Design Of Multivariable Feedback Systems Research Articles

Design of advanced robust decentralized control of parallel dc/dc converters

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.

A near-decoupling design of multivariable feedback systems with the V-canonical compensator

In this paper a practical procedure is proposed for the decoupling design of multivariable feedback systems. The so-called V-canonical compensator is used to remove the need for inversion of the plant transfer function matrix. The cross-coupling in the plant is first expressed in terms of the equivalent disturbance. Then a strictly-decoupling formula is established to reduce this equivalent disturbance. Ultimately, nearly-decoupling control is concerned with the design of a realizable compensator.

Multivariable stability and robustness of sequentially designed feedback systems

In sequential loop closure, the importance of evaluating the stability and stability robustness at the intermediate loop closures is well known. However, knowledge concerning how the intermediate loop closures, as well as the final loop closures, contribute to the stability and stability robustness of the overall feedback system holds special significance to the analysis and design of multivariable feedback systems. An analysis of the complete feedback system reveals the multivariable Nyquist contributions from the intermediate loop closures. It is also shown that the results greatly simplify if frequency separation exists between the intermediate loops. The analysis is presented with a two-step loop closure procedure using inner and outer loops that can be generalized to multistep situations. The control of the longitudinal dynamics of an aircraft is addressed to further clarify and demonstrate the results.

Branch-point placement

Power-series approximations to eigenvalue and eigenvector functions have a role to play in the design of multivariable feedback systems. The convergence and sensitivity properties of these approximations depend on the positions of the branch points of the characteristic function of the appropriate rational transfer function. This paper gives a quantitative treatment of this problem and proposes a set of suitable bounds for the case of isolated as well as “latent” branch points. Given the importance of the locations of the branch points, from a practical viewpoint it is desirable to know whether it is possible to precondition the transfer-function matrix so as to adjust the positions of the branch points. To this end the paper proposes suitable algorithms and concludes with two simple design studies which demonstrate the benefits of preconditioning.

Multivariable toolbox for use with MATLAB

A toolbox for the frequency-domain analysis and design of multivariable feedback systems, to be used with the software products PC-MATLAB or PROMATLAB, is described. The principal model representations used by the toolbox are described. Its capabilities are illustrated by a worked design example that shows the use of a Nyquist array method. Other design techniques supported by the toolbox are reviewed briefly. >

Method for robust design of multivariable feedback systems

Method for robust design of multivariable feedback systems

Design of multivariable feedback systems with infinite gain margin and decoupling

This letter discusses the problem of designing a feedback compensator that attains the infinite gain margin under the uncertainties of feedback gains. A sufficient condition is given for the existence of compensators and then it is shown that the condition becomes necessary subject to the requirement that the feedback system is decoupled. The nonlinear case is also discussed.

Design of Multivariable Feedback Systems Using Progressive Decoupling

A general procedure for the design of multivariable feedback systems is presented. The system is first rendered weakly coupled by a suitable choice of some controller ratios and then designed by conventional single-loop techniques. One major characteristic of the method is that various degree of coupling of the system can be obtained, dependent on the complexity of the controller ratios chosen. Furthermore, a criterion is given to decide when the system can be regarded as weakly coupled, such that single-loop design techniques can be applied. The method gives the designer more freedom in the design and provides him with many more choices for a suitable controller. The effectiveness of the method is demonstrated by an application to a 4 x 4 boiler furnace example.

Design of multivariable feedback systems with simple unstable plant

This paper proposes a design methodology for distributed linear multivariable feedback systems with simple unstable plants (a simple unstable plant has either first- or second-order unstable poles). The methodology developed provides a global characterization of all realizable compensators which stabilize a given simple unstable plant. A design example is given to show that this methodology can be used to generate, in an appropriate computer-aided design environment, controllers which are optimal with respect to designer-specified criteria. Additionally, it is shown that the nature of the design methodology gives geometric insight into the dynamics of the process whereby an unstable plant is stabilized.

A new approach for the design of multivariable feedback systems

A new design technique for multivariable feedback systems is presented. In this approach, n —1 open-loop transfer functions at different inputs of the plant, with all other feedback paths closed, are specified in advance, and are achieved exactly. The nth open-loop transfer function is a by-product of the design process, such that the overall feedback system is stabilized. The design approach is fitted to solve problems in which the plant elements can have non-stable poles and non-minimum phase zeros. The design process is straightforward, no iterations are necessary, and the achieved design copes exactly with the design specifications. The gainbandwidths of the different lis and the overall loop gain l* might be constrained due to non-stable poles and zeros of the plant elements. Based on the obtained different loop gains, any input output matrix T can bo achieved with the aid of an appropriate prefilter matrix F.

Design of multivariable feedback systems with stable plant

This paper considers, in a general algebraic framework, the design of a unity-feedback multivariable system with a stable plant. The method is based on a simple parameterization of the four closed-loop transfer functions in terms of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</tex> , the plant transfer function, and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q=H_{y_{1}u_{1}}</tex> . In particular, the I/O transfer function <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q=H_{y_{2},u_{1}}=PQ</tex> . Using the framework of rational transfer functions, we show that the closed-loop system will be exponentially stable if and only if <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> is exponentially stable. Furthermore, if both <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">P</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> are strictly proper then the controller is also strictly proper. The basic result is Design Theorem 2. An algorithm is given for obtaining strictly proper controllers such that the resulting I/O map is decoupled, all its poles can be chosen by the designer, and the same holds for zeros except, of course, for the C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</inf> -zeros prescribed by the C <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">+</inf> -zeros of the plant. A discussion is included to temper these results by the constraints imposed by noise and plant saturation.

Some unifying concepts in multivariable feedback design†

Frequency domain techniques for computer-aided design of multivariable feedback systems are now well established in the form of several, apparently distinct, design techniques. It is shown that a unified design structure can be developed based on the theoretical concepts of precompensation, eigenvalue approximation and permissible, constant, input/output transformations.

Extension of the design algorithm of "Design of multivariable feedback systems with stable plant" to the tracking problem

The design algorithm proposed in [1] is extended to include the tracking problem. The robustness of the design is also shown.

A method for design of multivariable feedback systems and its relation to mathematics syllabuses in electrical engineering

This paper presents a direct‐design procedure for synthesis of closed loop control systems. This method has been taught successfully to final year electrical engineering undergraduates and is of interest in that it illustrates the application of a considerable part of a typical engineering mathematics syllabus and may help to provide motivation for the study of mathematical topics. Additionally the method points the way to numerous other techniques for the synthesis of control systems and these methods are a fruitful source of project work for students of electrical engineering or of applied mathematics.

Some Unifying Concepts in Multivariable Feedback Design

Frequency domain techniques for computer-aided design of multi-variable feedback systems are now well established in the form of several, apparently distinct, design techniques. It is shown that a unified design structure can be developed based on the theoretical concepts of precompensation, eigenvalue approximation and permissible, constant, input/output transformations.

Design of multivariable feedback systems

A canonical form for a multivariable linear control system is described. This canonical form is important because it enables a linear-feedback law to be chosen to produce arbitrary characteristic modes in the closed-loop system. The computational difficulties and methods suggested for minimising then are discussed.