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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.