Uncertain Multivariable Systems Research Articles

Robust Decoupled System Design of Uncertain Multivariable Feedback Systems

This paper presents a design algorithm of involving robust decoupled control of uncertain multivariable feedback systems. Two-degree-of-freedom system structure is adopted to handle the quantitative robustness and decoupled performance requirements. Quantitative feedback theory is applied for loop compensator design to achieve quantitative robustness. A decoupled model matching approach is employed for prefilter design to achieve input-output decoupling performance. Thus, the design method of two-degree-of-freedom compensators is proposed to achieve decoupled system control with quantitative robust performance. Since internal stability is satisfied, this design method performs appropriately for any stable or unstable, minimum or non-minimum phase system. The AFTI/F-16 flight control system is considered as the design example to illustrate the design algorithm.

Design and application of multivariable robust optimal systems

In this paper, a design algorithm for quantitative robust optimal control of uncertain multivariable feedback systems is developed. By use of the frequency-domain approach, the two-degree-of-freedom Wiener–Hopf optimal control method and the quantitative feedback theory are employed to derive the linear quadratic optimal system design with quantitative performance robustness. Two frequency-dependent weighting matrices are shaped and two-degree-of-freedom compensators are designed to achieve quantitative robust optimal control. The proposed design algorithm is then applied to an AFTI/F-16 flight control system design to illustrate the design algorithm. © 1998 John Wiley & Sons, Ltd.

Quantitative design of uncertain multivariable control system with an inner-feedback loop

An additional inner-feedback loop is used to reduce the channel interaction of a multivariable control system such that the design of outer-feedback loop can be treated as a single-variable problem for ease in achieving the required main-channel performance. The relative error between the exact input–output relation tii(jω) of channel i and its approximation t̂ii(jω) = {li(jω)fii(jω)}/{1 + li(jω)} is introduced to provide an effective measure for assessing the achieved noninteraction. According to the approach proposed, the single-input/single-output quantitative-feedback-theory design method can be applied directly for the design of both inner- and outer-feedback loops.

Quantitative feedback design of uncertain multivariable control systems

An alternative QFT framework is proposed for the design of multiple-input multiple-output (MIMO) feedback systems with significant plant uncertainty. Sufficient conditions are first derived to assure the achievement of the given off-diagonal performance. Then the given performance bounds on each main channel are reallocated on a reasonable basis, such that not only is the main channel performance easily achieved, but also the trade-offs of performance bounds between the loops become transparent during the system synthesis.

Optimal Popov controller analysis and synthesis for systems with real parameter uncertainties

Robust performance analysis plays an important role in the design of controllers for uncertain multivariable systems. Recent research has investigated the use of absolute stability criteria to develop less conservative analysis tests for systems with linear and nonlinear real parameter uncertainties. This note extends previous work on optimal /spl Hscr/2 performance analysis using the Popov criterion by presenting a numerical homotopy algorithm that can be used to analyze systems with less restrictive assumptions on the structure of the uncertainty block. The technique is used to compare relative robustness capabilities of the various control algorithms that have been designed for the Middeck active control experiment (MACE). The analysis is combined with the previously presented Popov controller synthesis to yield compensators that guarantee robust performance for systems with real parameter uncertainty.

Quantitative Robust Optimal Design of Uncertain Multivariable Feedback System

The design algorithm of quantitative performance robustness optimal control for uncertain multivariable systems is developed The frequency-dependent weighting matrices are shaped and two-d ĩgree-of-freedom controllers are design to achieve the quantitative robust optimal control with feedback loop satisfying the return difference equality. So that the designed system achieves quantitative robust optimal control and simultaneously the feedback loop possesses the stability margins as in time-domain LQR optimal system

004 Robust integral stabilization and regulation of uncertain multivariable systems

004 Robust integral stabilization and regulation of uncertain multivariable systems

Almost decoupling of uncertain multivariable systems

An effective almost decoupling theory using an internal model reference loop is developed for linear uncertain multivariable systems. Based on non-negative matrix theory, a useful design guide is derived to achieve the generalized diagonal dominance condition for the internal model reference loop. Using a Perron root, a sufficient condition is given to guarantee the inverse transfer matrix to be generalized diagonally dominant for all plants in a given family. One of the main features of the proposed scheme is the reduction of uncertainty in the resultant compensated internal loop system, which makes the subsequent design process of the individual channels using standard SISO techniques much simpler.

Robust Integral Stabilization and Regulation of Uncertain Multivariable Systems

The recent concept of multivariable integral controllability (MIC) is generalized to uncertain multivariable systems. It is shown that MIC is strongly dependent on the all gain positive stability (AGPS) of the steady state open loop transfer matrix. Some sufficient conditions for AGPS are provided, from which a design scheme for inducing MIC on any given system can be determined.

Performance issues in the individual channel design of 2-input 2-output systems. Part 2. Robustness issues

In this second part of a three part series of papers examining the performance issues raised by the introductory paper (O'Reilly and Leithead 1991) on individual channel design for multivariable control, attention is focused on robustness: that is, on the meeting of performance specifications—in particular closed-loop system stability—in the face of plant uncertainty. The main results are that the use of phase margins and gain margins to assess robustness of 2-input 2-output multi-variable systems is justified. Further, it is shown that controllers for uncertain 2-input 2-output multivariable systems can be designed by classical SISO Nyquist-Bode local loop shaping using stable minimum phase controllers. Several additional results are also described in the paper.

Generalized Nyquist bands for structured and highly structured uncertainty

Additive uncertainty of multivariable systems is often assumed to be either unstructured or structured, depending on whether the size or uncertainty is defined in terms of maximum singular value bounds, or bounds on the moduli of individual elements. In many practical situations, however, more information is available, and in particular the frequency response of the elements of uncertainty often display ‘directionality’. To exploit this ‘directionality’ the present paper adopts elliptical rather than circular bounds on the elements of uncertainty and derives an algorithm that generates exact eigenvalue regions which, in turn, can be deployed in the construction of exact generalized Nyquist bands. With the aid of such bands it is possible to get an exact (non-conservative) assessment of the stability margins and of other aspects of the dynamic performance of a much wider class of uncertain multivariable systems.

Deterministic control for a new class of uncertain dynamical systems

We study the problem of stabilization of nonlinear multivariable uncertain systems. We show that for a nonlinear plant with nonlinear input, a class of stabilizing continuous-type controllers can he constructed.

Normality, scaling and eigenvalue inclusion regions

One approach to establishing eigenvalue inclusion regions for robust stability analysis of uncertain linear multivariable feedback systems involves replacing the nominal plant matrix by an approximating normal one. This approach incurs additional uncertainty but has the advantage that the resulting regions are insensitive to small perturbations. These regions are obviously conservative, and it is shown in this paper how this conservatism may be reduced by utilizing the eigenvalue preserving operation of similarity scaling

Singular-value and eigenvalue techniques in the analysis of systems with structured perturbations

A new range of techniques is introduced for the purpose of exploiting information about the structure of the perturbation associated with uncertain linear multi-variable feedback systems. The class of perturbation considered is wide and ignores only the phase information of the individual elements of the perturbation matrix; it encompasses diagonal, block-diagonal and other forms of block-structured perturbations. The techniques developed provide a means of assessing stability margins and also lead to an extension of the Nyquist criterion.

A new robust stability criterion for linear and non-linear multivariable feedback systems

Earlier eigenvalue inclusion regions are replaced by new regions which are tight and thus lead to sufficient and necessary stability conditions for uncertain linear multivariate systems in the presence of unstructured perturbations. The approach provides an exact and immediate assessment of gain and phase margins. When applied to systems with sector bounded but unstructured non-linearities, the inclusion regions produce a necessary and sufficient test for the circle criterion conditions to hold in the multivariable case; as such the resulting stability criterion gives the best possible Nyquist-type extension of the circle criterion to the multivariable case for unstructured non-linearities.

Extension of the direct Nyquist array design technique to uncertain multivariable systems subject to external disturbances

Abstract The properties of a linear matrix feedback system with two degrees of freedom which allows Rosenbrock's direct Nyquist array design method to be extended to the case of uncertain multivariable systems are examined. Criteria for assessing the global and loop disturbance rejection properties of a multivariable control system are developed, and a design methodology for uncertain multivariable plants, subject to external disturbance inputs is given. The proposed design method is illustrated by means of an example.

Analysis and design of linear multivariable feedback systems in the presence of additive perturbations

The paper introduces the concept of normal approximations to the analysis of uncertain linear multivariable feedback systems, in order to derive a new criterion for the stability of plants subject to additive perturbations. This criterion permits a complete assessment of stability margins in that it provides a measure of tolerance to uncertainty as well as providing a measure of gain/phase margins. The proposed approach leads to a systematic design procedure which minimizes the effects of uncertainty by attaining the condition of normality or which improves the stability margins by robust gain/phase sharing. The results presented in this paper are insensitive to small perturbations on the nominal plant model and provide the means for a consideration of information concerning the structure of uncertainty.

Optimal control of linear uncertain multivariable stochastic systems

A technique is described for the design of linear multivariable systems in which the plant parameters are constant but unknown. These parameters are represented by random variables with known mean values and variances. A Wiener type of z-domain solution is derived to the resulting generalised linear quadratic optimal control problem. These results are also interpreted in the time domain, and the equivalent Kalman filtering solution is derived. To enable the controller to be applied in self-tuning control systems, the plant is represented in discrete polynomial form and a simple diophantine equation solution is also obtained.