SEARCH · Search NASA

Results for “LQG”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 records

All sources NASA NTRS DOE OSTI

NASA NTRS1987

A parameter robust LQG design synthesis with applications to control of flexible structures

An asymptotic LQG design synthesis technique is described which explicitly includes a class of structured plant uncertainties by viewing plant parameter variations as an internal feedback loop. A direct structural relationship between this class of parameter uncertainties and the weighting matrices in the design of the LQG compensator is exploited by an asymptotic procedure in which either the regulator or the filter become insensitive to parameter variations. This asymptotic approach represents a generalization of the LQG/LTR technique. Controllers designed by this new LQG method and LQG/LTR are compared by application to a mass-spring-damper system which approximates the dynamics of flexible structures. For both colocated and noncolocated sensors and actuators configurations, the LQG/LTR design is extremely sensitive to parameter variations whereas the new LQG design allows considerably improved parameter robustness.

Tahk, Minjea↗

NASA NTRS1988

Approximation theory for LQG (Linear-Quadratic-Gaussian) optimal control of flexible structures

An approximation theory is presented for the LQG (Linear-Quadratic-Gaussian) optimal control problem for flexible structures whose distributed models have bounded input and output operators. The main purpose of the theory is to guide the design of finite dimensional compensators that approximate closely the optimal compensator. The optimal LQG problem separates into an optimal linear-quadratic regulator problem and an optimal state estimation problem. The solution of the former problem lies in the solution to an infinite dimensional Riccati operator equation. The approximation scheme approximates the infinite dimensional LQG problem with a sequence of finite dimensional LQG problems defined for a sequence of finite dimensional, usually finite element or modal, approximations of the distributed model of the structure. Two Riccati matrix equations determine the solution to each approximating problem. The finite dimensional equations for numerical approximation are developed, including formulas for converting matrix control and estimator gains to their functional representation to allow comparison of gains based on different orders of approximation. Convergence of the approximating control and estimator gains and of the corresponding finite dimensional compensators is studied. Also, convergence and stability of the closed-loop systems produced with the finite dimensional compensators are discussed. The convergence theory is based on the convergence of the solutions of the finite dimensional Riccati equations to the solutions of the infinite dimensional Riccati equations. A numerical example with a flexible beam, a rotating rigid body, and a lumped mass is given.

Gibson, J. S.↗

NASA NTRS2004

Antenna Linear-Quadratic-Gaussian (LQG) Controllers: Properties, Limits of Performance, and Tuning Procedure

Wind gusts are the main disturbances that depreciate tracking precision of microwave antennas and radiotelescopes. The linear-quadratic-Gaussian (LQG) controllers - as compared with the proportional-and-integral (PI) controllers significantly improve the tracking precision in wind disturbances. However, their properties have not been satisfactorily understood; consequently, their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller model and the selection of weights of the LQG performance index. This article analyzes properties of an open- and closed-loop antenna. It shows that the proper choice of coordinates of the open-loop model simplifies the shaping of the closed-loop performance. The closed-loop properties are influenced by the LQG weights. The article shows the impact of the weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. The bandwidth and the disturbance rejection characterize the antenna performance, while the acceleration represents the performance limit set by the antenna hardware (motors). The article presents the controller tuning procedure, based on the coordinate selection and the weight properties. The procedure rationally shapes the closed-loop performance, as an alternative to the trial-and-error approach.

Gawronski, W.↗

NASA NTRS2004

Antenna Linear-Quadratic-Gaussian (LQG) Ccontrollers: Properties, Limits of Performance, and Tuning

The LQG controllers significantly improve antenna tracking precision, but their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller, and the selection of weights of the LQG performance index. The paper selects the coordinates of the open-loop model that simplify the shaping of the closed-loop performance. and analyzes the impact of thc weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. Finally, it presents the LQG controller tuning procedure that rationally shapes the closed-loop performance.

control technology↗

NASA NTRS2004

Antenna LQG Controllers: Properties, Limits of Performance, and Tuning Procedure

The LQG controllers significantly improve antenna tracking precision, but their tuning is a trial-and-error process. A control engineer has two tools to tune an LQG controller: the choice of coordinate system of the controller, and the selection of weights of the LQG performance index. The paper selects the coordinates of the open-loop model that simplify the shaping of the closed-loop performance and analyzes the impact of the weights on the antenna closed-loop bandwidth, disturbance rejection properties, and antenna acceleration. Finally, it presents the LQG controller tuning procedure that rationally shapes the closed-loop performance.

antennas↗

DOE OSTI2019

False Data Injection and Detection in LQG Systems: A Game Theoretic Approach

Cyber-physical systems are vulnerable to false data injection by adversaries who compromise cyber communication links. In this paper, an infinite horizon linear quadratic Gaussian (LQG) system is considered wherein the control inputs transmitted over cyber links are vulnerable to compromise and false data injection by adversaries. The adversarial cyber-attack is driven to minimize the performance of the LQG system, and the controller is equipped with an intrusion detection system that monitors the sequence of internal physical states to detect adversarial input modification. The problem is formulated as a two-player zero-sum game with the false alarm probability as the reward, wherein the attacker aims to achieve a target increase in controller cost while maximizing the false alarm probability, and a detector who wishes to minimize the false alarm probability while remaining consistent. It is shown that in such a game, an ε-equilibrium exists. The equilibrium attacker strategy is the one that minimizes the Kullback-Leibler distance between legitimate and falsified state dynamics, and the equilibrium detector strategy is the corresponding likelihood-ratio test. Numerical simulations are presented that showcase the equilibrium strategy pair and the intuitive strategies comparisons.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Laboratory demonstration of the prediction of wind-blown turbulence by adaptive optics at 8 kHz with use of LQG control

The low-latency adaptive optical mirror system (LLAMAS) is designed to push the limits on achievable latencies and frame rates. It has 21 subapertures across its pupil. Here, a reformulated version of the linear quadratic Gaussian (LQG) method predictive Fourier control is implemented in LLAMAS; for all modes, it takes just 30 µs to compute. In the testbed, a turbulator mixes hot and ambient air to produce wind-blown turbulence. Wind prediction clearly improves correction when compared to an integral controller. Closed-loop telemetry shows that wind-predictive LQG removes the characteristic “butterfly” and reduces temporal error power by up to a factor of three for mid-spatial frequency modes. Strehl changes seen in focal plane images are consistent with telemetry and the system error budget.

47 OTHER INSTRUMENTATION↗

NASA NTRS1987

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗

NASA NTRS1988

Approximation of discrete-time LQG compensators for distributed systems with boundary input and unbounded measurement

The approximation of optimal discrete-time linear quadratic Gaussian (LQG) compensators for distributed parameter control systems with boundary input and unbounded measurement is considered. The approach applies to a wide range of problems that can be formulated in a state space on which both the discrete-time input and output operators are continuous. Approximating compensators are obtained via application of the LQG theory and associated approximation results for infinite dimensional discrete-time control systems with bounded input and output. Numerical results for spline and modal based approximation schemes used to compute optimal compensators for a one-dimensional heat equation with either Neumann or Dirichlet boundary control and pointwise measurement of temperature are presented and discussed.

Gibson, J. S.↗

NASA NTRS1993

Design of the reduced LQG compensator for the DSS-13 antenna

A linear-quadratic-Gaussian (LQG) compensator design procedure is proposed for the DSS-13 antenna. The procedure is based on two properties. It is shown that tracking and flexible motion of the antenna are almost independent (the separation property). As a consequence, compensators for the flexible and tracking parts can be designed separately. It is shown also that the balanced LQG compensator's effort is evenly divided between the controller and the estimator. This allows a minimization of the compensator order, which is important for implementation purposes. An efficient compensator reduction procedure that gives a stable low-order compensator of satisfactory performance is introduced. This approach is illustrated with a detailed compensator design for the DSS-13 antenna. The implementation of this compensator design requires an update of the antenna model.

Gawronski, W.↗

NASA NTRS1993

Design of the reduced LQG compensator for the Deep Space Network antennas

A linear quadratic Gaussian (LQG) compensator design procedure is proposed for the NASA Deep Space Network (DSN) antennas. The procedure is based on two properties of antennas. It is shown that tracking and flexible motion of the DSN antennas are almost independent (the separation property), and that for the balanced LQG compensator its performance is evenly divided between the controller and the estimator (balancing property). As a consequence compensators for the flexible and tracking parts can be designed separately, and the compensator order is reduced significantly, which is important for implementation purposes. The approach is illustrated with the detailed compensator design for the DSS-13 antenna.

Gawronski, W.↗

NASA NTRS1987

Problems associated with reaction mass actuators used in conjunction with LQG control on the Mini-Mast

The work being done at NASA LaRC on developing control laws for the Mini-Mast experimental facility is reviewed with particular attention given to the problems associated with the stroke limit of the reaction mass actuators used in conjunction with the LQG control. An algorithm for converting the force commands of the LQG algorithm into position command for the reaction mass devices is described. It is shown that the position command can be used as an input to a local controller so that the relative position of the reaction mass would track the commanded relative position. The stabilization of the integration scheme makes it possible to avoid the position drift arising in the direct double integration method of converting force commands to position commands.

Ghosh, D.↗

NASA NTRS1996

Iterative LQG Controller Design Through Closed-Loop Identification

This paper presents an iterative Linear Quadratic Gaussian (LQG) controller design approach for a linear stochastic system with an uncertain open-loop model and unknown noise statistics. This approach consists of closed-loop identification and controller redesign cycles. In each cycle, the closed-loop identification method is used to identify an open-loop model and a steady-state Kalman filter gain from closed-loop input/output test data obtained by using a feedback LQG controller designed from the previous cycle. Then the identified open-loop model is used to redesign the state feedback. The state feedback and the identified Kalman filter gain are used to form an updated LQC controller for the next cycle. This iterative process continues until the updated controller converges. The proposed controller design is demonstrated by numerical simulations and experiments on a highly unstable large-gap magnetic suspension system.

Hsiao, Min-Hung↗

NASA NTRS2000

Robust Control of Uncertain Systems via Dissipative LQG-Type Controllers

Optimal controller design is addressed for a class of linear, time-invariant systems which are dissipative with respect to a quadratic power function. The system matrices are assumed to be affine functions of uncertain parameters confined to a convex polytopic region in the parameter space. For such systems, a method is developed for designing a controller which is dissipative with respect to a given power function, and is simultaneously optimal in the linear-quadratic-Gaussian (LQG) sense. The resulting controller provides robust stability as well as optimal performance. Three important special cases, namely, passive, norm-bounded, and sector-bounded controllers, which are also LQG-optimal, are presented. The results give new methods for robust controller design in the presence of parametric uncertainties.

Joshi, Suresh M.↗

NASA NTRS1994

LQG and Feedforward Controllers for the Deep Space Network Antennas

The controller development and the tracking performance evaluation for NASA's Deep Space Network antenna are presented. A trajectory preprocessor, LQG (Linear Quadratic Gaussian) controller, feedforward controller, and their combination are designed, built, analyzed, and tested.

Deep Space Network (DSN)antennas feedforward contr↗

NASA NTRS1980

Robustness results in LQG based multivariable control designs

The robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria. Results are derived under a common framework in which the minimum singular value of the return difference transfer matrix is the key quantity. In particular, the LQ and LQG robustness results are discussed.

Lehtomaki, N. A.↗

NASA NTRS1979

Controller design approaches for large space structures using LQG control theory

The paper presents several approaches for the design of reduced order controllers for large space structures. These approaches are shown to be based on LQG control theory and include truncation, modified truncation regulators and estimators, use of higher order estimators, selective modal suppression, and use of polynomial estimators. Further, the use of direct sensor feedback, as opposed to a state estimator, is investigated for some of these approaches. Finally, numerical results are given for a long free beam.

Joshi, S. M.↗

NASA NTRS1981

Practical gust load alleviation and flutter suppression control laws based on a LQG methodology

A modified linear quadratic Gaussian (LQG) synthesis procedure has been used to design low-order robust multiloop controllers for a flexible airplane. The introduction of properly constructed fictitious Gauss-Markov processes in the control loops allowed meeting classical frequency-domain stability criteria using the direct synthesis procedures of modern time-domain control theory. Model reduction was used to simplify the control laws to the point where they could be easily implemented on onboard flight computers. These control laws provided excellent gust load and flutter mode control with good stability margins and compared very favorably to other control laws synthesized by the classical root-locus technique.

Gangsaas, D.↗