Transfer Function Matrix Research Articles

Frequency domain approaches to locate forced oscillation source to control device

The location of the control devices that produce forced oscillation sources is crucial to the elimination of forced oscillations. This paper proposes two frequency domain approaches to reliably locate oscillation sources from mechanical parts and excitation systems of generators to their control devices. Firstly, the transfer function matrix from mechanical disturbances to mechanical powers is demonstrated to be inherently diagonally dominant. The property is used to monitor and preliminarily locate oscillation sources from mechanical parts. Moreover, this paper proposes a systematic method of power spectral density prediction to further locate oscillation source to control device by using the generator terminal voltage (or generator current) to predict the power spectral density of generator responses. It is shown that for non-source generators, the responses are determined by the generator terminal voltage. The generator with distinct mismatch between predicted and measured power spectral density is identified as the oscillation source. The mismatches between predicted and measured power spectral density of different responses are different, further enabling the method to identify the control device producing the oscillation source. The method of power spectral density prediction is used as a general method to provide further and detailed location results. Demonstrative examples of a 39-bus system and the 547-machine 8647-bus North China Power Grid show the effectiveness of the proposed methods.

Random response of highly skewed propeller-shafting system induced by inflow turbulence

The random responses of a highly skewed propeller-shafting system in both axial and radial direction induced by inflow turbulence are numerically studied. Firstly, a fine finite element model is established, including propeller, shaft and surrounding fluid. The force-force transfer function matrix between each exciting node on the blade surfaces and the corresponding transmitted force is formed based on the FEM model. Secondly, the unsteady hydrodynamic pressure spectrum acting on the blade surface is calculated on the basis of strip theory and mapped onto all nodes that distribute on the blade surfaces. Finally, the random response of the system and the power spectral densities of the transmitted forces from both axial and radial bearings are obtained. By employing the numerical method, the relationship between the force amplification effect and the modal characteristics of the highly skewed propeller-shafting system is discussed. Furthermore, the influence of system dynamic parameters, such as propeller elasticity, axial and radial bearing stiffness on the random vibration is analyzed, which can thus provide a reference for the design of low noise propulsion system for ships.

Vibration load and transfer path identification of vehicle using inverse matrix method based on singular value decomposition

Based on the theory of inverse transfer matrix, a novel method for simultaneous load identification of vehicle vibration is presented in this paper. Some response, excitation, reference points (called key points) and their transfer paths, which have severe effects on the vibration of a whole vehicle, are defined. The transfer functions among the key points are measured by experiments, and thereby a transfer function matrix of vehicle vibration is established. To solve ill-conditioning problem in the transfer function matrix, the methodology of singular value decomposition is introduced into matrix inversion in the excitation load identification. To reduce the identification error, four transfer function matrices with different reference points and condition numbers are selected and discussed. The results show that the more the reference points are, the smaller the condition number of transfer function matrix is, the higher the accuracy of excitation load identification. The transfer function matrix with minimum condition number is used to identify the excitation loads at the vehicle key points. Experimental verifications suggest that the newly proposed method is effective and feasible for excitation load identification of vehicle vibration. Using the identified excitation loads, furthermore, the vibration causes of the steering wheel and seat rail are obtained, which is helpful for improving vibration performance of the sample vehicle. In applications, the excitation load identification method proposed in this paper may be applied not only to other types of vehicle, but also to other complex electromechanical products for load identification in engineering.

Structural Model and Diagram of Multilayer Electro Magneto Elastic Actuator for Nanotechnology

We obtained the structural model and the structural diagram of the multilayer electro magneto elastic actuator for nanotechnology in contrast to electrical equivalent circuits of the piezo transmitter and piezo receiver, the vibration piezo motor. We determined the structural model, the structural diagram and the matrix transfer function of the multilayer electro magnetoelastic actuator for nanotechnology.

Wave-Domain Residual Echo Reduction Using Subspace Tracking

This article proposes a wave-domain residual echo reduction method for two-way immersive sound communication, which is based on wave field synthesis and uses uniform linear arrays of loudspeakers and microphones. This method is intended to improve the echo reduction performance in a mildly reverberant room with moderate increase in computational complexity. For improving such performance, this method takes residual echo due to reflected waves into account and uses a multi-tap echo-path model. To mitigate the increase in the method's computational complexity, it uses a size-reduced transfer function (TF) matrix instead of the full TF matrix. Specifically, this method extracts the dominant components of the loudspeaker signals adaptively by subspace tracking and estimates a size-reduced TF matrix that relates these dominant components to the residual echo. Simulation showed that the proposed method plus a wave-domain acoustic echo canceller (AEC) improved echo return loss enhancement by 10 dB compared to the conventional wave-domain echo reduction method plus the wave-domain AEC in a room with a reverberation time 180 ms. Its total computational complexity is twice that of the conventional echo reduction method plus a wave-domain AEC.

Natural Frequency Analysis of Hydraulic Quadruped Robot and Structural Optimization of the Leg

Abstract Hydraulic quadruped robots can adapt to very complex ground conditions, as they have good maneuverability and high load capacity and, therefore, have received great attention in military research fields all over the world. However, there is no mature theory on how to ensure stable, efficient, and fast walking of robots. In this paper, from the point of view of the natural frequency of the hydraulic system, we first calculate the natural frequency of the robot's legs during the whole motion period of the robot and verify the accuracy of calculation through system identification. Then, through the analysis of the state equation and transfer function matrix of the multiple-input multiple-output system, it is found that the zero and pole of the system are very close, this is why the natural frequency is low but the system response is acceptable and then we prove that no parameter for the simultaneous zero-pole cancelation of two hydraulic cylinders exists. With the goal of increasing the natural frequency, we optimized the leg structure of the robot to find the best structural parameters. Finally, a single-leg test bench was built. The experimental results show that the optimization of the structure can actually increase the natural frequency of the system and significantly improve the response characteristics of the robot.

Dynamic Impact of Zero-Sequence Circulating Current on Modular Multilevel Converters: Complex-Valued AC Impedance Modeling and Analysis

The stability impacts of the internal control dynamics of the modular multilevel converters (MMCs) have been discussed recently. Yet, the impact of zero-sequence circulating-current (ZSCC) dynamics on the ac-side dynamics of the MMCs is hitherto unaddressed. This article develops the ac impedance model for the grid-connected MMCs by means of complex vectors and harmonic transfer-function matrices, which allows separately characterizing the dynamics of the ZSCC. Then, based on the complex-valued model, a single-input-single-output closed-loop equivalent impedance is derived for grid-connected MMCs, considering both the frequency-coupling dynamics of the MMCs and the interactions with the grid impedance, which enables a design-oriented analysis on the stability impact of the ZSCC. It is revealed that the resonant peaks in the ac impedance of the MMC are yielded due to the absence of the ZSCC control, which tends to destabilize the system in weak grids. A systematic parameter-tuning method of the ZSCC control loop is developed to guarantee the system stability. Case studies in time-domain simulations corroborate the theoretical analysis.

A Controller Architecture With Anti-Windup

This letter presents a framework for anti-windup controllers based on the Youla-Jabr-Bongiorno-Kucera (YJBK) parameterization. Applying this architecture gives an additional YJBK matrix transfer function related to the input saturation. This additional YJBK transfer function can be applied for optimizing the feedback loop around the input saturation. Further, the connection with other anti-windup controller architectures is also considered in this letter.

A control parameter analysis method based on a transfer function matrix of hybrid multi-terminal HVDC system with flexible adaptability for different operation modes

To achieve better controller performance, the impact of control parameters on the stability and dynamic performance is essential to be clarified mathematically for hybrid multi-terminal HVDC (Hybrid-MTDC) systems considering different operation modes (OMs). In this paper, a generic small-signal model (SSM) is established, which can be modified flexibly for different OMs. Then the SSM can be converted into a transfer function matrix (TF-Matrix), which avoids deriving the transfer function separately for each controller of the system, and greatly improves the work efficiency. By inputting a step into the TF-Matrix, the time-domain mathematical model for the all system state variables can be obtained, and it is more efficient than iterative solutions of high-order differential equations. To this end, a quantitative control parameter analysis method based on a TF-Matrix is proposed. Utilizing the proposed method, a typical Hybrid-MTDC system is investigated, and the results demonstrate the practicality and accuracy of the proposed method.

Analysis and Suppression of Slotting and Cross-Coupling Effects on Current Control in PM Synchronous Motor Drives

This paper proposes a d–q cross-coupling current controller for permanent magnet synchronous motor (PMSM) drives. Slotting and cross-coupling effects in PMSMs cause the effective air-gap length to vary with the rotor angle and distort the distribution of the air-gap flux. Such distortions have a significant influence on the current control by changing the relationship between the stator currents and voltages. To investigate their effects, a d–q model is established in this paper, which is suitable for describing the voltage characteristics of the actual PMSMs. The model contains the angle-dependent parameters, the cross-coupling inductance between d–q axes, and the q -axis permanent magnet flux linkage, unlike the ideal d–q model. The transfer function matrix from the d–q currents to d–q voltages of PMSM is newly derived from the model. Based on that, the current controller with the feedback and feedforward terms of 2-by-2 matrix is proposed. It is designed so that the independent gains are in low-pass filter forms and the coupling control gains are zero with eliminating interference between d–q axes. The proposed controller contributes to providing the stable control performance by canceling the slotting and cross-coupling effects. The performance of the proposed current controller is verified by experimental results.

Control Design and Stability Analysis of Power Converters: The MIMO Generalized Bode Criterion

Three-phase dynamic systems and multiphase generators are frequently modeled and controlled in the synchronous reference frame. To properly model the cross-coupling terms in this reference frame, complex vector theory and transfer function matrices are commonly applied, obtaining multiple-input multiple-output (MIMO) dynamic models. The stability of MIMO systems can be assessed through the Nyquist generalized stability criterion. However, the use of the Nyquist diagram complicates the controller design. The Bode diagram is a more intuitive tool for the controller design; however, the Bode stability criterion is not applicable to MIMO systems. In this article, the MIMO generalized Bode criterion is proposed. Since this stability criterion is based on the Nyquist generalized stability criterion, it can be applied to any system. Furthermore, it is simple to use, as it only requires information contained in the open-loop transfer matrix and the Bode diagram. The proposed stability criterion thus offers an interesting tool for the controller design procedure in MIMO systems, as it is shown in this article for two common applications: the current control loop of a power converter, a 2 × 2 system, and the current control loop of two independent power converters in parallel, a 4 × 4 system.

Optimal Model Approximation of Linear Time-Invariant Systems Using the Enhanced DE Algorithm and Improved MPPA Method

In this paper, the authors propose a novel model order reduction method integrating evolutionary and conventional approaches for higher-order linear time-invariant single-input–single-output (SISO) and multi-input–multi-output (MIMO) dynamic systems. The proposed method makes use of a differential evolution algorithm with enhanced mutation operation for the determination of reduced order model (ROM) denominator polynomial coefficients. In addition, an improved multi-point Pade approximation method is used to determine the optimal ROM numerator polynomial coefficients. The optimum property of the ROM is measured by minimising the integral square of the step response error between the original high-order dynamic system and the ROM. In the case of the MIMO system reduction approach, an optimal ROM transfer function matrix is determined by minimising a single objective function. This objective function is defined by a linear scalarising of the multi-step error function matrix components $$ \left( {E_{ij} } \right) $$. The proposed method guarantees the preservation of the stability, passivity and accuracy of the original higher-order system in the ROM. The proposed method is validated by applying it to a ninth-order SISO system, as well as to the tenth- and sixth-order linearised single-machine infinite-bus power system model with and without an automatic excitation control system. The simulation results and the comparison of the integral square error and impulse response energy values of the ROM demonstrate the dominance of the proposed method over the latest reduction methods available in the literature.

Improved disturbance observer-based control for multivariable processes with time delays based on modified inverse model

In this paper, a modified multivariable disturbance observer-based (MDOB) design method is proposed to improve disturbance rejection performance for multiple-input-multiple-output (MIMO) processes with multiple time delays. Two important issues in MDOB control are studied here: computation of the inverse model and design of the filter. First, to reduce the influence of time delays, the nominal process is factorized as a diagonal time delay matrix and a remaining transfer function matrix, and the remaining part is used to design the inverse model in MDOB. Considering the difficulty of matrix inversion, the Nyquist set is used to describe the dynamic of the inverse model, and accordingly, the simplified inverse model is obtained by the curve fitting technique. In addition, to guarantee the properness and stability of the simplified inverse model, a compensator is introduced. Rules for selecting compensator parameters are given. Finally, with the proposed inverse model and compensator, the filter [Formula: see text] is optimized by minimizing the H∞ norm of the disturbance estimation error. The filter constants are determined by fully consider the disturbance rejection performance and robustness of the system. Simulation examples are presented to illustrate the effectiveness and merits of the proposed method.

Seismic retrofit of two-way unsymmetric-plan buildings with added masses

A new methodology for retrofitting unsymmetric-plan buildings against earthquakes is proposed. When such buildings are subjected to ground acceleration, the lateral inertial forces created at the floors’ center-of-mass (CM) induce torsional moments about the center-of-rigidity (CR). The retrofit approach introduces masses to the building floors and places them so that the CM is moved closer to the CR to decrease the lever-arm of the torsional moment. The mass placement is challenging since adding mass also increases the lateral inertial forces linearly and changes the natural mode-frequencies nonlinearly. In order to determine the optimal mass placement, the proposed methodology seeks to develop a new sequential search algorithm. A transfer-function matrix, relating the interstory drifts of the floor-plan edges to the ground acceleration components, is presented and used to obtain the magnitude of the peak gains. The search algorithm examines the performance index (PI) of the square-root of the sum of the squares (SRSS) of the magnitudes of the peak gains over a range of added mass quantities, starting from the top-floor and sequentially stepping towards the first-floor. Thanks to the proposed transfer-function matrix, the minimum PI is obtained very quickly, saving computation time. The developed methodology is examined for retrofitting a three-story building of shear-frames, a ten-story building of moment-resisting-frames and an inelastic ten-story building of yielding shear-frames. The results show that the maximum interstory drifts within the structure, the maximum story shear-forces applied to the lateral-load carrying frames, and the maximum absolute acceleration are reduced by moving the CM closer to the CR, which mitigates the threat of structural failure and demonstrates the effectiveness of the proposed retrofit approach. The developed methodology introduces a new sequential search algorithm that calculates optimal mass quantities, and their location in the horizontal-plane, to minimize the frequency-response of the new transfer-function matrix, while subjected to side-constraints. This is a novel approach to the utilization of systematic search algorithms.

Structural-Parametric Model Multilayer Electromagnetoelastic Actuator for Nanomechatronics

In this work, the structural-parametric model and the parametric structural schematic diagram of the multilayer electromagnetoelastic actuator for nanomechatronics are received. The purpose of the research is to obtain structural-parametric model of the multilayer electromagnetoelastic actuator for the nanomechatronics systems. The method of mathematical physics is used to solve the matrix equation of the multilayer electromagnetoelastic actuator for its structural-parametric model. The generalized parametric structural schematic diagrams of the multilayer electromagnetoelastic actuator or the multilayer piezoactuator for nanomechatronics with the mechanical parameters the displacement and the force are determined in contrast to Cady and Mason’s electrical equivalent circuits for the calculation of the piezotransmitter, the piezoreceiver, the vibration piezomotor. We obtain the generalized structural-parametric model and the generalized parametric structural schematic diagram of the multilayer electromagnetoelastic actuator from the general equation of the electromagnetoelasticity and determination of the caused force, the system of the equations for the equivalent quadripole of the multilayer actuator, the equations of the forces on its faces. The decision matrix equation for the equivalent quadripole of the multilayer electromagnetoelastic actuator is used. The parametric structural schematic diagram of multilayer electromagnetoelastic actuator is obtained with the mechanical parameters the displacement and the force. The matrix transfer function of the multilayer electromagnetoelastic actuator is determined for nanomechatronics. The generalized parametric structural schematic diagram, the generalized matrix equation of the multilayer electromagnetoelastic actuator for nanomechatronics are obtained. The deformations of the multilayer electromagnetoelastic actuator for nanomechatronics are described by the matrix equation. The parametric structural schematic diagram and the matrix transfer function of the multilayer piezoactuator are obtained for calculations the nanomechatronics systems with the multilayer piezoactuator of micro and nanodisplacement.

Robust Sensor Fault Reconstruction via a Bank of Second-Order Sliding Mode Observers for Aircraft Engines

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 ∞ 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.

Distributed robust stabilization of networked multiagent systems with strict negative imaginary uncertainties

SummaryThis paper deals with the distributed robust stabilization problem for networked multiagent systems with strict negative imaginary (SNI) uncertainties. Communication among agents in the network is modelled by an undirected graph with at least one self‐loop. A protocol based on relative state measurements of neighbouring agents and absolute state measurements of a subset of agents is considered. This paper shows how to design the protocol parameters such that the uncertain closed‐loop networked multiagent system is robustly stable against any SNI uncertainty within a certain set for various different network topologies. Tools from negative imaginary (NI) theory are used as an aid to simplify the problem and synthesise the protocol parameters. We show that a state, input, and output transformation preserves the NI property of the network. Consequently, a necessary and sufficient condition for the transfer function matrix of the nominal closed‐loop networked system to be NI and satisfy a DC gain condition is that multiple reduced‐order equivalent systems be NI and satisfy a DC gain condition simultaneously. Based on the reduced‐order systems, we derive sufficient conditions in an LMI framework which ensure the existence of a protocol satisfying the desired objectives. A numerical example is given to confirm the effectivenesses of the proposed results.

Sound Absorption Rate and Sound Transmission Loss of Wood Bark Particle

In this study, sound absorption capability and sound transmission loss of several kinds of target densities and thickness for six species of wood bark particle were estimated by the transfer function and transfer matrix methods. Resultantly, the mean sound absorption coefficient of a 100-mm thick Hinoki wood bark particle mat was 0.90 in the frequency range of 100–6400 Hz, whereas the mean sound absorption rate of a 50-mm thick Hinoki wood bark particle mat was 0.84 in the same frequency range. Particularly, at a thickness of 100 mm, it reached almost up to 100% in the frequency range of 1 KHz. The sound transmission losses of 100-mm thick Hinoki wood bark particle mat with a target density of 0.16 at 500 and 1000 Hz were 15.30 and 15.73 dB, respectively. When a 10-mm thick plywood was attached to the back of the wood particle mat, the sound transmission losses was increased by 20–30 dB. Wood bark can be used as an acoustical material owing to its high sound absorption rate and transmission loss.

Structural-Parametric Model and Diagram of a Multilayer Electromagnetoelastic Actuator for Nanomechanics

In this work, the parametric structural schematic diagrams of a multilayer electromagnetoelastic actuator and a multilayer piezoactuator for nanomechanics were determined in contrast to the electrical equivalent circuits of a piezotransmitter and piezoreceiver, the vibration piezomotor. The decision matrix equation of the equivalent quadripole of the multilayer electromagnetoelastic actuator was used. The structural-parametric model, the parametric structural schematic diagram, and the matrix transfer function of the multilayer electromagnetoelastic actuator for nanomechanics were obtained.

A Novel Control-Performance-Oriented Data-Driven Fault Classification Approach

This paper selected nine novel feature quantities that can reflect control performance in the closed-loop. Combined with support vector machine (SVM) and k-nearest neighbor (KNN), they are used to perform accurate fault diagnosis. Stability margin describes the degree of stability of the transfer function matrix of system, and thus can be used as an indicator to reflect system’s control performance. Similarly to stability margin, the reciprocals of $\boldsymbol {H_{\infty }}$ -norms of eight subsystems related to stability margin can also be selected as the other eight features describing the control performance. To get the data-driven realization of nine feature quantities, stable image representation and stable kernel representation are constructed by data-driven method without system identification in closed-loop system. Through trained SVM and KNN, different types of faults can be accurately categorized by these feature quantities and the correctness of the entire algorithm is testified and demonstrated by a dc motor benchmark system.