Engineering topics
Publications and source records attributed to Armstrong, E. S..
Control-theory design package aids design of linear-quadratic-Gaussian (LOG) controllers and optimal filters. It is applicable to systems that can be modeled by linear time-invariant differential or difference equations.
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A modern control theory design package (ORACLS) for constructing controllers and optimal filters for systems modeled by linear time-invariant differential or difference equations is described. Numerical linear-algebra procedures are used to implement the linear-quadratic-Gaussian (LQG) methodology of modern control theory. Algorithms are included for computing eigensystems of real matrices, the relative stability of a matrix, factored forms for nonnegative definite matrices, the solutions and least squares approximations to the solutions of certain linear matrix algebraic equations, the controllability properties of a linear time-invariant system, and the steady state covariance matrix of an open-loop stable system forced by white noise. Subroutines are provided for solving both the continuous and discrete optimal linear regulator problems with noise free measurements and the sampled-data optimal linear regulator problem. For measurement noise, duality theory and the optimal regulator algorithms are used to solve the continuous and discrete Kalman-Bucy filter problems. Subroutines are also included which give control laws causing the output of a system to track the output of a prescribed model.
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The sampled-data optimal linear regulator problem provides a means whereby a control designer can use an understanding of continuous optimal regulator design to produce a digital state variable feedback control law which satisfies continuous system performance specifications. A basic difficulty in applying the sampled-data regulator theory is the requirement that certain digital performance index weighting matrices, expressed as complicated functions of system matrices, be computed. Infinite series representations are presented for the weighting matrices of the time-invariant version of the optimal linear sampled-data regulator problem. Error bounds are given for estimating the effect of truncating the series expressions after a finite number of terms, and a method is described for their computer implementation. A numerical example is given to illustrate the results.
A procedure is derived for stabilizing linear constant discrete systems which is a discrete analog to the extended Bass algorithm for stabilizing linear constant continuous systems. The procedure offers a method for constructing a stabilizing feedback without the computational difficulty of raising the unstable open-loop response matrix to powers thus making the method attractive for high order or poorly conditioned systems.
Two methods for stabilizing constant linear systems, namely, the extended Bass algorithm for continuous systems and a discrete system analog, are discussed. For the continuous algorithm, a new result on the degree of stability of the closed-loop eigenvalues is presented, and for both methods, typical results and asymptotic trends in the data are illustrated through an example computation.
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A digital computer program (ORACLS) for implementing the optimal regulator theory approach to the design of controllers for linear time-invariant systems is described. The user-oriented program employs the latest numerical techniques and is applicable to both the digital and continuous control problems.
In the optimal regulator formulation of discrete explicit model following the Riccati equation may fail to reach a steady-state value for model dynamics which are not asymptotically stable. Such conditions often arise in aircraft applications when flying quality criteria based on step inputs are used to define the model equations. Mathematical conditions are presented which insure a steady-state value of the model-following gain matrix regardless of the behavior of the underlying Riccati equation. These results are applied to the design of a model-following controller for the lateral motion of a typical fighter aircraft using unstable model equations.
For linear time-invariant digital systems, convergence of the Riccati equation associated with the optimal servo problem is examined. Necessary and sufficient conditions are established for the existence of finite gains when the command input trajectories may fail to be asymptotically stable.
Iterative solution of least squares programming problem for finite thrust rocket trajectory optimization
Extremal, maximum-range, thrust limited rocket trajectory computing method with lunar transport applications
Maximum range trajectories for rocket propelled lunar flying vehicles in uniform gravitational field
Computational method for time optimal space rendezvous between rocket vehicle and circular orbit target
Calculation of electron energy deposition in thin- film polymeric materials
Time optimal control law for lunar orbit rendezvous validated by using the pontryagm principle