David G. Meyer

Balancing and model reduction for second-order form linear systems

Model reduction of second-order form linear systems is considered where a second-order form reduced model is desired, The focus is on reduction methods that employ or mimic Moores balance and truncate (1981). First, we examine second-order form model reduction by conversion to first-order form and obtain a complete solution for this problem. Then, new Gramians and input/output (I/O) invariants for second-order systems are motivated and defined. Based on these, direct second-order balancing methods are developed. This leads naturally to direct second-order form analogs for the well-known first-order form balance and truncate model reduction method. Explicit algorithms are given throughout the paper.

A parametrization of stabilizing controllers for multirate sampled-data systems

All linear multirate controllers for a given multirate sampled-data system plant are parameterized in terms of a single parameter Q(z) that is allowed to be any stable transfer matrix provided that certain causality conditions are met. The result parallels a well-known parameterization result for single-rate sampled-data plants. The parameterization suggests architectures for multirate controllers. >

A new class of shift-varying operators, their shift-invariant equivalents, and multirate digital systems

A class of linear, shift-varying operators that generalize the notion of N-periodicity is defined. It is shown that shift-invariant equivalents for these operators exist, and that the equivalence is in a strong sense, preserving both algebraic and analytic system properties. It is shown that multirate sampled-data systems, although not generally periodic, fall into this class. Kranc vector switch decomposition and block filter implementations for single-input, single-output multirate systems are connected under the unifying framework of shift-invariant equivalents, and this framework provides a way to extend them both to multi-input, multi-output systems. >

The trajectory manifold of a nonlinear control system

In this paper, we show the set of exponentially stabilizable trajectories of a nonlinear system is a Banach manifold as smooth as the system. The main tool is a projection operator resulting a trajectory tracking control law. These results provide important insights into the nature of the trajectory exploration problem.

Cost translation and a lifting approach to the multirate LQG problem

It is shown how to translate an instance of a multirate sampled-data LQG problem into an equivalent, modified, single-rate, shift-invariant problem via a lifting isomorphism approach. Using this approach, one can solve the multirate LQG problem without using periodic system theory or solving periodic Riccati equations and without suffering any increases in state dimension. This translation procedure shows the correct way to translate RMS noise specification to the lifted domain for a multirate Q-design computer-aided-design package. >

Trajectory morphing for nonlinear systems

In this paper nonlinear trajectory morphing is introduced. We show how it can explore the trajectory space of a nonlinear system. A trajectory tracking projection operator is defined for practical implementation of morphing.

Two properties of l/sub 1/-optimal controllers

The solution of the l/sub 1/ sensitivity minimization problem is shown to have two properties which contrast markedly with properties of the solutions to the better-known H infinity sensitivity minimization problem or the LQG (linear quadratic Gaussian) problem is given of a one-parameter family of first-order plants where the order of the l/sub 1/-optimal compensator can be arbitrarily large, and thus it is impossible to bound the order of an l/sub 1/-optimal compensator in terms of the order of the plant. A plant is considered which has a continuous one-parameter family of l/sub 1/-optimal compensators, and thus l/sub 1/-optimal compensators need not be unique. The authors two examples are considered to answer two questions left open by M.A. Daleh and J.B. Pearson (ibid., vol.32, p.314-23, 1987). >

Optimizing the consolidation of titanium matrix composites

Abstract The high temperature consolidation of fiber reinforced metal matrix composite preforms seeks to eliminate matrix porosity (i.e. to increase the relative density) while simultaneously minimizing fiber microbending/fracture and the growth of reaction products at the fiber-matrix interface. By combining model predictive control concepts with previously developed time dependent consolidation models [18], a method is presented for the design of near optimal process schedules that evolve performance defining microstructural parameters (relative density, fiber fracture density and fiber-matrix reaction thickness) to prechosen microstructural goal states that result in composites of acceptable mechanical performance. The method is illustrated by exploring the design of process schedules for two titanium matrix composites with very different creep properties. Feasible process schedules resulting in acceptable composite mechanical performance are identified for a Ti 6Al 4V/SCS-6 system. However, the method reveals the absence of such schedules for the more creep resistant Ti 24Al 11Nb/SCS-6 intermetallic matrix composite. The optimization methodology is then used to explore modifications to the process environment, the composites component material properties (e.g. fiber strength or diffusion inhibiting coating), and the preforms initial microstructure that together enable the successful consolidation of the intermetallic matrix composite system.

Model-based feedback control of deformation processing with microstructure goals

A closed-loop feedback scheme for obtaining a goal microstructure during hot isostatic pressing (“hipping”) of powders is described. The control scheme relies on previously developed process models describing the process dynamics during a HIP run and sensors which can measure density and grain size. We use constantly updated linearization and coprime factorization and thus implement the control by convex programming. Simulation results showing the performance of the control scheme are presented.

Shift-invariant equivalents for a new class of shift-varying operators with applications to multi-rate digital control

A class of linear, shift-varying operators that generalizes the notion of N-periodicity is defined. It is shown that shift-invariant equivalents for these operators exist, and that the equivalence is in a strong sense, preserving both algebraic and analytic systems properties. It is shown that multi-rate sampled-data systems, though not generally periodic, fall into this class. Kranc vector switch decomposition and block filter implementations for single-input, single-output multi-rate systems are connected under the unifying framework of shift-invariant equivalents, and this framework is the way to extend them both to multi-input, multi-output systems. Possible applications include a parameterization of all stabilizing multi-rate controllers.<<ETX>>