Mark S. Whorton

Homotopy algorithm for fixed order mixed H2/H-infinity design

Recent developments in the field of robust multivariable control have merged the theories of H-infinity and H-2 control. This mixed H-2/H-infinity compensator formulation allows design for nominal performance by H-2 norm minimization while guaranteeing robust stability to unstructured uncertainties by constraining the H-infinity norm. A key difficulty associated with mixed H-2/H-infinity compensation is compensator synthesis. A homotopy algorithm is presented for synthesis of fixed order mixed H-2/H-infinity compensators. Numerical results are presented for a four disk flexible structure to evaluate the efficiency of the algorithm.

A study of fixed-order mixed norm designs for a benchmark problem in structural control

This study investigates the use of H 2 , μ-synthesis, and mixed H 2 /μ methods to construct full-order controllers and optimized controllers of fixed dimensions. The benchmark problem definition is first extended to include uncertainty within the controller bandwidth in the form of parametric uncertainty representative of uncertainty in the natural frequencies of the design model. The sensitivity of H 2 design to unmodelled dynamics and parametric uncertainty is evaluated for a range of controller levels of authority. Next, μ-synthesis methods are applied to design full-order compensators that are robust to both unmodelled dynamics and to parametric uncertainty. Finally, a set of mixed H 2 /μ compensators are designed which are optimized for a fixed compensator dimension. These mixed norm designs recover the H 2 design performance levels while providing the same levels of robust stability as the μ designs. It is shown that designing with the mixed norm approach permits higher levels of controller authority for which the H 2 designs are destabilizing. The benchmark problem is that of an active tendon system. The controller designs are all based on the use of acceleration feedback.

Adaptive Control of Truss Structures for Gossamer Spacecraft

Neural network-based adaptive control is considered for active control of a highly flexible truss structure which may be used to support solar sail membranes. The objective is to suppress unwanted vibrations in SAFE (Solar Array Flight Experiment) boom, a test-bed located at NASA. Compared to previous tests that restrained truss structures in planar motion, full three dimensional motions are tested. Experimental results illustrate the potential of adaptive control in compensating for nonlinear actuation and modeling error, and in rejecting external disturbances.

On-orbit model refinement for controller redesign

High performance control design for a flexible space structure is challenging since high fidelity plant models are difficult to obtain a priori. Uncertainty in the control design models typically require a very robust, low performance control design which must be tuned on-orbit to achieve the required performance. A new procedure for refining a multivariable open loop plant model based on closed-loop response data is presented. Using a minimal representation of the state space dynamics, a least squares prediction error method is employed to estimate the plant parameters. This control-relevant system identification procedure stresses the joint nature of the system identification and control design problem by seeking to obtain a model that minimizes the difference between the predicted and actual closed-loop performance. This paper presents an algorithm for iterative closed-loop system identification and controller redesign along with illustrative examples.

Adaptive Control of Evolving Gossamer Structures

A solar sail is an example of a gossamer structure that is proposed as an propulsion system for future space missions. Since it is a large scale flexible structure that requires a long time for its deployment, active control may be required to prevent it from deviating into a non-recoverable state. In this paper, we conceptually address control of an evolving flexible structure using a growing double pendulum model. Controlling an evolving system poses a major challenge to control design because it involves time-varying parameters, such as inertia and stiffness. By employing a neural network based adaptive control, we illustrate that the evolving double pendulum can be effectively regulated when fixed-gain controllers are deficient due to presence of time-varying parameters.

Deployment Modeling of an Inflatable Solar Sail Spacecraft

A simp le model for the dynamic response of an inflatable solar sailcraft during deployment has been developed and tested for several distinct scenarios. The basic kinematics for the model were formulated in a deliberate manner that in future studies will allow s ystematic increases in model fidelity (and complexity) while at the same time leading to a straightforward implementation as a state space model in Matlab/Simulink. Despite the low order of the current model, clear trends were evident. The results expose t he existence of deployment conditions that have a destabilizing effect on a flexible sailcraft which is not seen in a similar rigid -body spacecraft. Future work with higher order models will provide further insight into these conditions so that, ultimately , a robust deployment can be guaranteed.

Microgravity vibration isolation for the International Space Station

The International Space Station (ISS) is being envisioned as a laboratory for experiments in numerous microgravity (μg) science disciplines. Predictions of the ISS acceleration environment indicate that the ambient acceleration levels will exceed levels that can be tolerated by the science experiments. Hence, microgravity vibration isolation systems are being developed to attenuate the accelerations to acceptable levels. While passive isolation systems are beneficial in certain applications, active isolation systems are required to provide attenuation at low frequencies and to mitigate directly induced payload disturbances. To date, three active isolation systems have been successfully tested in the orbital environment. A fourth system called g-LIMIT is currently being developed for the Microgravity Science Glovebox and is manifested for launch on the UF-1 mission. This paper presents an overview of microgravity vibration isolation technology and the g-LIMIT system in particular.

Adaptive Control for a Microgravity Vibration Isolation System

Presented at the AIAA Guidance, Navigation, and Control Conference and Exhibit, 15 - 18 August 2005, San Francisco, California.

Fixed-Order Mixed Norm Designs for Building Vibration Control

This study investigates the use of H2, mu-synthesis, and mixed H2/mu methods to construct full order controllers and optimized controllers of fixed dimensions. The benchmark problem definition is first extended to include uncertainty within the controller bandwidth in the form of parametric uncertainty representative of uncertainty in the natural frequencies of the design model. The sensitivity of H2 design to unmodeled dynamics and parametric uncertainty is evaluated for a range of controller levels of authority. Next, mu-synthesis methods are applied to design full order compensators that are robust to both unmodeled dynamics and to parametric uncertainty. Finally, a set of mixed H2/mu compensators are designed which are optimized for a fixed compensator dimension. These mixed norm designs recover the H2 design performance levels while providing the same levels of robust stability as the mu designs. It is shown that designing with the mixed norm approach permits higher levels of controller authority for which the H2 designs are destabilizing. The benchmark problem is that of an active tendon system. The controller designs are all based on the use of acceleration feedback.

Mixed H2/H-Infinity Control of a Flexible Space Structure

As theory progresses for design and analysis of robust multivariable control laws, synthesis procedures and to a larger extent, experimental verification generally lags behind. Recent developments in robust control theory have extended the H-infinity and mu-synthesis methods to incorporate H2 properties in the control synthesis. A major difficulty in implementing robust controllers is the order of the compensator and associated complexity of the computation required for synthesis, especially when order constraints are imposed. This paper presents results of system identification and robust control design for the Controls/Structures Interaction Ground Test Facility at NASA/Marshall Space Flight Center.