear functional observers

This paper presents a methodological approach to design dynamic output feedback sliding-mode control for a class of uncertain dynamical systems. The control action consists of the equivalent control and robust control components. The design of the equivalent control and the sliding function are based on the pole-placement technique. Linear functional observers are developed to implement the sliding function and the equivalent control. Stability of the resulting system under the proposed control scheme is guaranteed. A numerical example is given to demonstrate its efficacy.<br /

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

Robust FDI/FTC using Set-membership Methods and Application to Real Case Studies

This paper reviews the use of set-membership methods in robust fault detection and isolation (FDI) and tolerant control (FTC). Set-membership methods use a deterministic unknown-but-bounded description of noise and parametric uncertainty (interval models). These methods aims to check the consistency between observed and predicted behavior by using simple sets to approximate the set of possible behaviors (in parameter or state space). When an inconsistency is detected a fault can be indicated, otherwise nothing can be stated. The same principle can be used to identify interval models for fault detection and to develop methods for fault tolerance evaluation. Finally, some real application of these methods will end the paper exemplifying the success of these methods in FDI/FTC.Postprint (published version

Identification of Unmodeled Dynamics in Rotor Systems Using Mu-Synthesis Approach

It is well recognized that analytical models only approximate the true dynamics of analyzed rotating machines, due to the presence of components that are inherently difficult to model. Such models of rotating machines are driven by the best engineering knowledge and experience, and very often are updated based on experimental results. The problem of unmodeled or missing dynamics can be exacerbated in the presence of rotor structural damage such as a transverse crack on a shaft. This thesis will present an effective approach for model updating using advanced tools developed in robust control theory, specifically mu-synthesis. The methodology will be introduced based on a simple three-mass system and then applied to identification of the minute changes in the dynamics of the rotor test rig due to the presence of a transverse crack. Experimental data collected from the cracked rotor rig will be utilized to validate the developed approac

Robustness and performance tradeoffs in control design for flexible structures

The design of control laws for the Caltech flexible structure experiment using a nominal design model with varying levels of uncertainty is considered. A brief overview of the structured singular value (µ) H∞ control design, and µ-synthesis design techniques is presented. Tradeoffs associated with uncertainty modeling of flexible structures are discussed. A series of controllers are synthesized based on different uncertainty descriptions. It is shown that an improper selection of nominal and uncertainty models may lead to unstable or poor-performing controllers on the actual system. In contrast, if descriptions of uncertainty are overly conservative, performance of the closed-loop system may be severely limited. Experimental results on control laws synthesized for different uncertainty levels on the Caltech structure are presented