Douglas P. Looze

A relationship between sensitivity and stability of multivariable feedback systems

Both comparison sensitivity and robust stability analysis attempt to extend concepts which are well understood in scalar feedback systems to multivariable control system design. Although the two bodies of work have developed about a decade apart, the basic philosophies are similar. Both attempt to maintain a system property (sensitivity reduction versus stability) in the presence of plant modeling errors. This paper demonstrates how the similarity in philosophy translates into a similarity in results and interpretations.

Design issues for fault tolerant-restructurable aircraft control

This paper discusses the problem of accommodating failures in aircraft. Techniques which may be used to either passively tolerate or actively detect and compensate for component failures and damage are reviewed, and suggestions are made for integrating these techniques into a restructurable flight control system (RFCS). The focus of the discussion is on near-term application of techniques now being researched.

Robustness analysis using singular value sensitivities

This paper introduces a linear time invariant system analysis tool, the singular value sensitivity function, which can be used in conjunction with singular value analyses to provide more complete estimates of system feedback properties. An important feature of this tool is the ability to analyze the effect of simultaneous variations in several system parameters.

Minimax control of linear stochastic systems with noise uncertainty

The problem of linear-quadratic-Gaussian control of multivariable linear stochastic systems with uncertain second-order statistical properties is considered. Uncertainty is modeled by allowing process and observation noise spectral density matrices to vary arbitrarily within given classes, and a minimax control formulation is applied to the quadratic objective functional. General theorems proving the existence and characterization of saddle-point solutions to this problem are presented, and the relationship of these results to earlier results on minimax state estimation are discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.

Limitations of feedback properties imposed by open-loop right half plane poles

An integral constraint on the closed-loop transfer function of unstable open-loop systems is used to quantify a tradeoff between feedback properties of the closed-loop system. This results in a lower bound on the peak of the complementary sensitivity function for unstable plants. The lower bound illustrates the nature of the tradeoff that is imposed, and provides insight into the difficulties imposed on the control of unstable systems. It can be used to quantitatively evaluate tradeoffs between the frequency of the open-loop unstable pole, the peak of the complementary sensitivity functions, and the bandwidth of the closed-loop system. Such a relationship has long been recognized, and is embodied in the classical design rule of thumb which states that the closed-loop bandwidth must be at least twice as large as the frequency of the unstable pole. Results which give insight into this rule and a theoretical basis for it are provided. >

Brief paper: A dual optimization procedure for linear quadratic robust control problems

This paper considers the problem of choosing a single constant linear state feedback control law which produces satisfactory performance for each of several operating points of a system. The model for each operating point is assumed to be linear and the criterion for satisfactory performance is taken to be an infinite horizon quadratic cost functional. This problem is reformulated as a finite dimensional optimization over the linear feedback gains which can be readily solved using standard nonlinear optimization techniques provided a stabilizing initial value of the gains can be found. Although the direct solution of this problem will be discussed briefly, the major portion of the paper will be devoted to solution techniques when an initial stabilizing guess is not available.

Gradient calculations for linear quadratic fixed-control structure problems

A general formula for the gradient of the linear quadratic fixed-control structure problem with respect to the free controller parameters is presented. This formula includes as special cases time-invariant, time-varying, and robust control formulations for both continuous- and discrete-time problems. Explicit formulas for the continuous-time formulations are presented.

An approach to restructurable control system design

This paper presents an approach to the automatic redesign of flight control systems for aircraft that have suffered one or more control element failures. The procedure is based on Linear Quadratic design techniques, and produces a control system that maximizes a measure of feedback system performance subject to a bandwidth constraint.

Brief papers: Hierarchical control of weakly-coupled systems

The usual concept of weakly-coupled systems is generalized to provide a definition in terms of the decomposition used. The definition includes a measure of the strength of the coupling. The main result of the paper is a local convergence result for natural decompositions (decompositions which exploit system structure) of systems which are sufficiently weakly coupled.

Quadratic Weight Adjustment for the Enhancement of Feedback Properties

This paper presents a procedure for improving the feedback properties of a linear multivariable state feedback system which was designed using linear quadratic optimization. The procedure adjusts the quadratic weights using information obtained from a singular value analysis of the closed loop system. Although attention is focused primarily on the linear quadratic design method, the basic approach can be applied to adjust the design parameters of any design method.