Design Of Multivariable Systems Research Articles

Discrete-Time Multivariable System Design by Means of Continuous-Time Methods

First, the continuous-time (CT) approximate models of discrete-time (DT) system composed of sampler, zero order hold and CT plant in series are reminded. Then, basing on these models a CT design method of DT controller is described. Next, the same approach is proposed for multivariable system with DT controllers which can have different and asynchronous sampling periods. By the way, the design method of CT multivariable systems basing on design of successive controllers for some replacement SISO plants is proposed. Finally, the proposed design methods are illustrated on an example of twovariable, tworate system.

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.

Output-sliding control design of multivariable systems

A theoretical development of output-sliding control for uncertain mismatched multivariable systems is presented. The control law consists of a continuous nominal control part and a discontinuous switching control part. The determination of controller gains is explicit and practical. The closed-loop eigenvalues assignment in the sliding mode is well addressed. System robustness against a larger class of parameter variations and disturbances than by conventional design methods is achieved. Simultation studies show the promise of the proposed method.

Robust control design via eigenstructure assignment, genetic algorithms and gradient-based optimisation

The paper presents a new approach for robust control design of multivariable systems via eigenstructure assignment, genetic algorithms and gradient-based optimisation. It takes the combination of the sensitivity and the complementary sensitivity functions of the closed-loop system as the robust control performance index. The gradient calculation of the performance index is described in detail for the closed-loop system with real and complex eigenvalues. The paper makes full use of the freedom provided by eigenstructure assignment to find a controller which stabilises the closed-loop system and minimises the performance index via the combination of genetic algorithms and gradient-based optimisation. The simulation results for the design of a lateral flight control system provide a tutorial demonstration of the power of the method.

A new method of switching surface design for multivariable variable structure systems

In this paper, we discuss the problem of the switching surface for a multivariable variable structure system. We first propose a new switching surface by which robustness of the controlled system to disturbances is provided. Based on the switching surface, we develop control input to drive the system to track the desired trajectory. This control input does not produce the chattering that normally occurs when a conventional control input is used. We apply the proposed method to a multivariable linear system and discuss the simulation results to show the computational procedure and its effectiveness.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Robust stabilization control design for multivariable nonlinear uncertain systems

Robust stabilization control design for multivariable nonlinear uncertain systems

091 Algebraic design of linear multivariate systems. Use of symbolic computation (MATHEMATICA)

091 Algebraic design of linear multivariate systems. Use of symbolic computation (MATHEMATICA)

TheL-dominance concept and its applications to multivariable system designs

A new type of dominance measure based on triangular factorizations is developed and is named the L-dominance measure. This new measure is tighter than any existing dominance measures and in particular is tighter than those based on generalized dominance and M-matrix theory. The L-dominance condition on matrices with non-positive off-diagonal elements is proved to be equivalent to the M-matrix condition. But in contrast to the M-matrix condition, the testing of the L-dominance condition is easier and can be carried out in sequential order. Furthermore, these special properties enable us to construct a synthesis based design procedure superior to those based on generalized dominance or M-matrix theory; the last two methods are generally regarded as post-mortem analytical tools only.

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

A design procedure is proposed for robust LQG (linear-quadratic-Gaussian) optimal controller synthesis against noise spectral uncertainties, nonlinear time-varying (NLTV) unmodeled dynamics in discrete saturating systems. A robust stability criterion is derived for multivariable stochastic discrete-time systems with NLTV unmodeled dynamics and constrained actuators. An algorithm based on the robust stabilization criterion is presented for synthesizing a robust controller not only to minimize the least favorable cost functional J but also to satisfy the robust stabilization criterion by specifying an appropriate weighting scalar in the cost functional. A necessary and sufficient condition for the solvability of such a robust stabilization problem is derived by means of Nevanlinna-Pick interpolation theory. The Weiner Z-domain solution for controller synthesis, the saddle point theory, and the properties of the Schur operator (Class S) are employed to treat this problem. Finally, a numerical example is given to illustrate the results.

Algebraic Design of Linear Multivariable Systems. Use of Symbolic Computation (Mathematica)

The aim of this paper is to present a software package for the algebraic design of linear multivariable control. The package is developed using the symbolic manipulation system : Mathemetica. The central idea is to perform all the basic algorithms over any Principal Ideal Domain (PID). Then the user can select from usual rings and can study both continuous and discrete time systems. Some classical control problems that can be solved with our package are presented.

Intelligent advisory system for achieving diagonal dominance

In the paper, an intelligent advisory system for achieving diagonal dominance in the design of multivariable systems is presented. The underlying design algorithms are the Perron-Frobenius eigenstructure and pseudodiagonalisation techniques. The adviser acts as an intelligent frontend to an existing CAD suite, MVDES, which performs the actual numerical calculations and generates associated graphical plots.

Expert aided sequential design of multivariable systems

This paper shows how an expert system can be used to learn about and to help with the design of control systems. As an example, the design of a multivariable system by a sequential method is presented. We show how an expert system can be used to provide both a design assistant and an intelligent front-end for existing software, and we argue that both roles are required. To provide this functionality we have assembled an environment which we call a knowledge-based support system entirely out of standard commercially available components: an expert system, a hypertext system, and numerical software for multivariable control. The system has been used successfully by industrial engineers who were familiar with classical servo design ideas, but were new to multivariable control.

Robust LQG optimal controller design for multivariable discrete saturating systems with noise spectral uncertainties and non-linear time-varying unmodelled dynamics

A design procedure is proposed for robust linear-quadratic-gaussian (LQG) optimal controller synthesis against noise spectral uncertainties, non-linear time-varying (NLTV) unmodelled dynamics in discrete saturating systems. A robust stability criterion is derived for multivariable stochastic discrete-time systems with NLTV unmodelled dynamics and constrained actuators. An algorithm based on the robust stabilization creterion is presented for synthesing a robust controller not only to minimize the least favourable cost functional but also to satisfy the robust stabilization criterion by specifying an appropriate weighting scalar in the cost functional. A necessary and sufficient condition for the solvability of such a robust stabilization problem is derived by means of the Nevanlinna-Pick interpolation theory. The Wiener Z-domain solution for controller synthesis, the saddle point theory, and the properties of Schur operator (Class S) are employed to treat this problem. Finally, a numerical example is given to illustrate the results.

Stability robustness bounds for discrete-time linear regulators

Stability robustness analysis and design for linear multivariable discrete-time systems with bounded uncertainties are discussed. Robust stability of the full-state feedback linear quadratic (LQ) regulator in the presence of perturbations (modelling errors) of the system matrices is investigated. These results are based on a recently developed bound on elemental (structured) time-varying perturbations of an asymptotically stable linear time-invariant discrete-time system. Lyapunov theory and singular value decomposition techniques are employed in deriving these bounds. Extensions of these results to linear stochastic systems with the Kalman filter as the stale estimator (LQG regulators) and to reduced-order dynamic compensator feedback are described. A state feedback control design method is presented for LQ regulators, using a quantitative measure called the Stability Robustness Index. Simple examples illustrate these new results.

Optimal uniform-damping ratio controller for sequential design of multivariable systems

An optimal uniform-damping ratio controller is developed for the sequential design of a multivariable control system so that the designed closed-loop poles of the respective multivariable system and reduced-order observer are exactly placed on the negative real axis and/or the boundaries of desired sectors with constant-damping ratios. The functions in the quadratic performance index to be minimized are chosen as a combination of the weighted outputs, reduced states and inputs. Also, the optimal uniform-damping ratio controller is a combination of optimal output-feedback and optimal reduced-order state-feedback controllers. A numerical example is given to demonstrate the design procedure.

Numerical Properties of Trajectory Representations of Polynomial Matrices

In the early 1970s, several researchers reported results relating to the design of multivariable linear systems represented by polynomial matrices. In particular, the book by Wolovich (1974) found widespread resonance. In the sequel, however, the success of these techniques was rather Emited since a manual application of the proposed algorithms is atrocious for all but the most trivial systems, whereas appropriate CACSD tools that would make use of these techniques were not available. The main reasons for this deficiency were twofold: (i) polynomial matrix operations require symbolic processing, a computational technique that was still in its infancy in the 1970s, and (ii) the numerical properties of frequency domain operations were considered dubious. In this paper, the numerical properties of frequency domain operations are analyzed. The two classical data representations (coefficients and roots) are reviewed, and two new data representations, trajectories and coefficient spectra, are proposed.

Controller design of multivariable variable structure systems with nonlinear switching surfaces

A sliding mode control for linear multivariable systems in the presence of disturbances and parameter variations is considered. In the previous sliding mode control, the switching surfaces are linear functions and therefore the speed of response is relatively slow. To solve this problem, a new method, using nonlinear switching surfaces, is introduced so that the speed of response is improved, and the good transient response can be obtained. Simulation results are presented and they show the advantage of the proposed nonlinear switching surfaces.

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.

IMC controller design for multivariable systems

A systematic internal model control (IMC) controller design methodology has been developed for various types of multivariable processes. When we try to apply IMC to various systems several implementation problems are encountered. In this paper, we resolve these problems and suggest a systematic IMC controller design methodology. IMC shows very good performance and is easy to tune for open-loop stable systems. For unstable systems we apply IMC after stabilizing the systems using the pole placement technique. A combination of quadratic programming and IMC can handle constraints on manipulated and controlled variables.