Design of Multivariable Feedback Systems Using Progressive Decoupling

This paper presents the useful analysis and synthesis technique for the design of multivariable feedback systems. Optimal robust decentralized controllers of nominal and diagonal dominant nominal model of parallel operating dc/dc converters using structured singular value approach are designed. The proposed controllers have different number of tuning parameters and they are robust for both reference signals and disturbances. The robustness of feedback systems with designed controllers is investigated and compared. Simulation results, both in frequency and time domain, demonstrate the preferable performance of the designed decentralized controllers in setpoint tracking and disturbance rejection.

SOME UNIFYING CONCEPTS IN MULTIVARIABLE FEEDBACK DESIGN

The root-locus-approximation procedure is extended to provide for the complex-plane analysis of equations which contain a term quadratic in the variable parameter in addition to the usual linear term. Such an extension will have many applications; in the paper, a discussion is given concerning the design of linear time-invariant multivariable feedback systems. It is shown that, particularly for 2-input/2-output problems, where the algebra involved in obtaining the equations to be analysed remains fairly simple, much useful information is available by straightforward hand calculation. Brief suggestions are given for further generalisations of the techniques (inclusion of a cubic gain term etc.)

The paper is concerned with the derivation of useful results that complement the linearisation-based analysis and design of multivariable systems with measurement nonlinearity. The approach is based on the closed-loop linearised system descriptions and certain nonlinearity related parameters representing sector and/or incremental sector properties, and also enables the consideration of nonlinearities with discontinuities at the origin. Nonlinear-system stability and performance is assessed on the basis of the stability and performance of the corresponding linearised system and certain easily computable sufficient conditions representing BIBO and asymptotic stability conditions, as well as absolute and derivative performance bounds. The results depend on useful linearised system descriptions such as the L∞ operator norm, thus offering the advantages of meaningful assessments and overall computational simplicity.

This paper presents an algebraic theory for analysis and design of linear multivariable feedback systems. The theory is developed in an algebraic setting sufficiently general to include, as special cases, continuous and discrete time systems, both lumped and distributed. Designs are implemented by construction of a controller with two vector inputs and one vector output. Use of controllers of this type is shown to generate convenient stability results, and convenient global parametrizations of all I/O maps and all disturbance-to-output maps achievable, for a given plant, by a stabilizing compensator. These parametrizations are then used to show that any such I/O map and any such disturbance-to-output map may be simultaneously realized by choice of an appropriate controller. In the special case of lumped systems, it is shown that the design theory. can be reduced to manipulations involving polynomial matrices only. The resulting design procedure is thus shown to be more efficient computationally. Finally, the problem of asymptotically tracking a class of input signals is considered in the general algebraic setting. It is shown that the classical results on asymptotic tracking can be generalized to this setting. Additionally, sufficient conditions for robustness of asymptotic tracking, and robustness of stability are developed.

A comprehensive survey is given of recent work on the use of matrix-valued functions of a complex variable for the analysis and design of linear multivariable feedback systems. Several emerging design techniques are outlined and a simple illustrative design example given showing how such methods may be used in practice.

A general approach for computing the stationary feedback gain of a linear system with specified response characteristic is outlined. The proposed approach can be applied with advantage to the design of multivariable systems as an alternative to the existing methods for design of such systems with specified pole locations.

In this paper a basis is developed for the systematic design of linear multivariable continuous-time tracking systems for plants with inaccessible states which thus extends the results for continuous-time plants with accessible states previously obtained by Porter and Bradshaw (1974). The design method is illustrated by the presentation of the results of computer simulation studies.

In this paper a basis is developed for the systematic design of linear multivariable discrete-time tracking systems for plants with inaccessible states, which thus extends the results for discrete-time plants with accessible states previously obtained by Bradshaw and Porter (1975). The design method is illustrated by the presentation of the results of computer simulation studies.

It is shown that the return difference matrix possesses the same functions and plays the same important role in stability analysis and design of a multivariable feedback network as it does in control theory. The generalized Nyquist criterion, characteristic loci and other methods of stability analysis and design for multivariable feedback systems in control theory are applicable directly to multivariable feedback networks. In particular, a general frequency stability criterion for a multivariable lumped and distributed-parameter feedback network is presented.

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.

Robust LQG optimal controller design for multivariable discrete saturating systems with noise spectral uncertainties and nonlinear time-varying unmodeled dynamics

A new designing method of multivariable linear time-varying tracking systems with stochastic disturbances for polynomial command inputs is proposed. It has been shown that it is possible to choose the matrices of gain elements placed in feedbacks and parallel paths of the closed-loop system so that the output y(t) tracks the polynomial command input v(t) with (E expectation operator).

Computer Aided Analysis and Design of Relay Systems

COMPUTER AIDED ANALYSIS AND DESIGN OF RELAY SYSTEMS