Robust gamma-stability analysis in a plant parameter space

Brief paper: Robustness against sensor failures

The classical results of Routh and Hurwitz on the stability of polynomials are generalized from the open left half plane to certain other subregions G of the complex plane. By our method, arbitrary conic sections can be handled. The results are interpreted as criteria for G -stability of linear systems. A numerical algorithm to compute the criteria is given. An application to a problem in robust controller design is outlined.

A generalization of the Routh-Hurwitz stability criteria and an application to a problem in robust controller design

The problem of control system design is stated with explicit uncertainty bounds for physical parameters in the plant model and performance bounds as design objectives. A finite number of typical plant parameter values is used to define a multi-model problem. Two design methods for fixed-gain controllers for this problem are reviewed: i) the simultaneous assignment of the poles to a given region for all members of the plant family by parameter space methods, ii) the interactive Pareto-optimization of a vectorial performance index. The controller for the representative family of plant models may then be tested for continuous intervals of the parameter uncertainties. Only few results are available on stability of interval polynomials and matrices. Also the problem of a systematic choice of a feasible controller structure has not yet been solved. The interactive multi-model approaches will particularly profit from the progress in computer graphics.

Multi-model approaches to robust control system design

This paper presents a new approach to parameter space design of linear multivariable control systems. The complete solution of a pole region assignment problem for single-input systems is obtained as an admissible region in the n -dimensional parameter space of state feedback gains. We develop a new modeling technique for these admissible parameter space regions which is superior to previous ones because it permits unambiguous and efficient graphical display of slices in 2D and 3D subspaces. In an interactive computer graphics implementation, this method provides an environment where the influence of stability, performance, robustness, integrity, and control constraints on design parameters can be directly visualized and complex tradeoffs are resolved in an interactive way. By judicious combination of overlays, color, and/ or animation, admissible ranges of up to five or six design parameters can be displayed simultaneously. A sequential decomposition technique which selects slices for full parameter space design of lower dimensional subsystems such that the remaining eigenvalues are invariant is used for systems of arbitrarily high order. Parameter space design of unity rank feedback for multiinput systems is done in exactly the same fashion, while systematic sequential design of full rank feedback is achieved as the sum of dyadic stages to which the single-input modeling techniques apply. Examples are given for all presented methods to show the flexibility and potential as a computer-aided control system design framework with a novel integration of computer graphics technology.

http://ieeexplore.ieee.org/iel5/9/24253/01104608.pdf

J. Ackermann

Papers

D-Decomposition in the Space of Feedback Gains for Arbitrary Pole Regions