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NASA NTRS1990

A first-order Lyapunov robustness method for linear systems with uncertain parameters

A method for stability-robustness analysis based on a quadratic Liapunov function that varies linearly with uncertainty parameters is derived. Linear time-invariant systems with structured uncertainties are discussed. The Liapunov function is optimized numerically to maximize the robustness region in parameter space. Numerical results are given for four examples in which the first-order method is compared to previous Liapunov methods. While the zero-order method is slightly better than the first-order method for one example, the first-order method is clearly superior in the other three (more realistic) examples. The first-order method is especially superior for the active control of flexible structures, where robustness with respect to (1) unmodeled coupling between modeled modes and (2) unmodeled modes is important. For such applications, the first-order method is much better at detecting the increased robustness associated with increased separation between frequencies.

Leal, M. A.↗

NASA NTRS1990

Towards a methodology for robust parameter identification

Consideration is given to the problem of estimating, from experimental data, real parameters for a model with uncertainty in the form of both additive noise and norm-bounded perturbations. Such models frequently arise in robust control theory, and a framework is introduced for the consideration of experimental data in robust control analysis problems. If the analysis tools applied include robust stability tests for real parameter variations (real mu), the framework can be used to address the problem of robust parameter identification. While the techniques discussed can quickly become computationally overwhelming when applied to physical systems and real data, the approach introduces a novel way of looking at the identification problem and may be helpful in arriving at a more tractable methodology.

Smith, Roy S.↗

NASA NTRS1991

Observer-based robust-H-infinity control laws for uncertain linear systems

Based on the algebraic Riccati equation approach, this paper presents a simple and flexible method for designing observer-based robust-H-infinity control laws for linear systems with structured parameter uncertainty. The observer-based robust-H-infinity output-feedback control law, obtained by solving three augmented algebraic Riccati equations, provides both robust stability and disturbance attenuation with H-infinity-norm bound for the closed-loop uncertain linear system. Several tuning parameters are embedded into the augmented algebraic Riccati equations so that flexibility in finding the symmetric positive-definite solutions (and hence, the robust-H-infinity control laws) is significantly increased. A benchmark problem associated with a mass-spring system, which approximates the dynamics of a flexible structure, is used to illustrate the design methodologies, and simulation results are presented.

Shieh, Leang S.↗

NASA NTRS1992

Robust control of flexible space vehicles with minimum structural excitation: On-off pulse control of flexible space vehicles

Both feedback and feedforward control approaches for uncertain dynamical systems (in particular, with uncertainty in structural mode frequency) are investigated. The control objective is to achieve a fast settling time (high performance) and robustness (insensitivity) to plant uncertainty. Preshaping of an ideal, time optimal control input using a tapped-delay filter is shown to provide a fast settling time with robust performance. A robust, non-minimum-phase feedback controller is synthesized with particular emphasis on its proper implementation for a non-zero set-point control problem. It is shown that a properly designed, feedback controller performs well, as compared with a time optimal open loop controller with special preshaping for performance robustness. Also included are two separate papers by the same authors on this subject.

Wie, Bong↗

NASA NTRS1991

Robust stabilization of the Space Station

A robust H-infinity control design methodology and its application to a Space Station Freedom (SSF) attitude and momentum control problem are presented. This approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the SSF control problem yields remarkable results in stability robustness with respect to moments of inertia variation of about 73 percent in one of the structured uncertainty directions. The performance and stability of this robust H-infinity controller for the SSF are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.

Wie, Bong↗

NASA NTRS1990

Computer-aided-analysis of linear control system robustness

Stochastic robustness is a simple technique used to estimate the stability and performance robustness of linear, time-invariant systems. The use of high-speed graphics workstations and control system design software in stochastic robustness analysis is discussed and demonstrated. It is shown that stochastic robustness makes good use of modern computational and graphic tools, and it is easily implemented using commercial control system design and analysis software.

Stengel, Robert F.↗

NASA NTRS1992

Robustness of solutions to a benchmark control problem

The robustness of 10 solutions to a benchmark control design problem presented at the 1990 American Control Conference has been evaluated. The 10 controllers have second-to-eighth-order transfer functions and have been designed using several different methods, including H-infinity optimization, loop-transfer recovery, imaginary-axis shifting, constrained optimization, structured covariance, game theory, and the internal model principle. Stochastic robustness analysis quantifies the controllers' stability and performance robustness with structured uncertainties in up to six system parameters. The analysis provides insights into system response that are not readily derived from other robustness criteria and provides a common ground for judging controllers produced by alternative methods. One important conclusion is that gain and phase margins are not reliable indicators of the probability of instability. Furthermore, parameter variations actually may improve the likelihood of achieving selected performance metrics, as demonstrated by results for the probability of settling-time exceedance.

Stengel, Robert F.↗

NASA NTRS1993

Robust nonlinear control of vectored thrust aircraft

An interdisciplinary program in robust control for nonlinear systems with applications to a variety of engineering problems is outlined. Major emphasis will be placed on flight control, with both experimental and analytical studies. This program builds on recent new results in control theory for stability, stabilization, robust stability, robust performance, synthesis, and model reduction in a unified framework using Linear Fractional Transformations (LFT's), Linear Matrix Inequalities (LMI's), and the structured singular value micron. Most of these new advances have been accomplished by the Caltech controls group independently or in collaboration with researchers in other institutions. These recent results offer a new and remarkably unified framework for all aspects of robust control, but what is particularly important for this program is that they also have important implications for system identification and control of nonlinear systems. This combines well with Caltech's expertise in nonlinear control theory, both in geometric methods and methods for systems with constraints and saturations.

Doyle, John C.↗

NASA NTRS1993

Robust crossfeed design for hovering rotorcraft

Control law design for rotorcraft fly-by-wire systems normally attempts to decouple angular responses using fixed-gain crossfeeds. This approach can lead to poor decoupling over the frequency range of pilot inputs and increase the load on the feedback loops. In order to improve the decoupling performance, dynamic crossfeeds may be adopted. Moreover, because of the large changes that occur in rotorcraft dynamics due to small changes about the nominal design condition, especially for near-hovering flight, the crossfeed design must be 'robust.' A new low-order matching method is presented here to design robost crossfeed compensators for multi-input, multi-output (MIMO) systems. The technique identifies degrees-of-freedom that can be decoupled using crossfeeds, given an anticipated set of parameter variations for the range of flight conditions of concern. Cross-coupling is then reduced for degrees-of-freedom that can use crossfeed compensation by minimizing off-axis response magnitude average and variance. Results are presented for the analysis of pitch, roll, yaw, and heave coupling of the UH-60 Black Hawk helicopter in near-hovering flight. Robust crossfeeds are designed that show significant improvement in decoupling performance and robustness over nominal, single design point, compensators. The design method and results are presented in an easily-used graphical format that lends significant physical insight to the design procedure. This plant pre-compensation technique is an appropriate preliminary step to the design of robust feedback control laws for rotorcraft.

Catapang, David R.↗

NASA NTRS1992

Robust linear quadratic designs with respect to parameter uncertainty

The authors derive a linear quadratic regulator (LQR) which is robust to parametric uncertainty by using the overbounding method of I. R. Petersen and C. V. Hollot (1986). The resulting controller is determined from the solution of a single modified Riccati equation. It is shown that, when applied to a structural system, the controller gains add robustness by minimizing the potential energy of uncertain stiffness elements, and minimizing the rate of dissipation of energy through uncertain damping elements. A worst-case disturbance in the direction of the uncertainty is also considered. It is proved that performance robustness has been increased with the robust LQR when compared to a mismatched LQR design where the controller is designed on the nominal system, but applied to the actual uncertain system.

Douglas, Joel↗

NASA NTRS1992

Robust control algorithms for Mars aerobraking

Four atmospheric guidance concepts have been adapted to control an interplanetary vehicle aerobraking in the Martian atmosphere. The first two offer improvements to the Analytic Predictor Corrector (APC) to increase its robustness to density variations. The second two are variations of a new Liapunov tracking exit phase algorithm, developed to guide the vehicle along a reference trajectory. These four new controllers are tested using a six degree of freedom computer simulation to evaluate their robustness. MARSGRAM is used to develop realistic atmospheres for the study. When square wave density pulses perturb the atmosphere all four controllers are successful. The algorithms are tested against atmospheres where the inbound and outbound density functions are different. Square wave density pulses are again used, but only for the outbound leg of the trajectory. Additionally, sine waves are used to perturb the density function. The new algorithms are found to be more robust than any previously tested and a Liapunov controller is selected as the most robust control algorithm overall examined.

Shipley, Buford W., Jr.↗

NASA NTRS1993

A robust controller for second-order systems using acceleration measurements

This paper presents a robust control design using strictly positive realness for second-order dynamic systems. The robust strictly positive real controller allows the system to be stabilized with only acceleration measurements. An important property of this design is that stabilization of the system is independent of the system parameters. The control design connects a virtual system to the given plant. The combined system is positive real regardless of system parameter uncertainty. Then any strictly positive real controllers can be used to achieve robust stability. A spring-mass system example and its computer simulations are presented to demonstrate this controller design. Robust performance property of this design is also demonstrated in a simple example.

Chuang, C.-H.↗

NASA NTRS1994

Semigroup approximation and robust stabilization of distributed parameter systems

Theoretical results that enable rigorous statements of convergence and exponential stability of Galerkin approximations of LQR controls for infinite dimensional, or distributed parameter, systems have proliferated over the past ten years. In addition, extensive progress has been made over the same time period in the derivation of robust control design strategies for finite dimensional systems. However, the study of the convergence of robust finite dimensional controllers to robust controllers for infinite dimensional systems remains an active area of research. We consider a class of soft-constrained differential games evolving in a Hilbert space. Under certain conditions, a saddle point control can be given in feedback form in terms of a solution to a Riccati equation. By considering a related LQR problem, we can show a convergence result for finite dimensional approximations of this differential game. This yields a computational algorithm for the feedback gain that can be derived from similar strategies employed in infinite dimensional LQR control design problems. The approach described in this paper also inherits the additional properties of stability robustness common to game theoretic methods in finite dimensional analysis. These theoretical convergence and stability results are verified in several numerical experiments.

Kurdila, A. J.↗

NASA NTRS1994

Multi-application controls: Robust nonlinear multivariable aerospace controls applications

This viewgraph presentation describes the general methodology used to apply Honywell's Multi-Application Control (MACH) and the specific application to the F-18 High Angle-of-Attack Research Vehicle (HARV) including piloted simulation handling qualities evaluation. The general steps include insertion of modeling data for geometry and mass properties, aerodynamics, propulsion data and assumptions, requirements and specifications, e.g. definition of control variables, handling qualities, stability margins and statements for bandwidth, control power, priorities, position and rate limits. The specific steps include choice of independent variables for least squares fits to aerodynamic and propulsion data, modifications to the management of the controls with regard to integrator windup and actuation limiting and priorities, e.g. pitch priority over roll, and command limiting to prevent departures and/or undesirable inertial coupling or inability to recover to a stable trim condition. The HARV control problem is characterized by significant nonlinearities and multivariable interactions in the low speed, high angle-of-attack, high angular rate flight regime. Systematic approaches to the control of vehicle motions modeled with coupled nonlinear equations of motion have been developed. This paper will discuss the dynamic inversion approach which explicity accounts for nonlinearities in the control design. Multiple control effectors (including aerodynamic control surfaces and thrust vectoring control) and sensors are used to control the motions of the vehicles in several degrees-of-freedom. Several maneuvers will be used to illustrate performance of MACH in the high angle-of-attack flight regime. Analytical methods for assessing the robust performance of the multivariable control system in the presence of math modeling uncertainty, disturbances, and commands have reached a high level of maturity. The structured singular value (mu) frequency response methodology is presented as a method for analyzing robust performance and the mu-synthesis method will be presented as a method for synthesizing a robust control system. The paper concludes with the author's expectations regarding future applications of robust nonlinear multivariable controls.

Enns, Dale F.↗

NASA NTRS1992

Robust H infinity control design for the space station with structured parameter uncertainty

A robust H-infinity control design methodology and its application to a Space Station attitude and momentum control problem are presented. This new approach incorporates nonlinear multi-parameter variations in the state-space formulation of H-infinity control theory. An application of this robust H-infinity control synthesis technique to the Space Station control problem yields a remarkable result in stability robustness with respect to the moments-of-inertia variation of about 73% in one of the structured uncertainty directions. The performance and stability of this new robust H-infinity controller for the Space Station are compared to those of other controllers designed using a standard linear-quadratic-regulator synthesis technique.

Byun, Kuk-Whan↗

NASA NTRS1994

Integration of the Response Surface Methodology with the Compromise Decision Support Problem in Developing a General Robust Design Procedure

In this paper we introduce a comprehensive and rigorous robust design procedure to overcome some limitations of the current approaches. A comprehensive approach is general enough to model the two major types of robust design applications, namely, robust design associated with the minimization of the deviation of performance caused by the deviation of noise factors (uncontrollable parameters), and robust design due to the minimization of the deviation of performance caused by the deviation of control factors (design variables). We achieve mathematical rigor by using, as a foundation, principles from the design of experiments and optimization. Specifically, we integrate the Response Surface Method (RSM) with the compromise Decision Support Problem (DSP). Our approach is especially useful for design problems where there are no closed-form solutions and system performance is computationally expensive to evaluate. The design of a solar powered irrigation system is used as an example. Our focus in this paper is on illustrating our approach rather than on the results per se.

Chen, Wei↗

NASA NTRS1997

The Problem of Size in Robust Design

To facilitate the effective solution of multidisciplinary, multiobjective complex design problems, a departure from the traditional parametric design analysis and single objective optimization approaches is necessary in the preliminary stages of design. A necessary tradeoff becomes one of efficiency vs. accuracy as approximate models are sought to allow fast analysis and effective exploration of a preliminary design space. In this paper we apply a general robust design approach for efficient and comprehensive preliminary design to a large complex system: a high speed civil transport (HSCT) aircraft. Specifically, we investigate the HSCT wing configuration design, incorporating life cycle economic uncertainties to identify economically robust solutions. The approach is built on the foundation of statistical experimentation and modeling techniques and robust design principles, and is specialized through incorporation of the compromise Decision Support Problem for multiobjective design. For large problems however, as in the HSCT example, this robust design approach developed for efficient and comprehensive design breaks down with the problem of size - combinatorial explosion in experimentation and model building with number of variables -and both efficiency and accuracy are sacrificed. Our focus in this paper is on identifying and discussing the implications and open issues associated with the problem of size for the preliminary design of large complex systems.

Koch, Patrick N.↗

NASA NTRS2000

Robust Fixed-Structure Controller Synthesis

The ability to develop an integrated control system design methodology for robust high performance controllers satisfying multiple design criteria and real world hardware constraints constitutes a challenging task. The increasingly stringent performance specifications required for controlling such systems necessitates a trade-off between controller complexity and robustness. The principle challenge of the minimal complexity robust control design is to arrive at a tractable control design formulation in spite of the extreme complexity of such systems. Hence, design of minimal complexitY robust controllers for systems in the face of modeling errors has been a major preoccupation of system and control theorists and practitioners for the past several decades.

Corrado, Joseph R.↗