Yelena Smagina

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.

Using Lyapunov's direct method for wave suppression in reactive systems

This paper proposes a new approach for stabilizing a homogeneous solution in reaction–convection–diffusion system with oscillatory kinetics, in which moving or stationary patterns emerge in the absence of control. Specifically, we aim to suppress patterns by using a spatially weighted finite-dimensional feedback control that assures stability of the solution according to Lyapunov’s direct method. A practical design procedure, based on spectral representation of the system and the dissipative nature of parabolic PDEs, is presented.

Robust modal P and PI regulator synthesis for a plant with interval parameters in the state space

We consider a problem of modal P and PI regulator synthesis for a linear multivariable dynamical system with uncertain (interval) parameters in the state-space. The designed regulator has to place all coefficients of the system characteristic polynomial within the assigned intervals. The solvability conditions of the problem and the proof of the correlation between interval system controllability and regulator existence are presented. The application of the developed method is illustrated on a numerical example.

New Approach to Transfer Function Matrix Factorization

Abstract A new form of the matrix fraction C(s)F(s) -1 of a transfer function matrix G(s) is presented where the polynomial matrices C(s) and F(s) have the form of a matrix (or generalized matrix) polynomials. The structure of C(s) and F(s) is uniquely defined by the controllability characteristics of a state-space model, and moreover, the block coefficients of C(s) consist of the Markov matrices H B, HAB ,…

Control of moving pulses in an one-dimensional model of cardiac tissue

Abstract This paper develops a new model-based control aimed to stabilize the propagation velocity of electrical pulses circulating in an one-dimensional ring model of the cardiac tissue. The controller induces small currents using electrodes placed along the ring. This current responds to the discrepancy between the pulse front voltage, measured at an electrode, and a voltage of a set pulse front at the same space point. The proposed control is, in fact, a distributed continuous-time feedback control that stabilizes the spatiotemporal evolution by using a finite number of electrodes implanted on the heart. We present a systematic methodology to predict conditions for pulse instability using linear analysis of the lumped truncated mathematical model of the cardiac tissue. The control effectiveness is measured by the critical length (L*) below which the pulse becomes oscillatory in a moving coordinate. This domain enlarges from L* = 10.1cm in the open-loop system to 9.0cm and 8.0cm in the closed-loop system with 2 and 8 electrodes. The validity of control is justified by using the map that connects sensor positions at neighboring time steps.

Using Sampled-Data Dynamic Controller to Stabilize Rotating Pulses

Abstract We consider the stabilization of a rotating temperature pulse moving in a continuous asymptotic model of many connected chemical reactors organized in a loop with continuously switching of the feed point synchronously with the motion of the pulse solution. We use the switch velocity as control parameter and design it to follow the pulse: the switch velocity is formed at every step on-line using the discrepancy between the temperature at the front of the pulse and a set point. The resulting feedback controller, which can be regarded as a dynamic sampled-date controller, is designed using root-locus technique. Convergence conditions of the control law are obtained in terms of the zero structure (finite zeros, infinite zeros) of the related lumped model. The theoretical results are applied to keep a moving solution in the typical loop reactor in which a single exothermic reaction occurs and is confirmed by numerical simulations.

Robust control of stationary planar fronts in reaction-diffusion systems

Abstract This paper considers a new approach to construct a feedback controller that stabilizes a front line solution of a nonlinear parabolic distributed (reaction- diffusion) system in a planar domain. The controller incorporates several space- dependent actuators that respond to sensors located at the front position. Sensor numbers and its locations are chosen by the multivariable root-locus technique for the finite-dimensional approximation of the original PDE model. The concept of finite and infinite zeros of linear multidimensional systems is used. The theoretical results are confirmed by computer simulations.

Front Stabilization by Finite-Output Control in Reaction-Diffusion Systems

Abstract It is suggested a new approach to design of a finite-dimensional feedback regulator stabilizing multifront solutions in a reaction-diffusion system described by the nonlinear PDEs with cubic nonlinearly. The method is based on shifting the critical diagonal elements of the related linearized spectral system dynamics matrix by a space-average feedback regulator. The critical diagonal elements, regulator gain coefficients and form of the space-average sensors are evaluated by applying the sufficient stability criterion which followes from the Gershgorin theorem. The control obtained stabilizes the solutions in the wide range of the bistability.

System Zero Determination in Large Scale System

Abstract It is shown that the system zeros of the linear multivariable system can be determinted as the finite eigenvalues (eigenvalues) of a reduced-order linear matrix pencil (matrix). Such an approach for system zero calculation decreases considerably the computational difficulties. Moreover, the special structure of the reduced order matrix pencil (matrix) which depends directly on Markov matrices HB, HAB, HA2B,… can be used for the analysis of the system invertibility, the number of system zeros, etc.