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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.

Rational transfer function matrices and linear time-invariant descriptor systems are the two main system representations employed in this book. The purpose of this chapter is to provide a concise statement of the main results on rational matrices and descriptor systems to facilitate the understanding of the mathematical terminology used throughout the book. The treatment in depth of most of concepts was not possible in the restricted size of this book. Therefore, at the end of this chapter, we indicate the main references covering the presented results and make suggestions for supplementary readings.

This paper proposes an approach of Internal Model Control (IMC) for the linear sampled multivariable non-square systems with outputs more than inputs. The proposed IMC, which is based on a specific inversion principle, is the extension of to the case of square systems, in the controller design, a simple method is presented to add a complementary transfer function matrix of the process to obtain a square transfer matrix. To guarantee the robust stability of the system and disturbance rejection, the controller design procedure is proposed to obtain the wish control. Simulation illustrate the effectiveness of the proposed method for non-square multivariable processes.

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

As discussed in the introduction, residuals are essential and play a key role in process monitoring systems. By observing the deviation between the actual measurement and its redundancy, real-time monitoring of the status of the industrial automation processes can be performed.

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.

To solve the coupling problems cause by flexible structure of Dynamic Tuned Gyroscope (DTG), solutions was proposed through the combination of loop control and decoupling within Individual Channel Design (ICD) framework during the DTG lock loop design. Firstly, theoretical model of DTG and its actual coupling property were presented. Then, the diagonal controller was designed for the diagonal elements and counter-diagonal elements of DTG transfer function matrix under the framework of ICD. The stability and coupling relationship of individual channel were also analyzed for both two cases. Finally, a validation experiment was carried out for a certain type of DTG when it works in tuned state and mistuned state with 20% perturbation of tuned speed. The experimental results show that the diagonal controller for both two cases can stabilize the loop. But in mistuned state, the coupling degree of diagonal elements case grows up to 15%.This shows that the controller robustness for counter-diagonal elements is greater.

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.

Transfer function matrix model of the bubbling fluidized bed boiler The paper presents proposal of a model of the fluidized bed boiler adapted for use in model-based controllers e.g. predictive, adaptive or internal model control (IMC). The model has been derived in the form of transfer function matrix which allows its direct implementation in the controller structure. Formulated model takes into consideration the principal cross-coupling between process variables which enables the opportunity to search for feasibility of decoupling control. The results of the identification of the dynamics of the 2 MW industrial bubbling fluidized bed boiler using the proposed model form was presented. According to the experimental data it was found that despite of introduced simplifications presented model allows the boiler behavior prediction.

Identifying dynamic forces with structural response signals is important when direct measurement is difficult or impossible. The minimized condition number method was introduced to reconstruct the forces with selected spatial distribution of response locations. This paper presents another way to optimize the selection of the response locations. The coherence of transfer function matrix is analyzed and the coherence factor of the transfer function matrix is introduced to optimize the response locations. Numerical simulations of the coherence analysis show that it is effective and requires less computational effort than the condition number method. The validity of the analysis is verified by applying it to the identification of the suspension forces on a vehicle cab.

This article investigates methods for decoupling multivariable linear parameter varying (LPV) systems and proposes a new interaction measure for decoupled proportional-integral (PI) feedback control design in LPV systems. The proposed approach seeks to benefit the multivariable control of multi-input multi-output (MIMO) systems with variable operating conditions, variable parameters or nonlinear behaviour. This method can improve the tracking performance and reduce the operating conditions variability of such systems with significant coupling in the system dynamics. We design MIMO decoupling feedback LPV controllers to address loop interaction effects. The proposed method uses a parameter-dependent static inversion or SVD decomposition of the system to minimise the effects of the off-diagonal terms in the MIMO system transfer function matrix. A new parameter-dependent interaction measure is introduced based on the SVD decomposition and static inversion which is subsequently utilised for tuning multi-loop ...

An interactor matrix plays several important roles in the control system theory. In this paper, we present a simple method to derive the right interactor for tall transfer function matrix using Moore-Penrose pseudo inverse. By the presented method, all zeros of the interactor lie at the origin. Moreover, the interactor by the proposed method has all-pass property in the discrete-time. The method will be applied to the inner-outer factorization which will be independent on the choice of the interactor.

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.

This paper concerns the disturbance rejection problem of a linear complex dynamical network subject to external disturbances. A dynamical network is said to be robust to disturbance, if the H∞ norm of its transfer function matrix from the disturbance to the performance variable is satisfactorily small. It is shown that the disturbance rejection problem of a dynamical network can be solved by analysing the H∞ control problem of a set of independent systems whose dimensions are equal to that of a single node. A counter-intuitive result is that the disturbance rejection level of the whole network with a diffusive coupling will never be better than that of an isolated node. To improve this, local feedback injections are applied to a small fraction of the nodes in the network. Some criteria for possible performance improvement are derived in terms of linear matrix inequalities. It is further demonstrated via a simulation example that one can indeed improve the disturbance rejection level of the network by pinning the nodes with higher degrees than pinning those with lower degrees.

Due to the deficiencies of prior modeling methods of systems of boilers in parallel operation through a common manifold, in this article we use simplified approximate distributed modeling based on the compartmentalization and combination of the manifold. First, a principle is established to plot out the manifold into some basic pipe sections between each pair of source/sink points. Second, a simplified approximate distributed decoupled transfer function matrix model without steady errors is built for each pipe section. Finally, a smooth joint arithmetic is adopted to combine all the conterminous subsections of the pipe section with boilers/turbines at its ends into a whole system model. This method can decrease the size of the equipment and, therefore, makes it easier to model larger systems. The model presents more distributed characteristics and fits well in control system simulating. Some experiments have been done with favorable results to prove the validity of the 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.

In this paper, a novel engineering oriented decoupling control system design method for two-input, two-output processes is presented. By employing the concept of integrated error, gain and phase changes of a transfer function when other loops are closed can be uniquely determined. Consequently, an equivalent transfer function matrix for a closed-loop control system can be obtained and its relations with the original process transfer function matrix are derived. On the basis of the equivalent transfer function matrix, parameters of a stable, proper, and causal ideal diagonal decoupler can then be easily determined by proper parameter assignments of the decoupled transfer function matrix elements. The method avoids the drawbacks of existing decoupling schemes, is very simple and can be easily understood, and can be implemented by field control engineers. An industrial process is employed to demonstrate its simplicity in design and effectiveness in control system performance.

In this paper the invariance of the characteristic values and of the L ∞ norm of linear time-invariant (LTI) systems under lossless positive real transformations is proven. Given a LTI system with transfer function matrix G ( s ) , the transformation s ← F ( s ) with F ( s ) being an arbitrary lossless positive real function of order nF is considered, and the algebraic Riccati equations (AREs) allowing to assess some properties of the transformed system G ( F ( s ) ) are investigated. It is proven that, under such transformations, the solutions of the AREs associated to system G ( F ( s ) ) are related to those of G ( s ) . From this property, it derives that G ( F ( s ) ) and G ( s ) have the same L ∞ norm and that the characteristic values of G ( F ( s ) ) are those of G ( s ) , each with multiplicity nF.

In this paper a method for decoupling has been presented for a specific case of MIMO system. Falb's row by row decoupling concept is utilized for developing the control law using proportional-derivative (PD) output feedback. The solutions for integrator type and specific pole type decoupled system are presented. Necessary and sufficient condition for the existence of PD output feedback decoupling is determined. Using this procedure, multiple sets of PD output feedback gains (Ko, Fo, Γo) can be obtained for a given decoupled system transfer function matrix. The results are validated using two examples.

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.

In this paper an attempt is made to design a dynamic state feedback based decoupler (PD compensator) for MIMO system. The condition for decoupling and mathematical expressions for the set of dynamic state feedback gain matrices (K, F and Γ) for a given decoupled system transfer function matrix is formulated. Further the robustness has been tested.

The problem of designing H∞ dynamic output-feedback controllers for linear discrete-time systems with polytopic type parameter uncertainties is considered. Given a transfer function matrix of a system with uncertain real parameters that reside in some known ranges, an appropriate, not necessarily minimal, state-space model of the system is described which permits reconstruction of all its states via the delayed inputs and outputs of the plant. The resulting model incorporates the uncertain parameters of the transfer function matrix in the state-space matrices. A recently developed linear parameter-dependent LMI approach to state-feedback H∞ control of uncertain polytopic systems is then used to design a robust output-feedback controllers that are of order comparable to the one of the plant. These controllers ensure the stability and guarantee a prescribed performance level within the uncertainty polytope.

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.

The singular-value decomposition has been used to analyze the robustness of closed-loop systems and to determine whether any controllability problems can be expected. Past controllability conditions have been derived in terms of the condition number and the minimum singular value of the process and the condition number of the controller transfer function matrix, in terms of potential sensitivities of the closed-loop system to model uncertainties or problems with saturation of the manipulated variables. This paper considers processes with a large maximum singular value. It is shown that the closed-loop control of such processes can result in poor transient performance as a result of valve accuracy considerations, even if the condition number is small and the minimum singular value is large, which would indicate no performance limitations according to existing controllability criteria. Further, processes with large singular values can be prone to sensor saturation. This indicates that the magnitude of all of the singular values should be considered when assessing the controllability of a process. A new interaction tool based on output correlation is introduced to help select measurements and manipulated variables that have a good range of singular values for practical application. The approach proposed is illustrated on two simple examples and on the Tennessee Eastman process.

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.

A simple necessary and sufficient condition for solvability of decoupling with internal stability for unity output feedback for non-singular plants is proposed.

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.