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NASA NTRS1985

Beyond singular values and loop shapes

The status of singular value loop-shaping as a design paradigm for multivariable feedback systems is reviewed. It shows that this paradigm is an effective design tool whenever the problem specifications are spacially round. The tool can be arbitrarily conservative, however, when they are not. This happens because singular value conditions for robust performance are not tight (necessary and sufficient) and can severely overstate actual requirements. An alternate paradign is discussed which overcomes these limitations. The alternative includes a more general problem formulation, a new matrix function mu, and tight conditions for both robust stability and robust performance. The state of the art currently permits analysis of feedback systems within this new paradigm. Synthesis remains a subject of research.

Stein, G.↗

NASA NTRS1986

Feedback system design with an uncertain plant

A method is developed to design a fixed-parameter compensator for a linear, time-invariant, SISO (single-input single-output) plant model characterized by significant structured, as well as unstructured, uncertainty. The controller minimizes the H(infinity) norm of the worst-case sensitivity function over the operating band and the resulting feedback system exhibits robust stability and robust performance. It is conjectured that such a robust nonadaptive control design technique can be used on-line in an adaptive control system.

Milich, D.↗

NASA NTRS1986

Feedback system design with an uncertain plant

A method is developed to design a fixed-parameter compensator for a linear, time-invariant, SISO (single-output single-output) plant model characterized by significant structured, as well as unstructured, uncertainty. The controller minimizes the H(infinity) norm of the worst-case sensitivity function over the operating band and the resulting feedback system exhibits robust stability and robust performance. It is conjectured that such a robust nonadaptive control design technique can be used on-line in an adaptive control system.

Milich, D.↗

NASA NTRS1989

Application of stochastic robustness to aircraft control systems

Stochastic robustness, a simple numerical procedure for estimating the stability robustness of linear, time-invariant systems, is applied to a forward-swept-wing aircraft control system. Based on Monte Carlo evaluation of the system's closed-loop eignevalues, this analysis approach introduces the probability of instability as a scalar stability robustness measure. The related stochastic root locus provides insight into robustness characteristics of the closed-loop system. Three Linear Quadratic controllers of decreasing robustness are chosen to demonstrate the use of stochastic robustness to analyze and compare control designs. Examples are presented illustrating the use of stochastic robustness analysis to address the effects of actuator dynamics and unmodeled dynamics on the stability robustness of the forward-swept-wing aircraft.

Stengel, Robert F.↗

NASA NTRS1991

Beyond singular values and loop shapes

Stein, Gunter↗

NASA NTRS1992

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

Research leading to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle of attack aircraft such as the F-18 is discussed. The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis, and simulation were studied in some detail as well. Studies indicated that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in angle of attack. Included here are studies on nonlinear model algorithmic controller design and an analysis of nonlinear system stability using robust stability analysis for linear systems.

Mohler, R. R.↗

NASA NTRS1993

A fixed H-infinity controller for a supermaneuverable fighter performing the Herbst maneuver

This paper presents an H-infinity flight control system design case study for a supermaneuverable fighter flying the Herbst maneuver. The Herbst maneuver presents an especially challenging flight control problem because of its large ranges of airspeed, angle of attack and angular rates. A fixed H-infinity controller has been developed via the mixed-sensitivity problem formulation for 20 linearized models representing the maneuver. Both linear and nonlinear full model evaluations indicate that this single H-infinity controller together with a fixed LQR inner loop feedback have achieved 'robust stability' and 'robust performance' for the entire maneuver without gain scheduling.

Chiang, R. Y.↗

NASA NTRS2001

Aeroservoelastic Uncertainty Model Identification from Flight Data

Uncertainty modeling is a critical element in the estimation of robust stability margins for stability boundary prediction and robust flight control system development. There has been a serious deficiency to date in aeroservoelastic data analysis with attention to uncertainty modeling. Uncertainty can be estimated from flight data using both parametric and nonparametric identification techniques. The model validation problem addressed in this paper is to identify aeroservoelastic models with associated uncertainty structures from a limited amount of controlled excitation inputs over an extensive flight envelope. The challenge to this problem is to update analytical models from flight data estimates while also deriving non-conservative uncertainty descriptions consistent with the flight data. Multisine control surface command inputs and control system feedbacks are used as signals in a wavelet-based modal parameter estimation procedure for model updates. Transfer function estimates are incorporated in a robust minimax estimation scheme to get input-output parameters and error bounds consistent with the data and model structure. Uncertainty estimates derived from the data in this manner provide an appropriate and relevant representation for model development and robust stability analysis. This model-plus-uncertainty identification procedure is applied to aeroservoelastic flight data from the NASA Dryden Flight Research Center F-18 Systems Research Aircraft.

Brenner, Martin J.↗

NASA NTRS2004

Robust Control for The G-Limit Microgravity Vibration Isolation System

Many microgravity science experiments need an active isolation system to provide a sufficiently quiescent acceleration environment. The g-LIMIT vibration isolation system will provide isolation for Microgravity Science Glovebox experiments in the International Space Station. While standard control system technologies have been demonstrated for these applications, modern control methods have the potential for meeting performance requirements while providing robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H infinity methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/mu controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark S.↗

NASA NTRS2003

Robust Control for Microgravity Vibration Isolation using Fixed Order, Mixed H2/Mu Design

Many space-science experiments need an active isolation system to provide a sufficiently quiescent microgravity environment. Modern control methods provide the potential for both high-performance and robust stability in the presence of parametric uncertainties that are characteristic of microgravity vibration isolation systems. While H2 and H(infinity) methods are well established, neither provides the levels of attenuation performance and robust stability in a compensator with low order. Mixed H2/H(infinity), controllers provide a means for maximizing robust stability for a given level of mean-square nominal performance while directly optimizing for controller order constraints. This paper demonstrates the benefit of mixed norm design from the perspective of robustness to parametric uncertainties and controller order for microgravity vibration isolation. A nominal performance metric analogous to the mu measure, for robust stability assessment is also introduced in order to define an acceptable trade space from which different control methodologies can be compared.

Whorton, Mark↗

NASA NTRS1994

Microgravity isolation system design: A modern control analysis framework

Many acceleration-sensitive, microgravity science experiments will require active vibration isolation from the manned orbiters on which they will be mounted. The isolation problem, especially in the case of a tethered payload, is a complex three-dimensional one that is best suited to modern-control design methods. These methods, although more powerful than their classical counterparts, can nonetheless go only so far in meeting the design requirements for practical systems. Once a tentative controller design is available, it must still be evaluated to determine whether or not it is fully acceptable, and to compare it with other possible design candidates. Realistically, such evaluation will be an inherent part of a necessary iterative design process. In this paper, an approach is presented for applying complex mu-analysis methods to a closed-loop vibration isolation system (experiment plus controller). An analysis framework is presented for evaluating nominal stability, nominal performance, robust stability, and robust performance of active microgravity isolation systems, with emphasis on the effective use of mu-analysis methods.

Hampton, R. D.↗

NASA NTRS1991

Dynamic dissipative compensator design for large space structures

Control system design is considered for attitude control and vibration suppression of flexible space structures. The problem addressed is that of controlling both the zero-frequency rigid-body modes and the elastic modes. Model-based compensators, which employ observers tuned to the plant parameters, are first investigated. Such compensators are shown to generally exhibit high sensitivity to the knowledge of the parameters, especially the elastic mode frequencies. To overcome this problem a class of dynamic dissipative compensators is next proposed, which robustly stabilize the plant in the presence of unmodeled dynamics and parametric uncertainties. An analytical proof of robust stability is given, and a method of implementing the controller as a strictly proper compensator is given. Methods of designing such controllers to obtain optimal performance and robust stability are presented. Numerical and experimental results of application of the methods are presented, which indicate that dynamic dissipative controllers can simultaneously provide excellent performance and robustness.

Joshi, S. M.↗

NASA NTRS1988

Robustness margin calculation with dynamic and real parametric uncertainty

The problem of robust stability in feedback control systems with real uncertain parameters and unmodeled dynamics, where the latter takes the form of one complex block dynamic uncertainty, is considered. A robustness margin Tm is defined with respect to such model uncertainty structure and robust stability is characterized in terms of it. An algorithm to calculate Tm and the closely related multivariable stability margin km and structured singular value mu measures of robust stability is developed. It is shown that other control problems, such as robust performance for real parametric uncertainty, can also be handled in this framework.

Sideris, Athanasios↗

NASA NTRS1986

Inherent robustness of discrete-time adaptive control systems

Global stability robustness with respect to unmodeled dynamics, arbitrary bounded internal noise, as well as external disturbance is shown to exist for a class of discrete-time adaptive control systems when the regressor vectors of these systems are persistently exciting. Although fast adaptation is definitely undesirable, so far as attaining the greatest amount of global stability robustness is concerned, slow adaptation is shown to be not necessarily beneficial. The entire analysis in this paper holds for systems with slowly varying return difference matrices; the plants in these systems need not be slowly varying.

Ma, C. C. H.↗

NASA NTRS1993

Exploiting structure: Introduction and motivation

Research activities performed during the period of 29 June 1993 through 31 Aug. 1993 are summarized. The Robust Stability of Systems where transfer function or characteristic polynomial are multilinear affine functions of parameters of interest in two directions, Algorithmic and Theoretical, was developed. In the algorithmic direction, a new approach that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty is found. This technique is called 'Stability by linear process.' In fact, the 'Stability by linear process' described gives an algorithm. In analysis, we obtained a robustness criterion for the family of polynomials with coefficients of multilinear affine function in the coefficient space and obtained the result for the robust stability of diamond families of polynomials with complex coefficients also. We obtained the limited results for SPR design and we provide a framework for solving ACS. Finally, copies of the outline of our results are provided in the appendix. Also, there is an administration issue in the appendix.

Xu, Zhong Ling↗

NASA NTRS1992

Parametric stability margin for multilinear interval control systems

Recently, a necessary and sufficient condition to determine the robust stability of a multilinear interval control system has been reported as an extension of the well-known Box theorem which deals with the linear affine case. A simple but computationally efficient algorithm, based on the above result, to check the robust stability of such systems is introduced. The method is also extended to find the parametric stability margin of such a system.

Keel, L. H.↗

NASA NTRS1990

A linear quadratic regulator approach to the stabilization of uncertain linear systems

This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.

Shieh, L. S.↗

NASA NTRS1994

Exploiting structure: Introduction and motivation

This annual report summarizes the research activities that were performed from 26 Jun. 1993 to 28 Feb. 1994. We continued to investigate the Robust Stability of Systems where transfer functions or characteristic polynomials are affine multilinear functions of parameters. An approach that differs from 'Stability by Linear Process' and that reduces the computational burden of checking the robust stability of the system with multilinear uncertainty was found for low order, 2-order, and 3-order cases. We proved a crucial theorem, the so-called Face Theorem. Previously, we have proven Kharitonov's Vertex Theorem and the Edge Theorem by Bartlett. The detail of this proof is contained in the Appendix. This Theorem provides a tool to describe the boundary of the image of the affine multilinear function. For SPR design, we have developed some new results. The third objective for this period is to design a controller for IHM by the H-infinity optimization technique. The details are presented in the Appendix.

Xu, Zhong Ling↗