Lawrence D. Davis

The optimal projection equations for fixed-order, sampled-data dynamic compensation with computation delay

For an LQG-type sampled-data regulator problem which accounts for computational delay and utilizes an averaging A/D device, the equivalent discrete-time problem is shown to be of increased order due to the inclusion of delayed measurement states. The optimal projection equations for reduced-order, discrete-time compensation are applied to the augmented problem to characterize low-order controllers. The design results are illustrated on a 10th-order flexible beam example.

The optimal projection equations for reduced-order, discrete-time modelling, estimation and control

The optimal projection equations derived previously for reduced-order, continuous-time modelling, estimation and control are developed for the discrete-time case. The design equations are presented in a concise and unified manner to facilitate their accessibility for the development of numerical algorithms for practical applications. As in the continuous-time case, the standard Kalman filter and linear-quadratic-Gaussian results are immediately obtained as special cases of the estimation and control results.

An input normal form homotopy for the L/sup 2/ optimal model order reduction problem

In control system analysis and design, finding a reduced-order model, optimal in the L/sup 2/ sense, to a given system model is a fundamental problem. The problem is very difficult without the global convergence of homotopy methods, and a homotopy based approach has been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. A homotopy algorithm based on the input normal form characterization of the reduced-order model is developed here and is compared with the homotopy algorithms based on Hyland and Bernsteins optimal projection equations. The main conclusions are that the input normal form algorithm can be very efficient, but can also be very ill conditioned or even fail. >

Discrete-time mixed-norm H2/H∞ controller synthesis

H 2 /H∞ optimal control synthesis enables the design of controllers for simultaneous rejection of both narrow-band and wide-band disturbances and also has applications in robust control. Synthesis equations in the form of coupled Riccati and Lyapunov equations are available for both full-order and reduced-order, continuous-time H 2 /H∞ control design and it is possible to base numerical algorithms on these synthesis equations. However, currently it has not been found feasible to develop such synthesis equations for the equivalent discrete-time problems. This highlights the necessity of parameter optimization approaches to the design of discrete-time H 2 /H∞ controllers. This paper considers H 2 /H∞ discrete-time controller design and develops a solution approach that relies on continuation algorithms. The results are illustrated using a benchmark non-collocated flexible structure example.

Numerical solution of the optimal projection/maximum entropy design equations for low-order, robust controller design

This paper summarizes some recent results obtained using the optimal projection/maximum entropy control-design equations. The main results include: low-order controllers for CSDL Model #2; robust controllers for the SCOLE and VCOSS A models with modal-frequency uncertainties; and Doylés example.

Toward self-reliant control for adaptive structures

Abstract Over the past two decades, control technology, including a wide spectrum of activities from algorithms to hardware, has made enormous strides in improving pointing and tracking precision and image quality for NASA and DoD space systems. However, the need for qualitative advances toward truly self-reliant control capability are illustrated, in this paper, by results of several highly successful laboratory demonstration programs that were completed within the last five years. We proceed to describe more recent results, both theoretical and experimental, in which various facets of self-reliant capability have been achieved, at least in nascent form. For example, intelligent vibration control built in to actuator hardware is illustrated by the “Frequency Domain LPACT” demonstration for JPL in which an actuator designs and implements its own local loop in situ. Results on the Adaptive Neural Control program for the Air Force using the ASTREX test bed showed the capability to rapidly recover control effectiveness following sudden hardware failures. Further, promising results to-date for the MACE II flight test program show the potential of neural control for autonomous spacecraft control. These and similar developments are used to illustrate the current promise, present limitations and future prospects of self-reliant, intelligent control of adaptive structures.

A parameterization of minimal plants

We present the input-normal Riccati parameterization, a generalization of Kabambas input-normal form, which allows the continuous parameterization of the set of minimal linear systems of a given order that have distinct singular values; the input-normal Riccati form has no requirement that the underlying system be stable. We also present formulas for the use of the input-normal Riccati parameterization for the synthesis of systems via gradient methods. >

Riccati equation approaches for small gain, positivity, and Popov robustness analysis

In recent years, small gain (or //<») analysis has been used to analyze feedback systems for robust stability and performance. However, since small gain analysis allows uncertainty with arbitrary phase in the frequency domain and arbitrary time variations in the time domain, it can be overly conservative for constant real parametric uncertainty. More recent results have led to the development of robustness analysis tools, such as extensions of Popov analysis, that are less conservative. These tests are based on parameter-dep endent Lyapunov functions, in contrast to the small gain test, which is based on a fixed quadratic Lyapunov function. This paper uses a benchmark problem to compare Popov analysis with small gain analysis and positivity analysis (a special case of Popov analysis that corresponds to a fixed quadratic Lyapunov function). The state-space versions of these tests, based on Riccati equations, are implemented using continuation algorithms. The results show that the Popov test is significantly less conservative than the other two tests and for this example is completely nonconservative in terms of its prediction of robust stability.

MACE II: A SPACE SHUTTLE EXPERIMENT FOR INVESTIGATING ADAPTIVE CONTROL OF FLEXIBLE SPACECRAFT

This paper presents an overview of the Middeck Active Control Experiment - Flight II (MACE II). MACE is a space shuttle flight experiment designed to investigate modeling and control issues for achieving high precision pointing and vibration control of future spacecraft. MACE was developed by NASA Langley Research Center, the Massachusetts Institute of Technology, and Payload Systems, Inc. The experiment was successfully flown on STS-67 in March 1995. The Air Force Research Laboratory (AFRL) has initiated a program to refly the MACE hardware to investigate the use of adaptive control algorithms for precision structural control. MACE II will answer key questions about the ability of adaptive algorithms to perform with respect to the constraints and uncertainties associated with space flight. It will also provide a basis for comparing these adaptive techniques with the fixed-gain linear control approach employed by MACE I.

Active vibration isolation with stiff actuators and inertial sensors

Operation of sensitive equipment aboard multi-sensor platforms requires active vibration isolation technology. In response to these needs, the active isolation fitting (AIF) was developed to replace passive mechanical end fittings and joints in truss structures. The AIF combines intrastructural and inertial devices to cancel vibration transmission into a vibration-sensitive subsystem. This paper discusses the AIF principles of operation, details its robust performance characteristics and reviews the extensive experimental results that have been accumulated over the past several years. Test results show 20 to 30 dB of broadband isolation for both single AIF tests and six degree-of-freedom isolation systems demonstrated on two major, government- supplied testbeds.