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NASA NTRS1988

Optimal discrete-time LQR problems for parabolic systems with unbounded input: Approximation and convergence

An abstract approximation and convergence theory for the closed-loop solution of discrete-time linear-quadratic regulator problems for parabolic systems with unbounded input is developed. Under relatively mild stabilizability and detectability assumptions, functional analytic, operator techniques are used to demonstrate the norm convergence of Galerkin-based approximations to the optimal feedback control gains. The application of the general theory to a class of abstract boundary control systems is considered. Two examples, one involving the Neumann boundary control of a one-dimensional heat equation, and the other, the vibration control of a cantilevered viscoelastic beam via shear input at the free end, are discussed.

Rosen, I. G.↗

NASA NTRS1988

On-line measurement of heat of combustion

An experimental method for an on-line measurement of heat of combustion of a gaseous hydrocarbon fuel mixture of unknown composition is developed. It involves combustion of a test gas with a known quantity of air to achieve a predetermined oxygen concentration level in the combustion products. This is accomplished by a feedback controller which maintains the gas volumetric flow rate at a level consistent with the desired oxygen concentration in the products. The heat of combustion is determined from a known correlation with the gas volumetric flow rate. An on-line microcomputer accesses the gas volumetric flow data, and displays the heat of combustion values at desired time intervals.

Chaturvedi, S. K.↗

NASA NTRS1986

Reconstruction and robust reduced-order observation of flexible variables

This paper discusses reconstruction and estimation of flexible variables from multiple strain measurements for use in state feedback control of flexible manipulators. Reconstruction is proposed for obtaining flexible mode amplitudes from the measurements, and estimation for the modal velocities. Design of the observer for estimation of the velocities is discussed with regard to robust implementation. The performance of the observer is examined experimentally for several specifications of the error dynamics.

Hastings, Gordon G.↗

NASA NTRS1987

Modeling and stability analysis for the upper atmosphere research satellite auxiliary array switch component

A feedback control system, called an auxiliary array switch, was designed to connect or disconnect auxiliary solar panel segments from a spacecraft electrical bus to meet fluctuating demand for power. A simulation of the control system was used to carry out a number of design and analysis tasks that could not economically be performed with a breadboard of the hardware. These tasks included: (1) the diagnosis of a stability problem, (2) identification of parameters to which the performance of the control system was particularly sensitive, (3) verification that the response of the control system to anticipated fluctuations in the electrical load of the spacecraft was satisfactory, and (4) specification of limitations on the frequency and amplitude of the load fluctuations.

Wolfgang, R.↗

NASA NTRS1986

Dynamic compensator design for robust stability of linear uncertain systems

This paper presents a robust linear dynamic compensator design algorithm for linear uncertain systems whose parameters vary within given bounded sets. The algorithm explicitly incorporates the structure of the uncertainty into the design procedure and utilizes the elemental perturbation bounds developed recently. The special cases of linear state feedback and measurement feedback controllers are considered and the relative trade offs are discussed. The design algorithm is illustrated with the help of a simple example.

Yedavalli, R. K.↗

NASA NTRS1986

A guidance law for the aeroassisted plane change maneuver in the presence of atmospheric uncertainties

A stochastic feedback control law for a space vehicle performing an aeroassisted plane-change maneuver is developed. The stochastic control law is designed to minimize the energy loss while taking into consideration the uncertainty in the atmospheric density. The solution is based on expansion of the stochastic Hamilton-Jacobi-Bellman equation (or dynamic programming) about a zeroth-order known integrable solution. The resulting guidance law is expressed as a series expansion in the noise power spectral densities. A numerical example indicates the potential improvement of this method.

Mishne, D.↗

NASA NTRS1987

Sensitivity of closed-loop eigenvalues and robustness

Analytical results are obtained in a present investigation of the way in which full state feedback controller and estimator eigenvalues in a closed-loop linear control system affect these eigenvalues' sensitivity with respect to uncertain plant parameters. A controller eigenvalue lying near an estimator eigenvalue yields large eigenvalue sensitivity, which should be reduced through the separation of controller eigenvalues from estimator eigenvalues.

Adamian, A.↗

NASA NTRS1988

Electron beam source molecular beam epitaxial growth of analog graded Al(x)Ga(1-x)As ballistic transistors

A new method has been developed for the growth of graded band-gap Al(x)Ga(1-x)As alloys by molecular beam epitaxy which is based upon electron beam evaporation of the group III elements. The metal fluxes are measured and feedback controlled using a modulated ion gauge sensor. The system is computer controlled which allows precise programming of the Ga and Al evaporation rates. The large dynamic response of the metal sources enables growth of variable band-gap III-V alloys with arbitrary composition profiles. This new technique is demonstrated by synthesis of analog graded Al(x)Ga(1-x)As unipolar ballistic electron transistors.

Malik, Roger J.↗

NASA NTRS1987

Charged drop levitators and their applications

An account is given of the charged drop levitation characteristics of two different devices: (1) a feedback-controlled electrostatic levitator able to lift a several mm-diameter drop in 1g conditions, which is applicable to drop dynamics, crystal growth, and supercooling/solidification experiments; and (2) a linear quadrupole levitator, whose advantages are demonstrated in light of the results obtained for the charged drop instability experiment. The cause of the premature drop burstings observed is suggested to be an electron avalanche in the surrounding gaseous medium rather than the Rayleigh limit.

Rhim, W. K.↗

NASA NTRS1988

Ultralow threshold graded-index separate-confinement heterostructure single quantum well (Al, Ga) As lasers

Broad area graded-index separate-confinement heterostructure single quantum well lasers grown by molecular-beam epitaxy (MBE) with threshold current density as low as 93 A/sq cm (520 microns long) have been fabricated. Buried lasers formed from similarly structured MBE material with liquid phase epitaxy regrowth had threshold currents at submilliampere levels when high reflectivity coatings were applied to the end facets. A CW threshold current of 0.55 mA was obtained for a laser with facet reflectivities of about 80 percent, a cavity length of 120 micron, and an active region stripe width of 1 micron. These devices driven directly with logic level signals have switch-on delays less than 50 ps without any current prebias. Such lasers permit fully on-off switching while at the same time obviating the need for bias monitoring and feedback control.

Derry, P. L.↗

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 NTRS1989

Chip Advancer For GPS Receiver

Instrument errors made negligible. For each integration interval, both delay and rate of change of delay initialized to small fraction of chip - for example, to order of 10 to the negative 7th power - thereby making feedback control and extraction of delay highly accurate and flexible. With appropriate selection of sampling rate relative to chip rate, commensurability errors reduced to extremely small levels. In Global Positioning System (GPS) receiver, pseudorandom code sequence generated by simple digital logic incorporating effects of time, delay, and rate of change of delay. Flexibility in starting time and sum interval very useful in aligning correlation interval with beginnings and endings of data bits.

Meehan, Thomas K.↗

NASA NTRS1988

On Hilbert-Schmidt norm convergence of Galerkin approximation for operator Riccati equations

An abstract approximation framework for the solution of operator algebraic Riccati equations is developed. The approach taken is based on a formulation of the Riccati equation as an abstract nonlinear operator equation on the space of Hilbert-Schmidt operators. Hilbert-Schmidt norm convergence of solutions to generic finite dimensional Galerkin approximations to the Riccati equation to the solution of the original infinite dimensional problem is argued. The application of the general theory is illustrated via an operator Riccati equation arising in the linear-quadratic design of an optimal feedback control law for a 1-D heat/diffusion equation. Numerical results demonstrating the convergence of the associated Hilbert-Schmidt kernels are included.

Rosen, I. G.↗

NASA NTRS1987

Robust eigenstructure assignment by a projection method: Application using multiple optimization criteria

New ideas which lead to feedback control laws for large flexible structures which are insensitive to model uncertainty are presented. A pole placement method is presented which leads to near-unitary closed loop eigenvectors, and a new method is introduced to design the control while simultaneously considering three competing measures of optimality. Robustness versus Integral algorithms are applicable to at least moderately high-dimensioned systems. In the present discussion, controls for two coupled flexible bodies are considered. A 6x24 gain matrix is designed to control a 12 modes system using 6 actuators. Researchers also developed control laws for the R2P2 simulator at Martin Marietta; in this case 3 actuators are used to control a 12th order system. Simulation studies indicate that researchers indeed achieved robust designs without significant difficulties associated with spillover into the uncontrolled modes. Here, several key ideas and numerical results are given. In the references, details of the formulation, discussions of salient features, and connection to the availiable literature are given.

Junkins, J. L.↗

NASA NTRS1989

Experimental verification of an eddy-current bearing

A new type of electromagnetic bearing was built and tested. It consists of fixed AC-electromagnets in a star formation surrounding a conducting rotor. The bearing works by repulsion due to eddy-currents induced in the rotor. A single bearing is able to fully support a short rotor. The rotor support is inherently stable in all five degrees of freedom. No feedback control is needed. The bearing is also able to accelerate the rotor up to speed and decelerate the rotor back to standstill. The bearing design and the experimentation to verify its capabilities are described.

Nikolajsen, Jorgen L.↗

NASA NTRS1988

Robustness with real parametric and structured complex uncertainty

The problem of robust stability and performance in feedback control systems with n real (possibly related) uncertain parameters and structured unmodeled dynamics (the latter taking the form of m complex blocks dynamic uncertainties) is considered. A robustness margin rm is defined with respect to such model uncertainty structure and an algorithm is developed to compute it. Robust stability and performance are characterized in terms of r sub m or the structured singular value mu. An iterative procedure using the above algorithm is given to compute tight bounds on k sub m and mu. These bounds are exact for the case m = 3 or less.

Pena, Ricardo S. Sanchez↗

NASA NTRS1989

Structural robustness with suboptimal responses for linear state space model

A relationship between the closed-loop eigenvalues and the amount of perturbations in the open-loop matrix is addressed in the context of performance robustness. If the allowable perturbation ranges of elements of the open-loop matrix A and the desired tolerance of the closed-loop eigenvalues are given such that max(j) of the absolute value of Delta-lambda(j) (A+BF) should be less than some prescribed value, what is a state feedback controller F which satisfies the closed-loop eigenvalue perturbation-tolerance requirement for a class of given perturbation in A? The paper gives an algorithm to design such a controller. Numerical examples are included for illustration.

Keel, L. H.↗

NASA NTRS1989

Small motion experiments on a large flexible arm with strain feedback

Initial experiments on state-space feedback control of a large flexible manipulator with a parallel linkage drive are described. A linear controller using joint angle and strain measurements has been designed to minimize a quadratic performance index with a prescribed stability margin. It is based on a simplified model that accounts for the constraints of the parallel linkage kinematically rather than through constraint forces. The results show substantial improvement over a simple proportional-derivative joint control.

Yuan, B. S.↗