Engineering topics

Franklin, Gene F.

Publications and source records attributed to Franklin, Gene F..

7 records

NASA NTRS1988

An averaging analysis of discrete-time indirect adaptive control

An averaging analysis of indirect, discrete-time, adaptive control systems is presented. The analysis results in a signal-dependent stability condition and accounts for unmodeled plant dynamics as well as exogenous disturbances. This analysis is applied to two discrete-time adaptive algorithms: an unnormalized gradient algorithm and a recursive least-squares (RLS) algorithm with resetting. Since linearization and averaging are used for the gradient analysis, a local stability result valid for small adaptation gains is found. For RLS with resetting, the assumption is that there is a long time between resets. The results for the two algorithms are virtually identical, emphasizing their similarities in adaptive control.

Phillips, Stephen M.↗

NASA NTRS1988

On a fractional representation approach to closed-loop experiment design

A plant model, based on a fractional representation of the loop, which is uniquely suited to the closed-loop experiment design problem, is proposed. The advantage of this model is that it substitutes an open-loop problem (for which there has been extensive work) for the original-closed loop problem. The results of Monte Carlo simulations which support the utility of this approach are included.

Hansen, Fred R.↗

NASA NTRS1988

Averaging analysis of adaptive control algorithms

The method of averaging is used to analyze discrete-time indirect adaptive control. The analysis focuses on various prediction-error-driven identification algorithms coupled with a general linear control law. The plant is not required to be in the model set of the identifier, which accounts for systems with unmodeled plant dynamics. Exogenous input signals including known command signals and unknown disturbances are also included. Both gradient and Newton-based algorithms are considered.

Phillips, Stephen M.↗

NASA NTRS1987

An error bound for a discrete reduced order model of a linear multivariable system

The design of feasible controllers for high dimension multivariable systems can be greatly aided by a method of model reduction. In order for the design based on the order reduction to include a guarantee of stability, it is sufficient to have a bound on the model error. Previous work has provided such a bound for continuous-time systems for algorithms based on balancing. In this note an L-infinity bound is derived for model error for a method of order reduction of discrete linear multivariable systems based on balancing.

Al-Saggaf, Ubaid M.↗

NASA NTRS1987

On the stability of adaptive pole-placement controllers with a saturating actuator

The question of how existing pole-placement algorithms work in the case of a saturating input is addressed. The stability of such algorithms and the modifications needed to make them work in the presence of saturation are examined. The net results of this examination are: a mathematical condition for closed-loop stability; physical intuition behind this condition; some explanation of why adaptive control has been successfully implemented, even while ignoring saturation; and some design rules for doing adaptive control on linear plants with saturating actuators.

Abramovitch, Daniel Y.↗

NASA NTRS1986

Adaptive control with saturating inputs

An extension of the results from Goodwin, Ramadge and Caines (1980) to the case where the input of the linear system saturates is presented. A necessary condition for closed loop stability of such a system is shown to be that the system must remain in a region from which y(t) = 0 is reachable with saturating inputs. With a slight modification of the original algorithm, the closed loop system is shown to be stable whenever the plant is exponentially stable.

Abramovitch, Daniel Y.↗

NASA NTRS1986

On model reduction

Three model reduction methods are described. These are the discrete balanced realizations of Mullis and Roberts (1976) where a characterization of the reduction error is given and a previously unknown L(infinity) norm bound on the reduction error, is obtained. Another method is a new model reduction technique for discrete time systems which has the advantage that the reduced order model is balanced and has an L(infinity) norm bound on the reduction error. The last method derived is a frequency weighting technique for continuous and discrete systems where it is possible to specify the approximation accuracy with frequency and also, for this method, an L(infinity) norm on the weighted reduction error is obtained.

Al-Saggaf, Ubaid M.↗