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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.

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.

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.

To predict accurate micro-vibration produced by a spaceborne payload mounted pulse tube cryocooler (PTC), a coupled disturbance analysis of cryocooler with flexible support structures have been discussed and investigated. A coupled transfer function matrix is introduced by improving the traditional disturbance analysis. According to the coupling disturbance relationship between the source and supporting structure, microvibration input load is accurately obtained. Based on the finite element model of the space camera, the performance of optical system is analyzed. Compared to the decoupled method, this coupled method can accurately predict the local transfer characteristics between cryocooler and interface.

Probe-and-drogue refueling (PDR) is widely adopted owing to its simple requirement of equipment and flexibility, but it has an apparent drawback that the drogue position is susceptible to disturbances. There are three types of disturbances: atmospheric turbulence, trailing vortex of the tanker, and bow wave effect caused by the receiver. The former two disturbances are independent of the receiver, whereas the bow wave effect, which depends on the state of the receiver, greatly influences the docking within a close distance. As far as the authors know, little attention has been paid to the bow wave effect on docking control in existing literature. The existing literature related to the bow wave focuses on either qualitative static results obtained from experiments, or lookup tables based on computational fluid dynamics (CFD) analysis. These are inapplicable to the PDR docking controller design directly. This paper proposes a lower order dynamic model to describe drogue dynamics under the bow wave effect. The model consists of two components: one is a second-order transfer function matrix to describe the drogue dynamics, and the other is a nonlinear function vector to describe the bow wave effect model. A closed-loop simulation including the two components shows that the generated drogue dynamics are similar to those of a real experiment reported in an existing literature.

Generalized independent coordinates are typically utilized within an analytical dynamics framework to model the motion of structural and mechanical engineering systems. Nevertheless, for complex systems, such as multi-body structures, an explicit formulation of the equations of motion by utilizing generalized, independent, coordinates can be a daunting task. In this regard, employing a set of redundant coordinates can facilitate the formulation of the governing dynamics equations. In this setting, however, standard response analysis techniques cannot be applied in a straightforward manner. For instance, defining and determining a transfer function within a frequency domain response analysis framework is challenging due to the presence of singular matrices, and thus, the machinery of generalized matrix inverses needs to be employed. An efficient frequency domain response analysis methodology for structural dynamical systems modeled via dependent coordinates is developed herein. This is done by resorting to the Moore–Penrose generalized matrix inverse in conjunction with a recently proposed extended modal analysis treatment. It is shown that not only the formulation is efficient in drastically reducing the computational cost when compared to a straightforward numerical evaluation of the involved generalized inverses, but also facilitates the derivation and implementation of the celebrated random vibration input–output frequency domain relationship between the excitation and the response power spectrum matrices. The validity of the methodology is demonstrated by considering a multi-degree-of-freedom shear type structure and a multi-body structural system as numerical examples.

This paper proposes a small-signal model of STATCOM based on theoretical derivation. This theoretical model is obtained by linearization of the dc-link control loop, Phase-Locked Loop (PLL), ac voltage control loop under the weak grid condition. In order to validate the correctness of this small-signal model, an identified model in the form of transfer function matrix is obtained by Output Error with Extended Prediction Model (OEEPM) identification method using the data acquired from the nonlinear time-domain simulation. The two developed models are compared using the time-domain simulations conducted in MATLAB/Simulink. Based on the compared results disturbance, the accuracy and applicability of the proposed small-signal model have been discussed.

Internal model control (IMC) design method based on quasi-LPV (Linear Parameter Varying) system is proposed. In this method, the nonlinear model is firstly transformed to the linear model based on quasi-LPV method; then, the quadrotor nonlinear motion function is transformed to transfer function matrix based on the transformation model from the state space to the transfer function; further, IMC is designed to control the controlled object represented by transfer function matrix and realize quadrotor trajectory tracking. The performance of the controller proposed in this paper is tested by tracking for three reference trajectories with drastic changes. The simulation results indicate that the control method proposed in this paper has stronger robustness to parameters uncertainty and disturbance rejection performance.

This paper deals with sensor faults of aircraft engines under uncertainties using a bank of second-order sliding mode observers (SMOs). In view of the effect of inevitable uncertainties on the fault reconstruction, a method combining H &infin, concepts and linear matrix inequalities (LMIs) is proposed, in which a scaling matrix is designed to minimize the gain of the transfer function matrix from uncertainty to reconstruction. However, robust design generally requires that engine outputs outnumber faults. In the case where the above-mentioned requirement is not satisfied, a bank of sliding mode observers is proposed to ensure the degrees of freedom available in robust design. In specific, each observer corresponds to a certain sensor with the hypothesis that the corresponding sensor will not have faults, to create one degree of design freedom for each observer. After fault occurrence, a large estimation error is expected in the observers with wrong hypothesis, and then a logic module is designed to detect sensor faults and obtain the optimal robust sensor fault reconstruction at the same time. The proposed approach is applied to a nonlinear engine component-level-model (CLM) simulation platform, and a numerical study is performed to validate the effectiveness.

Effective state transfer is one of the most important problems in quantum information processing. Typically, a quantum information device is composed of many subsystems with multi-input ports. In this paper, we develop a general theory describing the condition for perfect state transfer from the multi-input ports to the internal system components, for general passive linear quantum systems. The key notion used is the zero of the transfer function matrix. Application to entanglement generation and distribution in a quantum network is also discussed., Comment: 6 pages, 3 figures. A preliminary condensed version of this work will appear in Proceedings of the 55th IEEE Conference on Decision and Control

The Characteristic Locus Method constitutes a generalisation of the classical frequency response approach and as such provides a natural platform for design aimed at meeting specifications such as closed-loop stability and dynamic performance. However, to overcome problems of sensitivity to uncertainty, it is necessary to precondition the plant transfer function matrix (TFM) with the view to improving the orthogonality of the eigenvector functions. All that remains then is to use controllers which adjust the frequency response of the eigenfunctions of the TFM while leaving the eigenvectors unaltered. This implies the need for commutative controllers which may be irrational and may not be internally stabilising. The present paper gives a complete characterisation of the class of stabilising rational commutative controllers and derived necessary and sufficient conditions for the existence of this class. These ideas are illustrated by means of case study in which the degrees of freedom contained within the class of commutative controllers are deployed for the meeting design specifications on dynamic performance as well as tolerance to uncertainty.

A recently emerging approach to the feedback control of linear quantum systems involves the use of a controller which itself is a quantum linear system. This approach to quantum feedback control, referred to as coherent quantum feedback control, has the advantage that it does not destroy quantum information, is fast, and has the potential for efficient implementation. An important issue which arises both in the synthesis of linear coherent quantum controllers and in the modeling of linear quantum systems, is the issue of physical realizability. This issue relates to the property of whether a given set of linear quantum stochastic differential equations corresponds to a physical quantum system satisfying the laws of quantum mechanics. Under suitable assumptions, the paper shows that the question of physical realizability is equivalent to a frequency domain (J,J) -unitary condition. This is important in controller synthesis since it is the transfer function matrix of the controller which determines the closed loop system behavior. � 2012 IEEE.

A linear time-invariant system is defined as unitary if all singular values of its transfer matrix are equal. A method of constructing a unitary system in a fault detection observer form is developed in this paper. The singular values of the constructed system can be assigned as an analytical function of frequency with a selectable parameter. As the optimization of singular values related properties is important in balancing the sensitivity and robustness of fault detection observers, the study of unitary system has both theoretical importance and potential applications in model-based fault detection such as the H ∞ / H _ optimization to be discussed in Part II of the paper.

The proposed method for designing multivariable controller is based on ideal decoupler D(s) and PID controller optimization under constraints on the robustness and sensitivity to measurement noise. The high closed-loop system performance and robustness are obtained using the same controller in all loops. The method is effective despite the values and positions of the right half plane zeros and dead-times in the process transfer function matrix Gp(s). The validity of the proposed multivariable control system design and tuning method is confirmed using a test batch consisting of Two-Input Two-Output (TITO) stable, integrating and unstable processes, and one Three-Input Three-Output (TITO) stable process.

This paper aims to obtain an optimal viscous damper placement for building structures using H∞ optimization. The H∞ norm of the transfer function matrix is adopted as the objective function. Since it represents the magnitude of vibration transfer, one can attenuate the gain of the frequency response by minimizing this norm. The sequential quadratic programming (SQP) method is employed for optimization. The proposed method is also applicable to a various structural models as well, e.g., a bending-shear building model and a framed structure model. Numerical examples are presented to demonstrate the effectiveness of the proposed design method.

In this paper, an alternative method was introduced to conduct a transfer path analysis for airborne noise. The method used the transfer function matrix composed of acoustic transfer functions that are referenced by the input voltage of a calibration source. A calibration factor which is converting a virtual voltage to source strength was deduced by vibro-acoustical reciprocity theorem. The calibration factor is then multiplied to the virtual input voltage to estimate the operational source strength. Three loudspeakers were used to noise sources of acrylic half car model. The method was applied to airborne noise transfer path analysis of the half car. The estimated source strength by transfer path analysis was compared the deduced source strength by vibro-acoustical reciprocity to verify the method.

This paper deals with the decentralized pole assignability of interconnected systems by means of linear time-invariant (LTI) controllers. A simple graph-theoretic approach is proposed to identify the distinct decentralized fixed modes (DFMs) of the system, i.e., the unrepeated modes which cannot be moved by means of a LTI decentralized controller. The state-space representation of the system is transformed to the decoupled form using a proper change of coordinates. For any unrepeated mode, a matrix is then computed which resembles the transfer function matrix of the system at some point in the complex plane. A bipartite graph is constructed accordingly in terms of the computed matrix. Now, the problem of verifying if this mode is a DFM of the system reduces to checking if the constructed graph has a complete bipartite subgraph with a certain property. The sole restriction of this work is that it is only capable of identifying the distinct DFMs of a system. However, it is axiomatic that most of the modes of the real-world systems are normally distinct. The primary advantage of the present paper is its simplicity, compared to the existing ones which often require evaluating the rank of several matrices.

The paper treats the modelling and simulation of pipelines that transport different fluids. The problem is solved by including the fluid density in the model beside the pressure and the velocity of the medium that are used in the models of single medium pipelines. The starting model consists of nonlinear partial differential equations. Then, the model is linearised and transformed into the transfer function matrix form. Four different forms of the model are derived in the paper. Since transfer functions are transcendent, they cannot be simulated using classical tools. Rational transfer function approximation of the model is used instead to validate the model on the real industrial pipeline.

Given a controllable pair of matrices (A,B) Rosenbrock’s theorem on assignment of open-loop zeros states that a matrix C may be chosen so that the transfer function matrix G(s)=C(sIn−A)−1B has prescribed zeros, that is, prescribed numerator polynomials in its McMillan form. In the same way, Rosenbrock’s theorem on assignment of closed-loop poles states that a matrix C may be chosen so that the McMillan form of the transfer function matrix of the closed-loop system has prescribed denominator polynomials. Following Rosenbrock’s ideas we can prove that given any pair of matrices (A,B), matrices C and D may be chosen so that the transfer function matrix of the system, G(s)=D+C(sIn−A)−1B, has prescribed infinite structure.

Many multivariable (systems with many inputs/outputs) industrial processes can, to a good degree of approximation, be modelled by a transfer function matrix, where all of the interaction occurs in a matrix of constant coefficients. This reflects the fact that the dynamics of the section in which the interaction occurs are very fast compared with the other dynamics in the system. Examples of such systems include steel rolling mills and boiler systems.Such multivariable systems are relatively easy to design controllers for, since the system may be diagonalised by an inverse of the constant gain matrix, followed by suitable single-loop dynamic compensation. However, this approach depends on the linearity of the dynamical elements in the system. Such a condition is voilated by the presence of non-linear actuators, which are a feature of many industrial systems. The presence of such actuators within a multivariable control system as described above can cause very significant interaction problems, with associated degradation in performance, particularly during transients.This paper describes a straightforward technique, which is effective in linearising typical non-linear industrial actuators, allowing diagonalisation to be effectively achieved at all frequencies. The technique relies on a simple describing function analysis and manifests itself as a time-varying linearising precompensator for each non-linear actuator. A simple example is used to demonstrate the effectiveness of the method and it is then shown in application with multivariable boiler and steel mill models.

In this paper, the robustness of a manipulator mounted on a flexible base with a task-space feedback control to a fixed desired point is considered. We define the robust arm configuration (RAC), which is a special configuration where the linearized system is positive real. Lyapunov indirect method and the passivity theory guarantee a local asymptotic stability of the original nonlinear system. A finite but high closed-loop gain can be applied in the neighborhood of the RAC without considering the base flexibility, i.e., an additional sensor or a solution of whole inverse dynamics is not necessary. Considering the positive semidefiniteness of the residue matrices, a measure is proposed that measures the distance from the RAC. This measure represents the controllability of the manipulator itself, and does not depend on the underlying control law. The validity of the proposed approach is confirmed by a numerical example and experiments.

In this paper, we focus on the analysis of the scheduling problem in FMS using Unfolding Time Petri nets. We can divide original system into subsystems based on the machine’s operations and change iterated cycle module into acyclic module without changing any other behavior properties. We first show that properties can be studied through the unfolding nets concepts. Structural analysis on ‘‘unfolding‘’ is much easier than on the original net. The advantage of unfolding is that the state space explosion can be avoided since it is based on partial order semantics. A methods to analyze and optimize the control of such systems is presented and explained on an example.

We use the behavioural approach to define and characterize controllable and uncontrollable poles and zeros of multidimensional (nD) linear systems. We show a strong relationship between controllable poles and zeros and properties of the transfer function matrix, and we give characterizations of uncontrollable poles and zeros, in particular demonstrating that these have an input decoupling property.

Assessment of the controllability and observability of linear system models directly from their impedance matrix descriptions is considered. A simple test enabling controllability to be predicted is proposed. Similarly the dynamic content of the system output measurements is investigated and a comparable observability procedure is presented. An illustrative example is provided for reference purposes and the results obtained are confirmed by computing the transfer function matrix.

For m-input p-output descriptor systems involving disturbances, it is proven that if the problem of disturbance rejection is solvable via static-state feedback and the input-output transfer function matrix is right invertible, there always exists a static-state feedback control law yielding, simultaneously to disturbance rejection, a triangular input-output relation. The structural properties of the closed-loop system (stability, pole assignment, etc.) are extensively studied.

Matrix equation of generalized closed-loop complex order dynamic system (GCDS) motion is given. Frequency interpretation of complex order integrator is found. Frequency transfer function matrix (MCHPF) investigated GCDS is shown. MCHPF for DC electric drive is determined. Figs. 1. Ref: 8 titles.

A method is given to design multivariable PI/PID controllers for stable and unstable multivariable systems. The method needs only the steady state gain matrix (SSGM). The method is based on the static decoupler design followed by SISO PI/PID controllers design and combining the resulted decoupler and the diagonal PI(D) controllers as the centralized controllers. The result of the present method is shown to be equivalent to the empirical method proposed by Davison EJ. Multivariable tuning regulators: the feed-forward and robust control of general servo-mechanism problem. IEEE Trans Autom Control 1976;21:35-41. Three simulation examples are given. The performance of the controllers is compared with that of the reported centralized controller based on the multivariable transfer function matrix. � 2014 ISA.

In the paper, the problem of H ∞ decentralized state feedback control for large-scale systems is described. An algorithm is proposed which uses the method of a feasible direction matrix. The algorithm only reguires the solution of an algebraic Riccati equation(ARE) and makes the H ∞ -norm of the closed-loop transfer function matrix from disturbance inputs to controlled outputs be less than a given constant while ensuring, at each iteration, the stability of the overall controlled system. The given example shows that the convergence of the algorithm is good.

Plants with two inputs and two outputs are considered. Necessary and sufficient conditions are presented for the existence of a 2*2 precompensator such that the series connection of precompensator and plant is stabilizable and has a diagonal transfer function matrix. The set of all diagonal transfer function matrices achievable by a precompensator of the above form is characterized. The results admit a solution to the decoupling problem by unity output feedback compensation for 2*2 plants. >

Repeated simulations have been most widely applied in analyzing the sensitivities of the power system dynamics with respect to controller inputs. This approach is computationally intensive and it does not explicitly show the physical insights. A transfer function matrix based approach is proposed in this letter for control input sensitivity analysis. A bottom up method is also presented to build the respective transfer function matrix. The effectiveness of the method is demonstrated through case studies.

A direct and simple numerical method is presented for calculating the transfer function matrix of a linear time invariant multivariable system (A,B,C). The method is based on the matrix-determinant identity, and it involves operations with an auxiliary vector on the matrices. The method is computationally faster compared to Liverrier and Danilevsky methods.

We present a new method to remove the parasitics contribution to the VCSEL chip response, in order to obtain the intrinsic S21 behavior. The on-chip VCSEL is defined as two cascaded two-port subsystems representing the electrical access and the VCSEL optical cavity respectively. S11 and S21 parameters measurements are carried-out using a probe station to characterize the chip response. An electrical equivalent circuit defining the behavior of the electrical access is combined with T-Matrix formalism to remove the parasitics contribution from the measured S21 response. Results allow us to determine the intrinsic 3-dB bandwidth of the VCSEL.

A decentralized model predictive controller applicable for some systems which exhibit different dynamic characteristics in different channels was presented in this paper. These systems can be regarded as combinations of a fast model and a slow model, the response speeds of which are in two-time scale. Because most practical models used for control are obtained in the form of transfer function matrix by plant tests, a singular perturbation method was firstly used to separate the original transfer function matrix into two models in two-time scale. Then a decentralized model predictive controller was designed based on the two models derived from the original system. And the stability of the control method was proved. Simulations showed that the method was effective.

A model for multirate sampled-data systems is presented. A detailed analysis of nonconventional sampled-data control systems (SDCS) is performed. The block multirate input-output model illustrates the control possibilities of multirate SDCS. It is obtained from either a transfer function matrix or a state variable representation. The model provides a direct way to represent, design, and understand either periodic or predictive controllers. A controller design methodology suitable for multivariable, multirate, nonsynchronous SDCS is also presented. The main feature is the freedom to achieve important objectives such as structure assignment, decoupling, and desired transient behavior, as well as reference matching, optimal control, or disturbance rejection. >

This chapter addresses the problem of model-reference sliding mode control of uncertain linear multi-input-multi-output systems by output-feedback. After a brief revision of the main approaches and results available in the literature, a new method to solve the problem is presented using unit vectors as switching functions to induce sliding modes. It is named Unit Vector Model-Reference Adaptive Control (UV-MRAC).

This work presents a simulation application study on the design of centralized PI controllers for a MSF desalination plant. Various design methods based on the transfer function matrix of the plant are considered. The methods include (1) the Davison method, (2) the Maciejowski method, (3) the decoupler design and (4) the Tanttu and Lieslehto method. The performance of the closed loop system for a step change in the set point is compared. The robustness of the controlled system for uncertainties in the system steady-state gains is also evaluated.

A measuring system for measuring a transfer function matrix of a system to be controlled by applying sine-wave excitations to a test object simultaneously by multiple number of vibrators. In the measuring system, when sine-wave signals for driving multiple number of vibrators are generated, phases between the sine-wave signals are shifted randomly, first, and then multiple number of vibrators are excited simultaneously under the generated sine-wave signals. Then, an auto-spectrum and a cross-spectrum for one calculation are calculated from spectral data on a vibration frequency obtained from an analysis of excitation signals and response signals acquired during the excitations. These steps are repeated two or more times to calculate the auto-spectra and cross-spectra for two or more calculations, followed by arithmetically averaging these spectrums to find a mean value of the auto-spectra and a mean value of the cross-spectra, so that the transfer function matrix at a specific frequency is calculated from the both mean values. The steps up to this point are repeated at each frequency to calculate said transfer function matrix data at all frequency components. This can allow the same sine-wave signals and the same vibration condition as in a multi-degree of freedom sine-wave vibration test to be used in the test, for measuring the transfer function matrix of the system to be controlled with adequate accuracy.

It has been known for some time that many control system design requirements can be expressed as differentiate inequalities. More recently, it has been shown that important structural properties such as robustness and low noise sensitivity can be expressed as nondifferentiable inequalities involving the singular values of a system or return difference transfer function matrix. This paper presents an optimization algorithm which permits all these constraints to be considered.

Multiple-input, multiple-output systems are considered which are linear, time-invariant and finite dimensional and which possess a decentralized fixed mode. A transfer function characterization of this property is developed, which allows characterization also of the degree of a fixed mode, this concept being given a meaningful definition in the course of the paper.