Transfer Function Matrix Research Articles

Robust stabilization of discrete generalized systems

The robust stabilization problem for generalized discrete-time systems described by polynomial or improper transfer function matrices, subject to perturbations acting on the normalized coprime factors, is solved. The maximum achievable stability margin and the robust stabilizing controller are given in terms of realizations and solutions to appropriate Riccati equations.

Neural Polarimeter and Wavemeter

Numerous optical devices can be conveniently described in terms of a transfer function matrix formalism. An important example is the intensity-division Stokes polarimeter where four device outputs can be related to the four parameters of the Stokes vector using a linear 4 × 4 matrix transformation. In the present paper, we demonstrate how the functionality of such devices can be substantially enhanced by increasing the number of outputs and employing deep neural networks instead of the traditional linear algebra approach to establish correlations between device outputs and inputs. Specifically, we employ a neural network calibration of a metasurface-based intensity-division Stokes polarimeter with six outputs to accurately measure the four parameters of the Stokes vector of the input light across a much wider wavelength range than is afforded by a canonical linear transfer matrix model. Furthermore, the neural network model allows the device to determine the input wavelength from the measured data. We arg...

Optical propagation through anisotropic metamaterials: Application to metallo-dielectric stacks

We perform numerical simulations to compare the Berreman matrix method using effective medium results for an anisotropic material with exact calculations of a multi-layer metallo-dielectric stack using the transfer matrix method and finite element techniques. Results are given for a wide band of wavelengths and incident angles. For fixed sample thickness the number of layers is increased to study convergence of the optical characteristics (transmittance and reflectance). It is shown that the Berreman matrix method with effective medium results for an anisotropic material provides a fast and reliable estimate of the optical characteristics of the composite material. The Berreman technique readily leads to the transfer function matrix for propagation in anisotropic materials.

Persistence Analysis of Interconnected Positive Systems with MIMO Subsystems

This paper presents sufficient conditions for persistence of the interconnected positive systems for MIMO subsystems. The obtained conditions are on the structure of the transfer function matrix, the steady state gain for every subsystem and the structure of the interconnection matrix. As a result, the output of the subsystem converges to a vector on a convex cone which is included in the positive cone. The resulting conditions include the existing conditions for the persistence in the case where every subsystem is SISO. Numerical examples illustrate the persistence analysis results.

A Multiple-Input Multiple-Output Cepstrum

This letter extends the concept of scalar cepstrum coefficients from single-input single-output linear time invariant dynamical systems to multiple-input multiple-output (MIMO) models, making use of the Smith–McMillan form of the transfer function. These coefficients are interpreted in terms of poles and transmission zeros of the underlying dynamical system. We present a method to compute the MIMO cepstrum based on input/output signal data for systems with square transfer function matrices (i.e., systems with as many inputs as outputs). This allows us to do a model-free analysis. Two examples to illustrate these results are included: a simple MIMO system with three inputs and three outputs, of which the poles and zeros are known exactly, that allows us to directly verify the equivalences derived in this letter, and a case study on realistic data. This case study analysis data coming from a (model of) a non-isothermal continuous stirred tank reactor, which experiences linear fouling. We analyze normal and faulty operating behavior, both with and without a controller present. We show that the cepstrum detects faulty behavior, even when hidden by controller compensation. The code for the numerical analysis is available online.

Seismic upgrade of structures using the H∞ control problem for a general system interconnection paradigm

This paper presents a novel approach for the modification and seismic upgrading of shear-frame structures by attaining and implementing optimal changes in stiffness, changes in mass, and added damping (referred to as the structural changes). A general system interconnection paradigm is proposed and presented. The paradigm is assigned with a passive controller that consists of the structural changes and has simulated feedback on the structural response and the seismic excitation. A newly formulated optimization problem is required to satisfy constraints on maximum total story accelerations and maximum interstory drifts. The objective is to minimize the H∞ norm of a singled out response of the general system interconnection closed-loop transfer function matrix, making it a single-input single-output transfer function case. The control problem is solved by utilizing the first-order steepest descent method, an H∞ synthesis algorithm, for calculating the free parameters of a passive controller which consists of the structural changes. Their method is further enhanced for seismic design needs, by imposing boundaries on the free parameters according to the dynamic response of the structure to given ground motion ensemble. Two numerical examples of a 9-story shear-frame structure and 10-story moment resisting frame are studied. Optimal changes in mass, stiffness, and damping are obtained, and results show significant improvement in the peak dynamic response. The results indicate the efficiency of the proposed procedure that possesses the capability of attaining optimal changes in all physical characteristics of the structure (mass, stiffness, and damping) while adhering to preassigned maximum response levels.

A Study of All-fiber Different Bandwidth Interleaver Based on Linear Chirped Fiber Grating

To improve the utilization efficiency of interleaver bandwidth in 10Gbit/s plus 40Gbit/s mixed system, an all-fiber MZI different bandwidth optical interleaver based on linear chirped fiber grating is proposed and discussed in this paper. The same two linear chirped fiber gratings are written at the output of conventional Mach-Zehnder interferometer (MZI), which constitute a reflective cascaded MZI filter. Based on its structure, the output spectrum expression is established and described by using the principle of fiber transmission, reflex theory of fiber grating and the matrix transfer function. Influences on its transmission characteristics by such factors as the coupling coefficients of the couplers, structure parameters of fiber grating and the length differences of the interferometer arms are numerically analyzed and optimized. The results of numerical simulation indicate that when the above parameters are some certain values, 50GHz input single of device is separated into channel spacing of 100GHz odd-even two output signals. Their spectrum bandwidth are 64.67GHz and 36.98GHz at 3dB, they satisfy the requirement of different transmission rates on bandwidth in 10Gbit/s plus 40Gbit/s mixed system and implements different bandwidth transmission. The device has a certain ability to resist the deviation. Compared with the ordinary cascaded MZI interleaver, the advantage of the new interleaver is that reduced numbers of coupler. It has higher bandwidth utilization that compared with the equal bandwidth interleaver, and achieves different bandwidth transmission within 100GHz.

Analytical study of starting current of the induction motor stator

In a three-phase coordinate system, the induction motor is described by a system of nonlinear differential equations of the eighth order, which in a general case does not have an analytical solution. The system of IM equations can be considerably simplified for the starting mode with a stationary rotor. When analyzing the specified operating mode, periodic coefficients in the IM equations that depend on the angular position of the rotor are transformed into constant magnitudes. Further simplification of the system of IM equations implies the exclusion of motion equations, which is also associated with the accepted assumption about the immobility of the rotor. We assume that the stator of IM is connected to a power line according to the circuit without a zero wire. This makes it possible to exclude from the common system two equations of electrical equilibrium of the windings, for one stator and one rotor winding, by applying the Kirchhoff's first law. As a result of the performed transformations, we obtained a simplified system of IM equations with a stationary rotor, which, in contrast to the complete system, is a system of linear differential equations of the fourth order and is presented in the Cauchy form, which can be solved analytically. Using the methods of analysis of dynamic objects in a state space, we obtained expressions for the coefficients of IM characteristic equation and its roots, as well as for the matrix of IM transfer functions when the rotor is stationary. An analysis of expressions for the roots of the characteristic equation shows that the character of roots of the IM characteristic equation depends on the initial angular position of the IM rotor. This is explained by the fact that a change in the initial angular position of the rotor changes the magnitude of mutual inductance between separate windings of IM, which affects the processes of energy transfer between stator and rotor windings.

Structural-Parametric Model of Electromagnetoelastic Actuator for Nanomechanics

The generalized parametric structural schematic diagram, the generalized structural-parametric model, and the generalized matrix transfer function of an electromagnetoelastic actuator with output parameters displacements are determined by solving the wave equation with the Laplace transform, using the equation of the electromagnetolasticity in the general form, the boundary conditions on the loaded working surfaces of the actuator, and the strains along the coordinate axes. The parametric structural schematic diagram and the transfer functions of the electromagnetoelastic actuator are obtained for the calculation of the control systems for the nanomechanics. The structural-parametric model of the piezoactuator for the transverse, longitudinal, and shift piezoelectric effects are constructed. The dynamic and static characteristics of the piezoactuator with output parameter displacement are obtained.

Static output feedback canonical forms

Abstract We construct complete static output feedback (SOF) invariants and canonical forms of the set of strictly proper full rank, rational, transfer function matrices. We consider the induced action of the SOF group on the set of Plücker coordinates. Some of them are SOF-invariant and that some others vary linearly with the entries of the feedback gain. Further SOF-invariants are constructed based on the consistency conditions of linear systems of equations. The pair of the above two lists of invariants is complete. The proof is given, introducing a new type of factorization. We construct a SOF-canonical form. We apply the results to the class of systems with two inputs two outputs, characterizing the SOF-equivalence classes in the case of four states as to the property of SOF-pole assignability and calculating the constrained dynamics in the case of more than four states.

Observer-based parametric decoupling controller design for a class of multi-variable non-linear uncertain systems

ABSTRACTThis paper presents a novel decoupling control strategy for Lipschitz multi-variable non-linear uncertain systems. Using the explicit parametric design, an observer-based output feedback controller has been developed with free parameters while the closed-loop system can be further described by transfer function matrix with these free parameters. The coupling effects of the systems would be attenuated if the free parameters are optimised where the performance criterion is given based on the norm of the transfer functions. Moreover, the sufficient conditions of stabilization have been obtained for observer, controller and closed-loop system, respectively. Following the procedure of the presented control strategy, an illustrative numerical example is given to demonstrate the effectiveness of the presented control strategy. In addition, the similar design approach has been discussed for filtering problem which is a potential extension of the presented control strategy.

Optimal synthesis of the low-order model parameters for a large-scale energy system on the basis of the gramians spectral decomposition

Abstract The structure of the low-order model is characterized by the fact the eigenvalues of its dynamics matrix coincide with the weakly stable eigenvalues of the system, which are calculated using the spectrum of the system dynamics matrix and the method of the gramians spectral decompositions. The optimal synthesis of the simplified model parameters is based on the approximate solution of the matrix polynomial equation for the matrices of the numerator of the system matrix transfer function and its simplified model. The solution of the synthesis problem leads to the solution of the linear matrix algebraic equation formed by the adaptability matrices. The energy functionals of the system and its simplified model can be determined by means of spectral decompositions of the squared H2 -norm of the matrix transfer function of the system and its simplified model. When the system approaches to the stability boundary, the stability margins of the system and its simplified model determined by the dominant weakly stable eigenvalues coincide asymptotically. This makes it possible not only to guarantee the stability of the simplified model, but also to determine the stability margins of a high-order system with help of the stability margins of a low-order model. The method makes it possible to estimate the oscillational instability caused by the resonant interaction of intraregional and inter-area oscillations and also to evaluate the impact of the input and output system matrices on the system stability using input and output matrices of its simplified model.

A Unitary Construction of Takagi-Sugeno Fuzzy Fault Detection Filters

The unitary approach to fault detection filters design, intended to Takagi-Sugeno fuzzy continuous-time systems, is presented in the paper. Based on fuzzy observers guaranteing asymptotic convergence of the state estimation error, the matrix gains of all linear components of the fuzzy filter are designed to obtain the same singular values of the filter transfer function matrix. Related to the fuzzy state control, and for systems under influence of actuator faults, the problems are revealed for a three-tank system plant.

Stochastic stability in terms of an associated transfer function matrix for some hybrid systems with Markovian switching

This work is devoted to stability for a dynamical system withMarkovian switched controller and a finite number of linear diğerential subsystems. We suppose conditions on a state space representation ofan associated transfer function matrix which guarantees stochastic stability.The given examples are detailed to illustrate the main result

Numerical Analysis of Pipe System with Elbow by Transfer Function Matrix Method

Numerical Analysis of Pipe System with Elbow by Transfer Function Matrix Method

Anti-windup compensator design using Riccati inequality based approach

This paper presents a full-order dynamic anti-windup compensation design scheme for stable LTI systems using a Riccati inequality based approach. The scheme utilizes the Weston-Postlethwaite’s generalized anti-windup configuration and applies right coprime factorization of the plant transfer function matrix to obtain a linear conditioning scheme. The proposed anti-windup scheme ensures the internal stability of the closed-loop control system in presence of actuator saturation and also reduces the performance degradation caused by the saturation phenomena. The Riccati inequality based approach offers a simple and straightforward anti-windup compensator design method which is independent of the design of nominal controller. The effectiveness of the proposed technique is demonstrated through a MIMO example.

Adaptive Multi loop IMC Based PID controller tuning using Bat Optimization algorithm for Two Interacting Conical Tank Process

In this paper, multi-loop adaptive internal model controller (IMC)-based PID is designed for the two interacting conical tank level process (TICTLP). The nonlinear TICTLP is decomposed into linear transfer function matrix around the operating points and the effective open loop transfer function (EOTF) is developed using simplified decoupler. The IMC-based PID controller parameters are obtained for EOTF model using bat optimisation algorithm (BOA). A weighted sum of integral time absolute error is used as control design objective function for multi-loop IMC-PID design which yields faster settling time with minimum over shoot. The fuzzy-based adaptive gain scheduling is used to provide complete control to TICTLP and fuzzy-based adaptive decoupler is implemented to eliminate the dynamic interaction between control loops. The simulation results of proposed controller are compared with conventional ZN-PID, IMC controllers to show the superiority of proposed controller. The simulation response of proposed controller indicates the performance improvement control schemes interns of time domain performance indices, servo tracking, regulatory response and faster settling time.

Model based multivariable control scheme in a reset configuration for stable multivariable systems

The multivariable control scheme is a widely used advanced process control methodology to control key process variables in chemical engineering processes. However, successful implementation of multivariable control requires a simplified control structure, a lower number of tuning parameters, and an appropriate tuning method. In this work, a model based multivariable control scheme is realized in reset configuration for the control of stable multi‐input and multi‐output systems. This control scheme utilizes the process transfer function matrix and the inverse of the steady state gain matrix for its implementation. The control scheme has a single tuning parameter and also inherently takes into account the interaction that exists between process inputs and outputs. This scheme is easy to implement and apply in multivariable systems with multiple delays, high‐dimensional systems, non‐square systems, and systems with RHP zeros. Simulation examples from process system engineering such as industrial scale polymerization reactor system, quadruple‐tank system, temperature control for the four room process, and shell control problem are presented to show the efficacy of the proposed multivariable control scheme.

Structural-Parametric Model of Electromagnetoelastic Actuator for Nanomedicine and Nanobiotechnology

The generalized parametric structural schematic diagram the generalized structural parametric model the solution of wave equation the generalized matrix transfer function of the electromagnetoelastic actuator are determined The dynamic and static characteristics of the actuator are obtained The parametric structural schematic diagram and the transfer functions are determined for calculation of the control systems of the nanomedicine and the nanobiotechnology The structural parametric model of the piezoactuator for the transverse longitudinal shift piezoelectric effects are constructed

A Stochastic Approximation Method with Enhanced Robustness for Crosstalk Cancellation

The objective of acoustic crosstalk cancellation is to use loudspeakers to deliver prescribed binaural signals (that reproduce a particular auditory scene) to a listener's ears, which is useful for 3-D audio applications. In practice, the actual transfer function matrix will differ from the design matrix, because of either the listener's head movement or rotation, etc. Crosstalk cancellation system (CCS) is very non-robust to these perturbations. Generally, in order to improve the robustness of CCS, several pairs of loudspeakers are needed whose position varies continuously as frequency varies. With the help of assumed stochastic analysis, we propose a stochastic robust approximation crosstalk cancellation method based on random perturbation matrix modeling the variations of the transfer function matrix. Under the free-field condition, simulation results demonstrate the effectiveness of the proposed method.