Experimental experience with flexible structures

The focus is on a flexible 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 will be discussed. Also, the subject of uncertainty in structural plant models and the frequency shaping of performance objectives will be expounded upon. Theoretical and experimental results of control laws designed using the identified model and uncertainty descriptions will be presented

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

Feedback control laws for highly maneuverable aircraft

The results of a study of the application of H infinity and mu synthesis techniques to the design of feedback control laws for the longitudinal dynamics of the High Angle of Attack Research Vehicle (HARV) are presented. The objective of this study is to develop methods for the design of feedback control laws which cause the closed loop longitudinal dynamics of the HARV to meet handling quality specifications over the entire flight envelope. Control law designs are based on models of the HARV linearized at various flight conditions. The control laws are evaluated by both linear and nonlinear simulations of typical maneuvers. The fixed gain control laws resulting from both the H infinity and mu synthesis techniques result in excellent performance even when the aircraft performs maneuvers in which the system states vary significantly from their equilibrium design values. Both the H infinity and mu synthesis control laws result in performance which compares favorably with an existing baseline longitudinal control law

Vibration Attenuation of the NASA Langley Evolutionary Structure Experiment Using H(infinity) and Structured Singular Value (mu) Robust Multivariable Control Techniques

This final report summarizes the research results under NASA Contract NAG-1-1254 from May, 1991 - April, 1995. The main contribution of this research are in the areas of control of flexible structures, model validation, optimal control analysis and synthesis techniques, and use of shape memory alloys for structural damping

Robust Region-of-Attraction Estimation

We propose a method to compute invariant subsets of the region-of-attraction for asymptotically stable equilibrium points of polynomial dynamical systems with bounded parametric uncertainty. Parameter-independent Lyapunov functions are used to characterize invariant subsets of the robust region-of-attraction. A branch-and-bound type refinement procedure reduces the conservatism. We demonstrate the method on an example from the literature and uncertain controlled short-period aircraft dynamics

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

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

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