Search

Computing the McMillan degree of a transfer function matrix G requires writing G in the Smith-McMillan form or computing all of the minors of G. This becomes more difficult and computationally expe...

In this paper, a novel constructive procedure is proposed for the realization of a low-order Fornasini–Marchesini state-space model for a given multidimensional system. In particular, essential properties for the constructions of a backward shift space and a resolvent invariant space associated with the Gleason’s problem from a given transfer function matrix are investigated and some new sufficient conditions for such constructions are developed. Then, based on these conditions, a systematic constructive procedure is proposed for the multidimensional Fornasini–Marchesini model realization. It turns out that the new constructive procedure can generate Fornasini–Marchesini models with much lower orders and even the minimal realizations for a much larger class of multidimensional systems than the existing methods. Nontrivial examples are also provided to illustrate the basic idea as well as the effectiveness of the proposed procedure.

This paper presents a generalized formulation of a decoupling scheme for n ×n multivariable processes. The proposed Adj dynamic decoupling {mathcal{K}}-builds on deriving the decoupler based on the adjoint of the process transfer function matrix. The decoupler is designed such that it contains lesser dynamics yet ensures a performance close to the ideal decoupling. The proposed scheme always ensures the realiz-ability of the decoupler while providing a superior decoupling performance. Procedure for deriving the decoupler with simple rules is presented in this manuscript. The half-rule is utilized to obtain a simplistic description of the higher-order models. The applicability of the proposed decoupling scheme for lower as well as high-dimensional MIMO processes is demonstrated through various simulation studies. The effectiveness of the proposed scheme against existing decoupler is highlighted with a comparative performance evaluation study.

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.

In this paper, a novel centralized IMC (internal-model-control)-PID (proportion-integration-differentiation) controller is designed for multivariable processes with multiple time delays. To reduce the influence of time delays, the process model is divided into the minimum common time delay part and the remaining part. The IMC-PID controller, consisting of a full-matrix filter and a diagonal PID controller, is obtained based on the IMC principle. The full-matrix filter described as the inverse of the remaining part is too complex to compute. Hence, the Nyquist set is employed to describe the dynamics of the filter. The approximate transfer function matrix of the filter is calculated by complex curve fitting. Besides, to reduce the approximation error and obtain stable filter elements, a compensator is introduced. The rules of selecting compensator parameters are proposed for stable filter elements. Finally, the IMC-PID controller parameters are determined after comprehensively considering the performance a...

The cognizance of the fractional-order system (FOS) is flourishing among the researchers of science and engineering. Infinite dimension of the FOS is no more a problem nowadays as far as their practical implementations are concerned due to the advent of many rational approximation methods. This paper revisits one such recognized approximation method, namely, the Oustaloup approximation method, to acquire the approximation of a multivariable FOS signified by a transfer function matrix (TFM). Essential simulation results are deliberated.

The BOPP film thickness control system is a nonlinear and complex multivariable coupling system. The three-channel transfer function matrix model is obtained by analyzing the process, The existing decoupling algorithm has a good effect in the film thickness control system, but cannot completely eliminate the system coupling effect, and the system robustness still needs to be improved. So the RBF model is used to decouple the system and the RBFD algorithm is designed. Aiming at the long training process situation of RBF decoupling algorithm, fast self-learning, attaching differential term and particle swarm optimization (PSO) are used to optimize the RBF model to improve the anti-interference ability and response speed of the system, so as to design the ASRBFD decoupling algorithm and realize the complete dynamic decoupling control. The experiment results show that the ASRBFD decoupling method designed in this paper has strong anti-interference ability, high RBF model training efficiency and excellent decoupling performance.

For a differential-algebraic system described by a polynomial or an improper transfer function matrix subject to perturbations acting on the normalized coprime factors we solve the robust stability problem. A formula for the maximum achievable stability margin and an explicit construction of the robust stabilizing controller are given in terms of realizations and solutions to appropriate Riccati equations.

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.

In this contribution we show that under some circumstances the Kalman–Yakubovich–Popov (KYP) lemma can be applied for testing quadratic stability of multi-mode switched linear systems. Based on this observation, we introduce several constructive algorithms which enable us to associate a transfer function matrix to a switched linear system given in general form. The strict positive realness test of the resulting transfer function matrix can be easily achieved by available known algebraic conditions. By means of some examples we illustrate the step-by-step implementation of these algorithms.

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.

This paper investigates a hardware decoupling method in isolated three-port converters (TPCs). According to the equivalent AC circuit model of the series-resonance-based isolated TPC, the power exchange among different ports can be derived. Further, the transfer function matrix of output currents and the phase-shifting angles can be obtained, and the decoupling control between the ports of a TPC can be demonstrated. Simulation and experimental results show that independent control is achieved by using the hardware decoupling method.

In TMP-refining processes, the stabilization of the fiber pad inside the refining zone requires a new control approach. Specific energy control tends to be complex and most often affected by a number of disturbances not so well specified in traditional MPC-concepts. To describe the dynamics in such nonlinear processes is difficult, tedious and requires significant maintenance support. This paper focuses on two important issues related to modeling in mechanical pulping processes: measurements of internal states inside the refining zone and in particular natural decoupling to find a model suitable for future process optimization and improved control concepts of complete refiner lines. The idea is to show how this complex process, with serially linked refiners or refining zones, can be modeled and controlled using a simplified process description. In this series of papers, data from a commercial Twin-refiner and a CD-refiner are available as inputs. As an example of internal state measurements, refining zone temperature profiles and estimated distributed consistency in the refining zone are used. We show that the characteristics of the temperature profile dynamics makes it possible to introduce a decoupling scheme where the anti-diagonal elements in the transfer function matrix describing the process can be eliminated naturally, independent of which refiner is to be controlled.

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.

Multi-input multi-output control, also called multivariable control, is often met in practice. In this chapter, it is considered by the means of transfer function matrices. General stability properties, decoupling, relative gain array are explained with examples. Multivariable internal control concludes the chapter.

The design of coded apertures for compressive X-ray tomosynthesis is addressed here, based on the analysis of the coherence of the sensing matrix. It is shown that minimizing the inner products between the columns of the transfer function matrix, it is possible to obtain significant improvements with respect to the results obtained with the use of random codes. The computational cost of optimization is dramatically lower than other approaches introduced recently.

This study studies coordinated control of a platoon of vehicles consisting of a leader and multiple followers when multiple vehicles suffer from disturbances. Small disturbances acting on one vehicle may cause large spacing errors between intervehicles. In addition, the spacing errors propagate up or down in a vehicle platoon. To mitigate the adverse effect of the disturbances, a control law is proposed based on only the position information of the vehicle itself and its preceding vehicle. To analyse the disturbances propagation among the platoon, the upper bounds of two transfer functions are presented including the transfer function matrix 𝒢 de from external disturbances to spacing errors as well as the transfer function matrix 𝒢 ue from a leader's input control to spacing errors. Furthermore, an alternative control law is proposed when the velocity of the leader is known by the followers. In this case, two tighter upper bounds of 𝒢 l de and 𝒢 l ue are presented. The derived upper bounds of the transfer functions are independent of the number of vehicles in the platoon. Simulations verify the effectiveness of the proposed approach.

Active magnetic bearings (AMBs) are widely applied in high-speed rotating machinery, especially in special environments. In designing and adjusting an AMB system, the mathematical model of the system plays an important role. Identification is a useful method to obtain the models of AMB systems. This paper concentrates on identification method for an AMB system with a flexible rotor. Based on the theoretical system model and the measured frequency–response model, the proposed method estimates the unknown parameters and establishes the transfer function matrix model of the AMB system. According to the theoretical model, this paper decomposes the identification procedure into a few steps and the model is sequentially reduced by these steps. In this procedure, the submodels are identified separately and finally combined together. The proposed method is validated by experiments on three AMB systems.

The negative imaginary (NI) property is exhibited by many systems such as flexible structures with force actuators and position sensors and can be used to prove the robust stability of flexible structure control systems. In this paper, we derive methods to check for the NI and strict negative imaginary (SNI) properties in both the single-input single-output as well as multi-input multi-output cases. The proposed methods are based on spectral conditions on a corresponding Hamiltonian matrix obtained for a given system transfer function matrix. Under certain conditions, a given transfer function matrix satisfies the NI property if and only if the corresponding Hamiltonian matrix has no pure imaginary eigenvalues with odd multiplicity. It is also shown that a given transfer function matrix satisfies the SNI property if and only if the corresponding Hamiltonian matrix has no eigenvalues on the imaginary axis, except at the origin. The results of this paper are applied to check the NI property in two nanopositioning applications.

A novel design method of decoupling internal model control is proposed for non-square processes with multiple time delays that are often encountered in complicated industrial processes. The method can obtain a realizable decoupling controller of non-square processes with more inputs than outputs by inserting some compensated terms, which are derived analytically. Meanwhile, based on the relative normalized gain array, an equivalent transfer function matrix is introduced to approximate the pseudo-inverse of the process transfer function matrix, which makes the design of decoupling internal model control simple and easy to calculate. Filters are added to the control structure to improve the robustness. Simulation results have proved the effectiveness and reliability of the proposed method.

For a generalized discrete-time system, whose transfer function matrix may be improper or polynomial, we give realization based formulas for the H 2 optimal output feedback controller. The formulas bear essentially the same elegant simplicity of the proper case.

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.