Robustness and performance trade-offs in control design for flexible structures

Linear control design models for flexible structures are only an approximation to the “real” structural system. There are always modeling errors or uncertainty present. Descriptions of these uncertainties determine the trade-off between achievable performance and robustness of the control design. In this paper it is shown that a controller synthesized for a plant model which is not described accurately by the nominal and uncertainty models may be unstable or exhibit poor performance when implemented on the actual system. In contrast, accurate structured uncertainty descriptions lead to controllers which achieve high performance when implemented on the experimental facility. It is also shown that similar performance, theoretically and experimentally, is obtained for a surprisingly wide range of uncertain levels in the design model. This suggests that while it is important to have reasonable structured uncertainty models, it may not always be necessary to pin down precise levels (i.e., weights) of uncertainty. Experimental results are presented which substantiate these conclusions

Identification of flexible structures for robust control

Documentation is provided of the authors' experience with modeling and identification of an experimental flexible structure for the purpose of control design, with the primary aim being to motivate some important research directions in this area. A multi-input/multi-output (MIMO) model of the structure is generated using the finite element method. This model is inadequate for control design, due to its large variation from the experimental data. Chebyshev polynomials are employed to fit the data with single-input/multi-output (SIMO) transfer function models. Combining these SIMO models leads to a MIMO model with more modes than the original finite element model. To find a physically motivated model, an ad hoc model reduction technique which uses a priori knowledge of the structure is developed. The ad hoc approach is compared with balanced realization model reduction to determine its benefits. Descriptions of the errors between the model and experimental data are formulated for robust control design. Plots of select transfer function models and experimental data are included

Results in semi-inner-product spaces and generalized cosine operator functions

Ph.D.Ronald W. Shonkwile

Determination of a Total Body Model of Efficiency Applied to a Rowing Movement in Humans

Efficiency represents the ratio of work done to energy expended. In human movement, it is desirable to maximise the work done or minimise the energy expenditure. Whilst research has examined the efficiency of human movement for the lower and upper body, there is a paucity of research which considers the efficiency of a total body movement. Rowing is a movement which encompasses all parts of the body to generate locomotion and is a useful modality to measure total body efficiency. It was the aim of this research to develop a total body model of efficiency and explore how skill level of participants and assumptions of the modelling process affected the efficiency estimates Three studies were used to develop and evaluate the efficiency model. Firstly, the efficiency of ten healthy males was established using rowing, cycling and arm cranking. The model included internal work from motion capture and efficiency estimates were comparable to published literature, indicating the suitability of the model to estimate efficiency. Secondly, the model was developed to include a multi-segmented trunk and twelve novice and twelve skilled participants were assessed for efficiency. Whilst the efficiency estimates were similar to published results, novice participants were assessed as more efficient. Issues such as the unique physiology of trained rowers and a lack of energy transfers in the model were considered contributing factors. Finally the model was redeveloped to account for energy transfers, where skilled participants had higher efficiency at large workloads. This work presents a novel model for estimating efficiency during a rowing motion. The specific inclusion of energy transfers expands previous knowledge of internal work and efficiency, demonstrating a need to include energy transfers in the assessment of efficiency of a total body action

Collocated versus Non-collocated Multivariable Control for Flexible Structure

Future space structures have many closely spaced, lightly damped natural frequencies throughout the frequency domain. To achieve desired performance objectives, a number of these modes must actively be controlled. For control, a combination of collocated and noncollocated sensors and actuators will be employed. The control designs will be formulated based on models which have inaccuracies due to unmodeled dynamics, and variations in damping levels, natural frequencies and mode shapes. Therefore, along with achieving the performance objectives, the control design must be robust to a variety of uncertainty. This paper focuses on the benefits and limitations associated with multivariable control design using noncollocated versus collocated sensors and actuators. We address the question of whether performance is restricted due to the noncollocation of the sensors and actuators or the uncertainty associated with modeling of the flexible structures. Control laws are formulated based on models of the system and evaluated analytically and experimentally. Results of implementation of these control laws on the Caltech flexible structure are presented

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

On the Caltech Experimental Large Space Structure

This paper focuses on a large space structure experiment developed at the California Institute of Technology. The main thrust of the experiment is to address the identification and robust control issues associated with large space structures by capturing their characteristics in the laboratory. The design, modeling, identification and control objectives are discussed within the paper

Identification for Robust Control of Flexible Structures

An accurate multivariable transfer function model of an experimental structure is required for research involving robust control of flexible structures. Initially, a multi-input/multi-output model of the structure is generated using the finite element method. This model was insufficient due to its variation from the experimental data. Therefore, Chebyshev polynomials are employed to fit the data with a single-input/multi-output transfer function models. Combining these lead to a multivariable model with more modes than the original finite element model. To find a physically motivated model, as ad hoc model reduction technique which uses a priori knowledge of the structure is developed. The ad hoc approach is compared with balanced realisation model reduction to determine its benefits. Plots of select transfer function models and experimental data are included

ISC (Integrated Spacecraft Computer) Case Study of a Proven, Viable Approach to Using COTS in Spaceborne Computer Systems

By judiciously using COTS technology a new space computer product that has lower cost, higher performance, is easy to use and retains the high reliability necessary for use in spaceborne missions was developed. Modern COTS processors and memories are used with a mixture of military and radhard components to meet the unique thermal-mechanical environment and radiation environment of space and still satisfy the need for highreliability, low power consumption and low weight

The Process of Control Design for the NASA Langley Minimast Structure

he NASA Langley Minimast Facility is an experimental flexible structure designed to emulate future large space structures. The Minimast system consists of a 18 bay, 20 meter-long truss beam structure which is cantilevered at its base from a rigid foundation. It is desired to use active control to attenuate the response of the structure at bay 10 and 18 due to impulse disturbances at bay 9 while minimizing actuator torque commanded from the torque wheel actuators. This paper details the design process used to select sensors for feedback and performance weights on the Minimast facility. Initially, a series of controllers are synthesized using H2 optimal control techniques for the given structural model, a variety of sensor locations and performance criteria to determine the "best" displacement sensor and/or accelerometers to be used for feedback. Upon selection of the sensors, controllers are formulated to determine the affect of using a reduced order model of the Minimast structure instead of the higher order structural analysis model for control design and the relationship between the actuator torque level and the closed-loop performance. Based on this information, controllers are designed using μ-synthesis techniques and implemented on the Minimast structure. Results of the implementation of these controllers on the Minimast experimental facility are presented