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All sources NASA NTRS DOE OSTI

NASA NTRS2012

Robustness Analysis and Optimally Robust Control Design via Sum-of-Squares

A control analysis and design framework is proposed for systems subject to parametric uncertainty. The underlying strategies are based on sum-of-squares (SOS) polynomial analysis and nonlinear optimization to design an optimally robust controller. The approach determines a maximum uncertainty range for which the closed-loop system satisfies a set of stability and performance requirements. These requirements, de ned as inequality constraints on several metrics, are restricted to polynomial functions of the uncertainty. To quantify robustness, SOS analysis is used to prove that the closed-loop system complies with the requirements for a given uncertainty range. The maximum uncertainty range, calculated by assessing a sequence of increasingly larger ranges, serves as a robustness metric for the closed-loop system. To optimize the control design, nonlinear optimization is used to enlarge the maximum uncertainty range by tuning the controller gains. Hence, the resulting controller is optimally robust to parametric uncertainty. This approach balances the robustness margins corresponding to each requirement in order to maximize the aggregate system robustness. The proposed framework is applied to a simple linear short-period aircraft model with uncertain aerodynamic coefficients.

Dorobantu, Andrei↗

NASA NTRS1993

Robust control of hypersonic vehicles considering propulsive and aeroelastic effects

The influence of propulsion system variations and elastic fuselage behavior on the flight control system of an airbreathing hypersonic vehicle is investigated. Thrust vector magnitude and direction changes due to angle of attack variations affect the pitching moment. Low structural vibration frequencies may occur close to the rigid body modes influencing the angle of attack and lead to possible cross coupling. These effects are modeled as uncertainties in the context of a robust control study of a hypersonic vehicle model accelerating through Mach 8 using H-infinity and mu synthesis techniques. Various levels of uncertainty are introduced into the system. Both individual and simultaneous appearance of uncertainty are considered. The results indicate that the chosen design technique is suitable for this kind of problem provided that a fairly good knowledge of the effects mentioned above is available. The order of the designed controller is reduced but robust performance is lost which shows the need for fixed order design techniques.

Buschek, Harald↗

NASA NTRS1994

Robust control design techniques for active flutter suppression

In this paper, an active flutter suppression problem is studied for a thin airfoil in unsteady aerodynamics. The mathematical model of this system is infinite dimensional because of Theodorsen's function which is irrational. Several second order approximations of Theodorsen's function are compared. A finite dimensional model is obtained from such an approximation. We use H infinity control techniques to find a robustly stabilizing controller for active flutter suppression.

Ozbay, Hitay↗

NASA NTRS1998

Robust Control Design via Linear Programming

This paper deals with the problem of synthesizing or designing a feedback controller of fixed dynamic order. The closed loop specifications considered here are given in terms of a target performance vector representing a desired set of closed loop transfer functions connecting various signals. In general these point targets are unattainable with a fixed order controller. By enlarging the target from a fixed point set to an interval set the solvability conditions with a fixed order controller are relaxed and a solution is more easily enabled. Results from the parametric robust control literature can be used to design the interval target family so that the performance deterioration is acceptable, even when plant uncertainty is present. It is shown that it is possible to devise a computationally simple linear programming approach that attempts to meet the desired closed loop specifications.

Keel, L. H.↗

NASA NTRS1994

Matlab as a robust control design tool

This presentation introduces Matlab as a tool used in flight control research. The example used to illustrate some of the capabilities of this software is a robust controller designed for a single stage to orbit air breathing vehicles's ascent to orbit. The global requirements of the controller are to stabilize the vehicle and follow a trajectory in the presence of atmospheric disturbances and strong dynamic coupling between airframe and propulsion.

Gregory, Irene M.↗

NASA NTRS1992

A problem formulation for glideslope tracking in wind shear using advanced robust control techniques

A formulation of the longitudinal glideslope tracking of a transport-class aircraft in severe wind shear and turbulence for application to robust control system design is presented. Mathematical wind shear models are incorporated into the vehicle mathematical model, and wind turbulence is modeled as an input disturbance signal. For this problem formulation, the horizontal and vertical wind shear gradients are treated as real uncertain parameters that vary over an entire wind shear profile. The primary objective is to examine the formulation of this problem into an appropriate design format for use in m-synthesis control system design.

Belcastro, Christine M.↗

NASA NTRS1991

Robust control systems design by H-infinity optimization theory

In this paper, step-by-step procedures of applying the H-infinity theory to robust control systems design are given. The objective of the paper is to eliminate the possible difficulties a control engineer may encounter in applying H-infinity control theory and to clear up some misconceptions about H-infinity theory like high-gain controller and numerical obstacles, etc. An efficient algorithm is used to compute the optimal H-infinity norm. The Glover and Doyle (1988) controller formulas are slightly modified and used to construct an optimal controller without any numerical difficulties.

Chang, B. C.↗

NASA NTRS1998

A Robust Control Approach for the Formation Flying of Multiple Spacecraft

We present a disturbance rejection mechanism for the formation flying of multiple spacecraft based on a robust control approach in terms of an H(sub infinity) control problem. The corresponding H(sub infinity) control problem is then solved numerically using linear matrix inequalities.

Mesbahi, M.↗

NASA NTRS1990

Intergration of system identification and robust controller designs for flexible structures in space

An approach is developed using experimental data to identify a reduced-order model and its model error for a robust controller design. There are three steps involved in the approach. First, an approximately balanced model is identified using the Eigensystem Realization Algorithm, which is an identification algorithm. Second, the model error is calculated and described in frequency domain in terms of the H(infinity) norm. Third, a pole placement technique in combination with a H(infinity) control method is applied to design a controller for the considered system. A set experimental data from an existing setup, namely the Mini-Mast system, is used to illustrate and verify the approach.

Juang, Jer-Nan↗

NASA NTRS1992

Nonlinear robust controller design for multi-robot systems with unknown payloads

This work is concerned with the control problem of a multi-robot system handling a payload with unknown mass properties. Force constraints at the grasp points are considered. Robust control schemes are proposed that cope with the model uncertainty and achieve asymptotic path tracking. To deal with the force constraints, a strategy for optimally sharing the task is suggested. This strategy basically consists of two steps. The first detects the robots that need help and the second arranges that help. It is shown that the overall system is not only robust to uncertain payload parameters, but also satisfies the force constraints.

Song, Y. D.↗

NASA NTRS1993

Experimental Robust Control Studies on an Unstable Magnetic Suspension System

This study is an experimental investigation of the robustness of various controllers designed for the Large Angle Magnetic Suspension Test Fixture (LAMSTF). Both analytical and identified nominal models are used for designing controllers along with two different types of uncertainty models. Robustness refers to maintain- ing tracking performance under analytical model errors and dynamically induced eddy currents, while external disturbances are not considered. Results show that incorporating robustness into analytical models gives significantly better results. However, incorporating incorrect uncertainty models may lead to poorer performance than not designing for robustness at all. Designing controllers based on accurate identified models gave the best performance. In fact, incorporating a significant level of robustness into an accurate nominal model resulted in reduced performance. This paper discusses an assortment of experimental results in a consistent manner using robust control theory.

Lim, Kyong B.↗

DOE OSTI2023

Additive-Mixing Fuel Injection (AMFI): A device for robust control and improved performance of high-efficiency LTGC engines

Low-temperature gasoline combustion (LTGC) engines can provide high efficiencies with very low NOx and particulate emissions. Despite these major advantages, methods for controlling LTGC combustion timing, achieving robust autoignition, and good low-load performance have challenged the development of practical LTGC engines. A key reason is that the ideal reactivity of the fuel varies with operating conditions, with low-reactivity fuels working well at high loads and higher-reactivity fuels working better at low loads. This article introduces a new technique called Additive Mixing Fuel Injection (AMFI) that adjusts the reactivity of the gasoline to obtain good performance over the operating map. Moreover, AMFI can provide robust combustion-timing control because it precisely meters very small amounts (0.01–0.6 mm 3 ) of an ignition-enhancing additive into the fuel each engine cycle. The additive used was 2-ethylhexyl nitrate (EHN), a common, inexpensive diesel-fuel ignition improver, but other additives could be used. Because additive amounts are so small, a 2-gal reservoir would be sufficient for medium-duty applications with refilling only at service intervals of about 8000 mi. The AMFI system has been installed on a single-cylinder LTGC research engine and demonstrated to provide robust combustion-timing control over wide ranges of combustion phasing, fueling rate, intake boost, engine speed, and intake temperature. AMFI also increases the fuel’s reactivity sufficiently to greatly reduce or eliminate the need for charge heating, simplifying engine design and significantly increasing thermal efficiency and the maximum load at low-boost conditions. The nitrogen in the EHN produced a modest increase in NOx, but it was mitigated by lower intake temperatures, and NOx emissions remained very low. Finally, the additive increases the sensitivity of autoignition reactions to variations in the local fuel/air mixture within the charge. This allows the use of controlled fuel stratification for improved LTGC-engine performance, and its potential to improve low-load operation was demonstrated.

Dec, John E.↗

NASA NTRS1990

Integration of system identification and robust controller designs for flexible structures in space

A novel approach is developed using experimental data from the structural testing of a physical system to identify a reduced-order model and its error for a robust controller design. There are three steps involved in the approach. First, an approximately balanced model is identified using the eigensystem realization algorithm, which is an identification algorithm. Second, the model error is calculated and described in frequency domain in terms of the H(infinity) norm. Third, a pole-placement technique in combination with an H(infinity) control method is applied to design a controller for the system. A set of experimental data from an existing setup, namely the Mini-Mast system, is used to illustrate and verify the approach development in this paper.

Juang, Jer-Nan↗

DOE OSTI2020

Robust control of the minima of high-order harmonics by fine-tuning the alignment of CO 2 molecules for shaping attosecond pulses and probing molecular alignment

In a recent paper, we reported that the position and depth of the minima in the harmonic spectra of CO 2 molecules can be dramatically manipulated by a slight change of the degree of alignment, thus providing a convenient method of shaping attosecond pulses which could lead to the splitting of a typical single attosecond burst into two. Here, we demonstrate that harmonic minima can also be dramatically controlled by changing the pump-probe angles to shape attosecond pulses. In the meanwhile, since the pump-probe angle-dependent harmonic spectra are very sensitive to the degree of alignment, harmonic spectra can also be used to calibrate the alignment distribution of molecules. In this work we identify such robust control of harmonic generation is due to the optical property of CO 2 and the coherent harmonic emission from the oriented molecules. The photoionization transition dipoles (PITDs) of CO 2 exhibit deep minima that change rapidly with molecular orientations accompanied by large phase changes of π in PITDs, thus leading to strong interference when the dipoles are added up coherently.

74 ATOMIC AND MOLECULAR PHYSICS↗

NASA NTRS2021

Non-Causal Controller Approximation Methodology Augmented with Model Reference Control – Robust Design

This paper describes the development of a new control design methodology based on a non-causal controller structure and its approximation. The non-causal controller design is based on a loop shaping approach. Partial fraction decomposition is used, along with derivative approximations, to derive a proper transfer function design for a causal control structure. The premise for this non-causal control methodology is that the phase delay as a function of frequency ideally remains within approximately -90o, which tends to make the system robustly stable to uncertainties in the plant dynamics. To have a predictable control system response in lieu of the tolerance of this methodology to relatively large uncertainty in the plant dynamics, the approach is augmented with model reference control. The addition of model reference control can potentially further enhance the robustness of the design. A control system design example is presented in this paper, along with simulation results, to demonstrate the high degree of robustness of this non-causal methodology and its augmentation.

Control Systems↗

NASA NTRS1992

Model validation - A connection between robust control and identification

The gap between the models used in control synthesis and those obtained from identification experiments is considered by investigating the connection between uncertain models and data. The model validation problem addressed is: given experimental data and a model with both additive noise and norm-bounded perturbations, is it possible that the model could produce the observed input-output data? This problem is studied for the standard H-infinity/mu framework models. A necessary condition for such a model to describe an experimental datum is obtained. For a large class of models in the robust control framework, this condition is computable as the solution of a quadratic optimization problem.

Smith, Roy S.↗

NASA NTRS1993

Linear, multivariable robust control with a mu perspective

The structured singular value is a linear algebra tool developed to study a particular class of matrix perturbation problems arising in robust feedback control of multivariable systems. These perturbations are called linear fractional, and are a natural way to model many types of uncertainty in linear systems, including state-space parameter uncertainty, multiplicative and additive unmodeled dynamics uncertainty, and coprime factor and gap metric uncertainty. The structured singular value theory provides a natural extension of classical SISO robustness measures and concepts to MIMO systems. The structured singular value analysis, coupled with approximate synthesis methods, make it possible to study the tradeoff between performance and uncertainty that occurs in all feedback systems. In MIMO systems, the complexity of the spatial interactions in the loop gains make it difficult to heuristically quantify the tradeoffs that must occur. This paper examines the role played by the structured singular value (and its computable bounds) in answering these questions, as well as its role in the general robust, multivariable control analysis and design problem.

Packard, Andy↗

NASA NTRS1994

Parametric robust control and system identification: Unified approach

Despite significant advancement in the area of robust parametric control, the problem of synthesizing such a controller is still a wide open problem. Thus, we attempt to give a solution to this important problem. Our approach captures the parametric uncertainty as an H(sub infinity) unstructured uncertainty so that H(sub infinity) synthesis techniques are applicable. Although the techniques cannot cope with the exact parametric uncertainty, they give a reasonable guideline to model the unstructured uncertainty that contains the parametric uncertainty. An additional loop shaping technique is also introduced to relax its conservatism.

Keel, Leehyun↗