Linear Multivariable Dynamic Systems Research Articles

Self-terminating growth of platinum by electrochemical deposition

In this paper, an islanded microgrid is modelled as a linear multivariable dynamic system. Then, the multivariable analysis tools are employed. The generalized Nyquist diagram and the relative gain array are used respectively for the stability assessment and solving the paring problem among the inputs and outputs. Droop control dependency on the X/R ratio of the microgrid DERs is recognized and its type is proposed using the relative gain array concept. Robust stability, nominal performance and robust performance requirements are evaluated in order to a better understanding of the system dynamics. Finally, three different controllers including H∞, H2 and sequential proportional-integral-derivative controls are designed and compared.

Robust Multivariable Microgrid Control Synthesis and Analysis

In this paper, an islanded microgrid is modelled as a linear multivariable dynamic system. Then, the multivariable analysis tools are employed. The generalized Nyquist diagram and the relative gain array are used respectively for the stability assessment and solving the paring problem among the inputs and outputs. Droop control dependency on the X/R ratio of the microgrid DERs is recognized and its type is proposed using the relative gain array concept. Robust stability, nominal performance and robust performance requirements are evaluated in order to a better understanding of the system dynamics. Finally, three different controllers including H∞, H2 and sequential proportional-integral-derivative controls are designed and compared.

Assigning the set of zeros in control systems with parallel compensation

The problem of ensuring a given set of zeros in a linear multivariable dynamical system with the equal number of inputs and outputs that includes a parallel compensator and feedback loop is considered. Methods reducing this problem to the control of eigenvalues of a certain matrix are proposed; the simultaneous assignment of poles and zeros is reduced to the control of poles of two plants using a single controller. The calculations are based on well-known and well-tested modal control techniques.

Using interval arithmetic for robust state feedback design

A problem of a modal P-regulator synthesis for a linear multivariable dynamical system with uncertain (interval) parameters in state space is considered. The designed regulator has to place all coefficients of the system characteristic polynomial within assigned intervals. We have developed the approach proposed earlier in Dugarova and Smagina (Avtomat. i Telemech. 11 (1990) 176) and proved a direct correlation between interval system controllability and existence of robust modal P-regulator.

Hybrid modelling for analysis and identification of rotors

In this paper a rotating shaft-disc system, modelled as a series of interconnected, distributed and lumped elements is considered. The overall transfer matrix of the system formed by series flexible distributed elements and rigid disc elements is determined, then applying supporting end boundary conditions the characteristic determinant of the system is computed. The damped natural frequency of the system is computed by a direct determinant search method. Thereafter a novel method is proposed for the determination of the frequency response function. The overall system is identified as a linear multivariable dynamic system with second order transfer function elements. Future applications of this hybrid technique are discussed.

A method for simplifying linear multivariable dynamic systems

AbstractA method for reducing the order of linear multivariable stable dynamic systems is proposed. The main advantage of this method is that the problem of determining a simplified model is reduced to few matrix manipulations and solution of a few algebraic equations which can be easily programed. The simplified model is obtained so that a quadratic functional of the difference between the output vector and that of the original model is automatically minimized for either step or impulse inputs. Applications of the method include simplification of a dynamic model of a pilot plant for the azeotropic distillation of n‐butyl acetate and n‐butanol. Very good agreement between the step responses of the original and simplified model is obtained.

Eigenvalue and state-transition sensitivity of linear systems

Differential changes in the elements of a matrix associated with a linear multivariable dynamic system produce changes in the corresponding eigenvalues and in the state-variable solution. Previous methods for determining the eigenvalue sensitivity are outlined, and an alternative development based on Sylvester's expansion theorem is discussed which illustrates the basic role of the constituent matrices associated with the theory of linear systems. Methods for determining the corresponding variations in the transition- and driving-matrix elements related to the time response of linear systems are also illustrated.The inverse eigenvalue sensitivity problem concerned with the requirement to synthetise a differential change in the elements of a matrix to produce a desired eigenvalue change is also considered. A numerical procedure is proposed, together with a solution based on the generalised inverse of a matrix, for solving the defining singular equations.