Reduced Order Transfer Function Research Articles

Resilient Frequency-shifted IMC-PID Scheme for Mitigating Scaling and Random Attacks in Thermal Plants Amid Delay

In recent times, several network-related scenarios like Communication Delays (CDs) and malicious Cyber Attacks (CAs) have posed a major challenge in keeping the operational frequency of automatic generation systems within admissible levels. Hence, the proposed work focuses on investigating the applicability of an Frequency-Shifted Internal Model Control-Proportional Integral Derivative (FIMC-PID) controller for Load Frequency Control (LFC) of a non-identical dual-area Power System (PS) in the presence of inherent CDs and CAs. The FIMC approach is based on the integration of concepts like model order reduction and pole-zero shifting of the reduced order transfer function by the constant (ψ) which indicates the amount by which system robustness can be manipulated. In addition to that, an analytical approach for obtaining a stable numerical range of the tunable parameter ψ is introduced using Routh-Hurwitz criteria. This range serves as the input for the Golden Jackal Optimizer (GJO) for finding the optimal value of ψ by minimizing the Integrated Time-Squared Error (ITSE). False Data Injection (FDI) threats to the cyber-physical systems like scaling and random attacks have been modeled and the efficacy of GJO-tuned FIMC strategy in mitigating the same is vindicated. Finally, hardware-in-loop real-time verification of the suggested strategy in mitigating frequency fluctuations is carried out in the OPAL-RT platform.

Educational aid for dynamic study of DC converter with Leverrier's and Pole clustering technique using simulation software

Abstract : In this paper, the dynamic analysis of the dc-dc converter is proposed with an educational aid to ease the process in which the study is carried out. This study's primary importance is that it can be added to the curriculum of Master's program in Electrical Engineering. This article mainly focuses on the mathematical modelling of the dc-dc converter with which the dynamic analysis is carried out to regulate the load and line condition. The main problems in the analysis of higher-order dc-dc converter is addressed with techniques available in the literature. A quadratic boost converter with DCL cell is chosen for studying the dynamic analysis with the flow of the technique proposed. The solution to the resolvent matrix of the converter is obtained using Leverrier's algorithm. The higher-order system's transfer function is reduced using the pole clustering technique to ease the controller design. Finally, the PI controller is tuned with Ziegler-Nichols tuning and it is incorporated with the converter using the reduced-order transfer function. The input to output transfer function is analyzed with the step response in MATLAB software and compared with the full order transfer function to validate the reduced-order transfer function. The closed-loop response is also validated both with full order and reduced-order system. Keywords : Bloom's taxonomy, Leverrier's algorithm, Pole clustering, DC-DC converter, dynamic, reduced-order, controller

Reduced-Order Transfer Function Model of the Droop-Controlled Inverter via Jordan Continued-Fraction Expansion

This article proposes a reduced-order small-signal closed-loop transfer function model based on Jordan continued-fraction expansion to assess the dynamic characteristics of the droop-controlled inverter and provide the preprocessing method for the real-time simulation of power systems. Firstly, dynamic phasors, time delay and zero-order hold are embedded into the small-signal model at the same time, then the closed-loop transfer function of the droop-controlled inverter is built. Compared with the existing closed-loop transfer function approaches, the accuracy of the built transfer function model is dramatically enhanced. Meanwhile, the inner cascaded voltage/current controller parameters are also designed. In order to directly obtain and preserve the maximum overshoot and settling time, which are main features to evaluate the system input-output dynamic response characteristics, the reduced second order closed-loop transfer function is proposed through the continued-fraction expansion regarding arbitrary points on the real frequency axis. Therein, this second order closed-loop transfer function with dynamic response of the original inverter is reduced to the lowest order. Furthermore, combined with the impedance-based approach, the proposed stability assessment approach is utilized to analyze the stability of the microgrid with multiple converters. Finally, simulations and experimental results demonstrate the convenience and accuracy of the proposed approach.

A transfer function type of simplified electrochemical model with modified boundary conditions and Padé approximation for Li-ion battery: Part 1. lithium concentration estimation

Abstract To guarantee the safety, high efficiency and long lifetime for lithium-ion battery, an advanced battery management system requires a physics-meaningful yet computationally efficient battery model. The pseudo-two dimensional (P2D) electrochemical model can provide physical information about the lithium concentration and potential distributions across the cell dimension. However, the extensive computation burden caused by the temporal and spatial discretization limits its real-time application. In this research, we propose a new simplified electrochemical model (SEM) by modifying the boundary conditions for electrolyte diffusion equations, which significantly facilitates the analytical solving process. Then to obtain a reduced order transfer function, the Pade approximation method is adopted to simplify the derived transcendental impedance solution. The proposed model with the reduced order transfer function can be briefly computable and preserve physical meanings through the presence of parameters such as the solid/electrolyte diffusion coefficients (Ds&De) and particle radius. The simulation illustrates that the proposed simplified model maintains high accuracy for electrolyte phase concentration (Ce) predictions, saying 0.8% and 0.24% modeling error respectively, when compared to the rigorous model under 1C-rate pulse charge/discharge and urban dynamometer driving schedule (UDDS) profiles. Meanwhile, this simplified model yields significantly reduced computational burden, which benefits its real-time application.

Experimental Identification and Vibration Control of A Piezoelectric Flexible Manipulator Using Optimal Multi-Poles Placement Control

This paper presents experimental identification and vibration suppression of a flexible manipulator with piezoelectric actuators and strain sensors using optimal multi-poles placement control. To precisely identify the system model, a reduced order transfer function with relocated zeros is proposed, and a first-order inertia element is added to the model. Comparisons show the identified model match closely with the experimental results both in the time and frequency domains, and a fit of 97.2% is achieved. Based on the identified model, a full-state multi-poles placement controller is designed, and the optimal locations of the closed loop poles are determined where the move distance of the closed loop poles is the shortest. The feasibility of the proposed controller is validated by simulations. Moreover, the controller is tested for different locations of the closed loop poles, and an excellent performance of the optimal locations of the closed loop poles is shown. Finally, the effectiveness of the proposed controller is demonstrated by experiments. Results show that the vibrations of the expected modes are significantly diminished. Accordingly, multi-mode vibrations of the manipulator are well attenuated.

An improved reduced-order model of an electric pitch drive system for wind turbine control system design and simulation

To obtain satisfactory dynamic characteristics and enhance numerical simulation efficiency, an improved reduced-order transfer-function model of an electric pitch drive system (EPDS) for a wind turbine is proposed. First, a detailed transfer-function model of an EPDS is developed on the basis of its mathematical model. Thereafter, the improved reduced-order transfer-function model for an EPDS is derived from the detailed model by transfer-function approximation, sensitivity analysis, and block diagram reduction. The frequency-domain characteristics of the proposed model and their effects on the stability of the pitch angle control system are also analyzed and compared with that of a first-order transfer-function model. Finally, the dynamic characteristics of an EDPS using the improved model are analyzed and verified by a practical EPDS test platform. Furthermore, based on the FAST–MATLAB/Simulink co-simulation tool, simulation comparisons are performed on the loading characteristics of a wind turbine to further validate its availability in it. Results show that the improved model is superior to the first-order model for the performance analysis of a wind turbine pitch angle controller, and it also can meet the requirements of large-scale loading simulations for wind turbines both in terms of the precision and the time efficiency.

IJARCCE - Computer and Communication Engineering

In a high speed digital integrated circuit, annex delay can be momentous and hold for factual exploration by using moments of impulse response delay exploration has been done. Elmore delay is (the first moment of impulse response) interpretation, to moment matching approach which establish reduced order trans-impedance and transfer function approximations. The elmore delay is swift becoming inadequate for deep submicron technologies and reduced order transfer function delays are un-functional for use as early phase design matrices. This paper interpret access for fitting moments of the impulse response to probability density function, so that delay can be appraisal factually for RLC trees, it is a demonstrated that inverse gamma function provides a provable stable approximation. For prolong delay matrices for ramp inputs to the more general and realistic non-step input, we use PERI (probability distribution function extension for ramp input) technology. The factual model consequence compared with MATLAB simulation.

Linearized Large Signal Modeling, Analysis, and Control Design of Phase-Controlled Series-Parallel Resonant Converters Using State Feedback

This paper proposes a linearized large signal state-space model for the fixed-frequency phase-controlled series-parallel resonant converter. The proposed model utilizes state feedback of the output filter inductor current to perform linearization. The model combines multiple-frequency and average state-space modeling techniques to generate an aggregate model with dc state variables that are relatively easier to control and slower than the fast resonant tank dynamics. The main objective of the linearized model is to provide a linear representation of the converter behavior under large signal variation which is suitable for faster simulation and large signal estimation/calculation of the converter state variables. The model also provides insight into converter dynamics as well as a simplified reduced order transfer function for PI closed-loop design. Experimental and simulation results from a detailed switched converter model are compared with the proposed state-space model output to verify its accuracy and robustness.

Model Reduction of Descriptor Systems by Interpolatory Projection Methods

In this paper, we investigate interpolatory projection framework for model reduction of descriptor systems. With a simple numerical example, we first illustrate that employing subspace conditions from the standard state space settings to descriptor systems generically leads to unbounded H2 or H-infinity errors due to the mismatch of the polynomial parts of the full and reduced-order transfer functions. We then develop modified interpolatory subspace conditions based on the deflating subspaces that guarantee a bounded error. For the special cases of index-1 and index-2 descriptor systems, we also show how to avoid computing these deflating subspaces explicitly while still enforcing interpolation. The question of how to choose interpolation points optimally naturally arises as in the standard state space setting. We answer this question in the framework of the H2-norm by extending the Iterative Rational Krylov Algorithm (IRKA) to descriptor systems. Several numerical examples are used to illustrate the theoretical discussion.

Delay Estimation for Global RC Interconnect UsingInverse Gamma Distribution Function

In this paper, we present an efficient model for on- chip interconnects delay analysis. Several approaches have already been proposed for approximating the interconnect delay accurately and efficiently. Moments of the impulse response are widely used for interconnect delay analysis, from the explicit Elmore delay (the first moment of the impulse response) expression to the moment matching methods which create reduced order trans-impedance and transfer function approximations. However, the Elmore delay is fast becoming ineffective for deep submicron technologies and reduced order transfer function delays are impractical for use as early-phase design metrics or as design optimization cost functions. This paper describes an accurate approach for fitting moments of the impulse response to probability density functions so that delay can be estimated accurately at an early physical design stage. For RC trees, it is demonstrated that inverse gamma functions provide a probably stable approximation. The accuracy of the proposed model is justified with the results obtained from that of SPICE simulations.

Delay Analysis on-chip VLSI Interconnect using Gamma Distribution Function

Moments of the impulse response are widely used for interconnect delay analysis, from the explicit Elmore delay (the first moment of the impulse response) expression, to moment matching methods which creates reduced order trans-impedance and transfer function approximations. However, the Elmore delay is fast becoming ineffective for deep submicron technologies, and reduced order transfer function delays are impractical for use as early-phase design metrics or as design optimization cost functions. This paper describes an approach for fitting moments of the impulse response to probability density functions so that delay can be estimated accurately at an early physical design stage. For RC trees it is demonstrated that the incomplete gamma function provides a provably stable approximation. The accuracy of our model is justified with the results compared with that of SPICE simulations.

Simple Modeling and Identification Procedures for “Black-Box” Behavioral Modeling of Power Converters Based on Transient Response Analysis

Today, black-box behavioral models of power converters are becoming interesting for system level simulation of power electronics systems. These models can be used to evaluate the response of systems that are composed of commercial converters, since they can be fully parameterized by analyzing the actual converter response. To optimize the required computational resources, these models should be as simple as possible. Furthermore, the identification of the parameters should be carried out easily, looking for simple experiments and straightforward adjusting algorithms. Easy modeling and identification procedures, based on a transient response analysis, are proposed in this paper. Using this method, a large-signal black-box behavioral model of a power converter is composed of reduced-order transfer functions, which are identified by analyzing the step response of the converter. Both an actual commercial dc-dc converter and a line-commutated rectifier have been modeled and identified by means of this approach, in order to validate the proposed procedures.

Analysis of on-chip distributed interconnects based on Pade expansion

In this paper, on-chip interconnects are modeled as distributed parameter RLCG transmission lines, based on which the matrix ABCD of interconnects is deduced. With help of the ABCD matrix, a voltage transfer function of an interconnect system, consisting of a driver, interconnect line and load, is obtained analytically in the form of a transcendental function, and it is reduced to a finite order system based on high order Pade approximation. With the reduced-order transfer function, response waveforms with step input can be obtained, and signal delay can be calculated consequently. Two numerical experiments are conducted to demonstrate its efficiency.

MIMO System Reduction Using Modified Pole Clustering and Genetic Algorithm

A new mixed method for reducing the order of the large-scale linear dynamic multi-input-multi-output (MIMO) systems has been presented. In this method, the common denominator polynomial of the reduced-order transfer function matrix is synthesized by using modified pole clustering while the coefficients of the numerator elements are computed by minimizing the integral square error between the time responses of the original and reduced system element using Genetic Algorithm. The modified pole clustering generates more dominant cluster centres than cluster centres obtained by pole clustering technique already available in literature. The proposed algorithm is computer-oriented and comparable in quality. This method guarantees stability of the reduced model if the original high-order system is stable. The algorithm of the proposed method is illustrated with the help of an example and the results are compared with the other well-known reduction techniques.

Reduced order modelling of linear MIMO systems using genetic algorithm

In this paper, an algorithm for order reduction of linear multivariable systems is proposed using the combined advantages of the dominant pole retention method and the error minimization by Genetic algorithm. The denominator of the reduced order transfer function matrix is obtained by retaining the dominant poles of the original system while the numerator terms of the lower order transfer matrix are determined by minimizing the integral square error in between the transient responses of original and reduced order models using Genetic algorithm. Each element of the transfer function matrix of the original system is considered separately. The reduction procedure is simple and computer oriented. The proposed algorithm guarantees stability of the reduced order transfer function matrix if the original high order system is stable and is having superior features, including easy implementation and good computational efficiency. The proposed algorithm has been applied successfully to the transfer function matrix of a 10 th order two-input two-output linear time invariant model of a practical power system. The performance of the algorithm is tested by comparing the relevant computer simulation results.

Reduced order modelling of linear multivariable systems using particle swarm optimisation technique

In this paper, an algorithm for order reduction of linear multivariable systems is proposed using the combined advantages of the dominant pole retention method and the error minimisation by Particle Swarm Optimisation (PSO) technique. The denominator of the reduced order transfer function matrix is obtained by retaining the dominant poles of the original system while the numerator terms of the lower order transfer matrix are determined by minimising the Integral Square Error (ISE) in between the transient responses of original and reduced order models using PSO technique. The proposed algorithm guarantees stability of the reduced order transfer function matrix if the original High Order System (HOS) is stable and is having superior features, including easy implementation, stable convergence characteristic and good computational efficiency. The proposed algorithm has been applied successfully to the transfer function matrix of a 10th order two-input two-output linear time invariant model of a practical power system. The performance of the algorithm is tested by comparing the relevant computer simulation results.

Shift-and-scale model reduction: An alternative stability-preserving approach

A new stability-preserving model order-reduction method is presented for continuous-time systems. It makes use of the relatively new idea of transformed whole-system parameter matching for calculating the poles of the reduced-order transfer function. This has the advantage of using more of the system information than traditional methods in the approximation of the poles. The method is seen to be flexible and computationally attractive, relying only on readily available algorithms. It is based on a shift-and-scale transformation of the transfer function before applying the order-reduction process. Further, it is shown to be a viable alternative to existing stability-preserving techniques. Some examples illustrate the method.

Model Reduction of MIMO Systems via Tangential Interpolation

In this paper, we address the problem of constructing a reduced order system of minimal McMillan degree that satisfiesa set of tangential interpolation conditions with respect to the original system under some mild conditions. The resulting reduced order transfer function appears to be generically unique and we present a simple and efficient technique to construct this interpolating reduced order system. This is a generalization of the multipoint Padé technique which is particularly suited to handle multiinput multioutput systems.

DTT: direct truncation of the transfer function - an alternative to moment matching for tree structured interconnect

A method is introduced to evaluate time domain signals within RLC trees with arbitrary accuracy in response to any input signal. This method depends on finding a low frequency reduced-order transfer function by direct truncation of the exact transfer function at different nodes of an RLC tree. The method is numerically accurate for any order of approximation, which permits approximations to be determined with a large number of poles appropriate for approximating RLC trees with underdamped responses. The method is computationally efficient with a complexity linearly proportional to the number of branches in an RLC tree. A common set of poles is determined that characterizes the responses at all of the nodes of an RLC tree which further enhances the computational efficiency. Stability is guaranteed by the DTT method for low-order approximations with less than five poles. Such low-order approximations are useful for evaluating monotone responses exhibited by RC circuits.

Weld penetration control system design and testing

The design, implementation, and testing of a feedback control system for regulating gas tungsten arc weld (GTAW) penetration are presented in this study. The derivation of reduced-order transfer function models representing the welding heat flow is also discussed. The control problem was cast in a robust design setting, and an H∞ controller was designed for regulating weld penetration. The H∞ control theory could quantify the trade-off between performance and robustness and achieve both good performance and robustness. The feedback control system, which used infrared temperature measurements, was implemented and tested. The dynamic and steady-state responses of the system to step input changes as well as unmodeled base metal width variations were studied by simulation and experimentally. The experimental results were similar to the simulation predictions. The controller was able to provide regulation to achieve full penetration for GTAW and was also robust to control weld penetration during perturbations in base metal width.