Transfer Function Matrix Of System Research Articles

Harmonic Interaction Analysis of Inverters Based on Harmonic State-Space Model Considering Dead-Zone Effect

In the context of increasing device switching frequencies year by year, non-ideal factors such as dead-zone effects in inverters not only cause output waveform distortion, but also generate harmonics that make the interaction between inverters and power grids more complex. In order to accurately describe and analyze this phenomenon and establish a more practical grid-connected inverter model, this paper proposes and establishes a three-phase LCL grid-connected inverter harmonic state space model that considers dead-zone effects. By incorporating dead-zone effects into the modeling process, the system transfer function matrix is derived to quantify the harmonic interaction coefficient between the inverter and the power grid, and the influence mechanism of dead-zone effects on the harmonic interaction process at high switching frequencies is analyzed in depth. The necessity of considering dead-zone effects is illustrated through simulation, and the effectiveness and accuracy of the inverter HSS model considering the effects of dead-zone effects are verified through experiments.

An Improved Quantitative Analysis Method of Oscillation Mode for DFIG-Based Wind Power Base With LCC-HVDC Transmission Considering Frequency Coupling Characteristic

The line-commutated converter-based high-voltage direct-current (LCC-HVDC) transmission has become one of the main forms to deliver wind power in China. However, due to the connections of a large number of power electronic devices (PEDs), there emerges a risk of sub/super-synchronous oscillations in the DFIG-based wind power base with LCC-HVDC transmission. The existing multi-node system analysis methods have ignored the frequency coupling characteristic (FCC) of PEDs, unable to obtain accurate oscillation characteristics. Besides, the relationship between the oscillation and multi-level factors has not been revealed yet. Therefore, this paper proposes an improved quantitative analysis method of oscillation mode which considers the FCC on the basis of the system admittance network model. Firstly, the impedance model of the system considering the FCC is established. Then, the improved quantitative analysis method of the oscillation mode considering the FCC is proposed and its steps are as follows. 1) To establish the system transfer function matrix considering the FCC, and determine the system stability accurately by the dominant oscillation mode; 2) To define the node oscillation participation factor, considering the effect of the coupling frequency, and quantify the participation degree of each node and identify the origin and weak point of oscillation; 3) To carry out multi-level oscillation mode sensitivity analysis. Finally, the oscillation characteristics and laws of the DFIG-based wind power base with LCC-HVDC transmission are studied, and the time-domain simulations in MATLAB/Simulink validate the analytical results.

Long-distance mid-wave infrared super-resolution compressive imaging

Super-resolution imaging (SRI) for mid-wave infrared (MWIR) has attracted increasing attention in recent years due to the expensive price for a large number of pixels MWIR cameras. Investigation of the compressed sensing method can partially improves the resolution. However, the quality of SRI is highly related to the transfer function matrix of the optical system, which is difficult to be accurately measured because of the noise existed in MWIR detection, especially in long-distance systems. In this work, we propose a transfer function matrix calculation method which overcomes the issues of low imaging contrast and signal-to-noise ratio compared with previous studies. And we further establish a long-distance focal plane array-based compressive imaging system with a resolution of two digital micro-mirror device pixels which just satisfies the system diffraction limit. In addition, we achieve the 4 × 4 times super-resolution high-quality reconstruction of long-distance digital and physical objects with only six measurements.

MIMO system identification using common denominator and numerators with known degrees

SummaryIn system identification, prior knowledge about the model structure may be available. However, imposing this structure on the identified model may be nontrivial. A new discrete‐time linear time‐invariant identification method is presented in the article that imposes prior knowledge of the degree of the common denominator of the system's transfer function matrix and the degrees of the numerators. First, a method is outlined for the solution in case of exact data. Then, this method is extended for noisy data in the output error setting. An initial estimate obtained by a subspace method is improved by a structured low‐rank approximation method. The performance of the method imposing the structure is compared on simulated data with the performance of classical identification methods that do not impose the structure.

Research and Improvement on Active Compliance Control of Hydraulic Quadruped Robot

This paper focuses on active compliance control of hydraulic quadruped robot, especially the analysis of the inner-loop of the coupled system. Current researches on active compliance control regard the bandwidth of the inner loop of the system as infinite, while ignoring that the extra-load will cause the inner-loop response characteristics to deteriorate when the leg is in the stance phase. In this work, we first briefly introduced the structure of the robot, and its kinematics and dynamics are analyzed. Next, the robot’s active compliance control framework is established, and the inner-loop two-cylinder coupling system is analyzed in depth. It can be concluded that the existence of low frequency poles in the system is the main reason for the poor response characteristics. Then through the analysis of the state equation and transfer function matrix of the multi-input multi-output system, we show that the equivalent hydraulic spring stiffness (EHSS) is the main factor affecting the zero-pole distribution. Furthermore, we optimize the structure to increase the EHSS to improve the response characteristics of the system. Finally, the co-simulation platform and single-leg experiment bench are introduced. The simulation and experimental results show that the response speed of the inner-loop control is significantly improved after optimization, and the robot with active compliance control strategies can significantly reduce the impact of the foot.

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.

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.

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.

Optimum Design of Power Converter Current Controllers in Large-Scale Power Electronics Based Power Systems

In a large-scale power electronic system such as a wind farm, the mutual interactions between the power converter controllers and passive components may lead to instability problems or undesired dynamic response. This paper presents an optimum parameter design procedure for the power converter controllers in a power electronic system in order to guarantee a stable operation and to guarantee an acceptable dynamic response. In the approach, first, all oscillatory modes are calculated by a multi-input multi-output (MIMO) transfer function matrix of the power system; then, a multi-objective optimization procedure based on the genetic algorithm (GA) is presented to place the modes in the desired locations in order to increase the stability margin and to improve the dynamic response. Time-domain simulations of a 400-MW wind farm in the PSCAD/EMTDC environment confirms the effectiveness of the presented design approach.

An improved identification and control of 3 × 3 multi-input multi-output system using relay and subspace method

ABSTRACTIn this work, a simple closed-loop identification method for Multi-Input Multi-Output (MIMO) system has been proposed. Subspace closed-loop identification method is employed for identification of MIMO system, while relay is used as a replacement to pre-design PID controllers. The transfer function matrix of the dynamic system is identified in the form of state-space model using N4SID algorithm from system identification toolbox of MATLAB. The proposed method neither requires pre-designed controller nor involves extensive calculation. Due to the use of ideal relay as a replacement, the proposed method fails to identify systems containing unstable transfer functions while retaining the other advantages of subspace identification method. The identified model is further controlled by the designed tuning of controller parameters. Firstly, decoupler is designed to eliminate the interaction in MIMO system. The estimated transfer function, derived by Relative Normalised Gain Array – Relative Gain Array (RNGA-RGA) method, is further used to calculate ideal, stable, causal and proper decoupler. Introduction of decoupler into the system decomposes 3 × 3 MIMO system into ‘3’ SISO systems which are further controlled by basic controller tuning methods such as Zeigler–Nichol’s PID tuning method and Skogested’s IMC tuning method.

Positive-real systems under lossless transformations: Invariants and reduced order models

In this paper, positive-real systems under lossless positive-real transformations are investigated. Let G(s) be the transfer function matrix of a continuous-time positive-real system of order n and F(s) a lossless transfer function of order nF. We prove here that the lossless positive-real transformed system, i.e. G(F(s)), is also positive-real. Furthermore, the stochastic balanced representation of positive-real systems under lossless positive-real transformations is considered. In particular, it is proved that the positive-real characteristic values πj of G(F(s)) are the same of G(s) each with multiplicity nF, independently from the choice of F(s). This property is exploited in the design of reduced order models based on stochastic balancing. Finally, the proposed technique is a passivity preserving model order reduction method, since it is proven that the reduced order model of G(F(s)) is still positive-real. An error bound for truncation related to the invariants πj is also derived.

Дискретне керування лінійними багатовимірними системами з виродженою або погано обумовленою матрицями передавальних функцій

Розглянуто керування багатовимірними лінійними дискретними стаціонарними системами, матриці передавальних функцій яких або вироджені, або погано обумовлені. Показано, що є довільні невимірювальні, але обмежені збурення, а параметри цих систем можуть бути частково невідомими. Оптимальний регулятор побудовано з використанням псевдоінверсії матриці передавальних функцій системи. Доведено обмеженість усіх сигналів, породжуваних цим регулятором, а також властивості робастності регулятора за наявності параметричної невизначеності. Для підтвердження теоретичних досліджень наведено числові приклади.

Spectral Conditions for Negative Imaginary Systems With Applications to Nanopositioning

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.

Singular formalism and admissible control of spacecraft with rotating flexible solar array

This paper is concerned with the attitude control of a three-axis-stabilized spacecraft which consists of a central rigid body and a flexible sun-tracking solar array driven by a solar array drive assembly. Based on the linearization of the dynamics of the spacecraft and the modal identities about the flexible and rigid coupling matrices, the spacecraft attitude dynamics is reduced to a formally singular system with periodically varying parameters, which is quite different from a spacecraft with fixed appendages. In the framework of the singular control theory, the regularity and impulse-freeness of the singular system is analyzed and then admissible attitude controllers are designed by Lyapunov’s method. To improve the robustness against system uncertainties, an H∞ optimal control is designed by optimizing the H∞ norm of the system transfer function matrix. Comparative numerical experiments are performed to verify the theoretical results.

Synchronization of chaotic systems with variable coefficients

In this paper, a novel method, to synchronize two identical or different chaotic/hyperchaotic systems with variable coefficients, is proposed based on the strictly positive real transfer function matrix. By adding a synchronization controller to the response system, the nonlinear parts of the error system derived from the synchronized systems are identified as the inputs of the error system, and the error state variables are identified as the outputs of the error system. Then the transfer function matrix of the error system can be strictly positive real. As a result, the error system can be asymptotically stable at the origin, i.e., the two chaotic/hyperchaotic systems can reach stable synchronization. Moreover, the designed synchronization controllers are linear, clear in parameter selections and robust to the changes of the coefficients of the error system. The specific design processes of the synchronization controllers and the corresponding results are presented in the paper. Also, the numerical simulation results are given to verify the feasibility and effectiveness of this method.

System Identification Based on Recursive Least Square Method for the Magnetic Suspension Active Vibration Isolation System

In this paper, we use recursive least squares method for magnetic single layer vibration isolation system identification to get the system transfer function matrix. By considering the fitting degree, pole-zero, the step response to adjust the order of model and noise structure for optimizing the model Identification. Applying the system transfer function matrix to the magnetic active vibration control system to improve the isolation effect. The results showed that: significantly improved isolation effect, verify the validity of this identification model for magnetic single isolation system.

Direct Voltage Control for a Stand-Alone Wind-Driven Self-Excited Induction Generator With Improved Power Quality

An improved direct voltage control (DVC) strategy is proposed for the control of terminal voltage and frequency of a stand-alone wind-driven self-excited induction generator with variable loads. The DVC strategy, including a proportional-integral (PI) regulator, lead-lag corrector, and a feed-forward compensator, is designed based on the system transfer function matrix. The PI regulator can eliminate the steady-state tracking errors of the terminal voltage. The lead-lag corrector is employed to enlarge the phase stability margin of the dominant loops while the feed-forward compensator is adopted to mitigate the voltage harmonics resulting from the cross-coupling dynamics. The procedures for capacity design of the excitation capacitors, the voltage source inverter, and the consumer load are also presented. The simulation and experimental results verify that the proposed strategy has a fast dynamic response and can effectively control the generated voltage with low harmonic distortions under different linear or nonlinear loads.

LPV decoupling for control of multivariable systems

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 PI controller gains. Numerical examples are presented to illustrate the validity of the proposed LPV decoupling methods, as well as the use of the proposed interaction measures for a decoupled multi-loop PI control design.

A Negative Imaginary Lemma and the Stability of Interconnections of Linear Negative Imaginary Systems

The note is concerned with linear negative imaginary systems. First, a previously established Negative Imaginary Lemma is shown to remain true even if the system transfer function matrix has poles on the imaginary axis. This result is achieved by suitably extending the definition of negative imaginary transfer function matrices. Secondly, a necessary and sufficient condition is established for the internal stability of the positive feedback interconnections of negative imaginary systems. Meanwhile, some properties of linear negative imaginary systems are developed. Finally, an undamped flexible structure example is presented to illustrate the theory.

An Alternate Method for Computation of Transfer Function Matrix

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