Multi-input Multi-output Transfer Function Research Articles

A Quasi-Oppositional Method for Output Tracking Control by Swarm-Based MPID Controller on AC/HVDC Interconnected Systems With Virtual Inertia Emulation

This paper presents a comprehensive evaluation of the effect of quasi oppositional - based learning method utilization in output tracking control through a swarm-based multivariable Proportional-Integral-Derivative (SMPID) controller, which is tuned by a novel performance index based on the step response characteristics in multi-input multi-output (MIMO) system. The role of the proposed quasi oppositional based SMPID controller is to modify the tracking strategy on AC/HVDC interconnected systems while reducing the related cost function. The proposed analysis is established considering the most highly cited, well-known tested and newly expanded swarm-based optimization algorithms (SBOAs), such as Grasshopper Optimization Algorithm (GOA), Grey Wolf Optimization (GWO), Artificial Fish Swarm Algorithm (AFSA), Artificial Bee Colony (ABC) and Particle Swarm Optimization (PSO). These methods are used in the tuning process of multivariable PID (MPID) controller for output tracking control of an interconnected AC/DC system with virtual inertia emulation-based HVDC capabilities. The virtual inertia-based HVDC model, which is using a derivative technique, is attached for enhancing the system frequency dynamics with fast power injection during the contingency. The potential possibility for achieving a suitable assessment about the velocity reaction, the flexibility response, and the accuracy of the tracking process is provided by four different scenarios which are operated by step load changes as essential inputs in AC/HVDC interconnected MIMO system. Also the proposed fitness function, as deviation characteristics of the step response in MIMO transfer function in virtual inertia emulation based HVDC model, is compared with integral time absolute error (ITAE), as the standard performance index in the optimization process. The results are compared with the conventional tuned MPID (C - MPID) controller using MATLAB software. The obtained analysis emphasizes how the tuned SMPID can significantly increase the capability of tracking control on the proposed AC/HVDC interconnected model.

Thermoacoustics and combustion instability analysis for multi-burner combustors

This paper presents a low-order thermoacoustic model for multi-burner combustors and proposes a control theoretic approach to linear combustion instability analysis in frequency domain, taking acoustic and flame interaction effects among burners into account under a non-zero mean flow condition. Our thermoacoustic model can deal with can-annular and annular combustors in a unified way and is given as a multi-input multi-output transfer function matrix from heat fluctuation input vector to velocity fluctuation output vector. We also propose a flame transfer function matrix description where off-diagonal components describe the effects of a local acoustic field of one burner location on the flame response at another burner location. The discrete rotational symmetry of burner arrangement in a combustor makes it possible to diagonalize both the aforementioned thermoacoustic and flame transfer function matrices analytically from a spatial discrete-time Fourier transformation. The decoupled thermoacoustic transfer function matrix provides a characterization of acoustic resonances, particularly the longitudinal-azimuthal coupled modes unique to multi-burner combustors. In addition, from the Bloch wave interpretation, we find general patterns in the mode shape of a multi-burner combustor and its relations to the mode shape of a single-burner combustor. Furthermore, from a diagonalized closed loop transfer function matrix, a simple combustion instability condition for a multi-burner combustor is developed. This stability condition shows how a single-burner combustor and a multi-burner combustor are different quantitatively, when it comes to combustion instability. Numerical examples are presented to validate our thermoacoustic model against three-dimensional FEM results, and to illustrate our developments and findings.

Subsynchronous Oscillation Analysis of Grid-Connected Converter Based on MIMO Transfer Functions

Subsynchronous oscillations (SSOs) induced by the interaction between wind farms based on direct-drive permanent magnet synchronous generators (D-PMSGs) and weak grids have attracted extensive attention. To better understand this SSO phenomenon, this paper derives multi-input multi-output (MIMO) transfer functions between the references of the current controller and the current of a grid-connected converter in the d-q frame, where the dynamic of PLL is considered. The dynamic of PLL lead to positive feedback in the MIMO transfer function, which impairs the stability of the overall system and induces the SSO phenomenon. Using the classical root locus method, the influence of correlated control parameters and different operation conditions on the system stability is substantially analysed. It is found that heavy load, low short circuit ratio (SCR) will intensify the SSO instability of system. Nonlinear electromagnetic transient simulations of a D-PMSG-based weak-grid-connected wind-farm system using PSCAD/EMTDC software effectively verify the correctness of the model proposed in the SSO analysis.

Bus Participation Factor Analysis for Harmonic Instability in Power Electronics Based Power Systems

Compared with the conventional power systems, large-scale power electronics based power systems present a more complex situation, where harmonic instability may be induced by the mutual interactions between the inner control loops of the converters. This paper presents an approach to locate which power converters and buses are more sensitive and have a significant contribution to the harmonic instability. In the approach, a power electronics based system is introduced as a multi-input multi-output (MIMO) dynamic system by means of a dynamic admittance matrix. Bus participation factors (PFs) are calculated by the oscillatory mode sensitivity analysis versus the elements of the MIMO transfer function matrix. The PF analysis detects which power electronic converters or buses have a higher participation in harmonic instability excitation than others or at which buses such instability problems have a higher impact. In order to confirm the effectiveness of the presented approach, time-domain simulation results are provided for a 400-MW wind farm in PSCAD software environment.

Internal Model-Based Active Resonance Damping Current Control of a Grid-Connected Voltage-Sourced Converter With an LCL Filter

Three-phase passive harmonic filters (e.g., LCL filters) are often utilized to attenuate harmonic currents caused by pulsewidth modulation of voltage-sourced converters (VSC) to achieve high power quality. However, LCL filters may jeopardize the system stability due to their inherent susceptibility to resonance. This paper proposes an active damping current controller based on the internal model principle for a grid-connected VSC equipped with an LCL filter. This controller can be considered a high-order multi-input multi-output transfer function, implemented in the $dq$ reference frame, including decoupling terms for improved transient behavior. Simulation case studies are performed in the PSCAD/EMTDC environment to evaluate the transient behavior of the controller and test its robustness against parameter variations and unbalanced and distorted grid conditions. Experimental results verify the performance of the proposed controller and confirm its ability to operate at low switching frequencies. The results are compared with two existing active damping strategies (virtual RC and notch filter methods), confirming that the proposed controller shows significantly improved robustness with no degradation of transient behavior, has the ability to operate at low switching frequencies, and does not need additional sensors.

Formula omitted]-optimal model approximation by input/output-delay structured reduced order models

In this paper, the H2-optimal approximation of a multi-input multi-output transfer function by a finite dimensional system including input/output delays, is addressed. This problem is of particular interest when the full order model represents a transport phenomenon. The contribution is twofold : firstly, based on the pole/residue decomposition, an H2-inner product formula in the presence of input/output delays is derived. Secondly, the underlying H2 optimality conditions of the approximation problem are obtained as an extension of the tangential interpolatory conditions. It is also demonstrated that for fixed delay values, this problem can be recast as a rational function approximation one. An iterative algorithm is sketched out and numerical results assess the theoretical contributions.

Model-based framework for multi-axial real-time hybrid simulation testing

Real-time hybrid simulation is an efficient and cost-effective dynamic testing technique for performance evaluation of structural systems subjected to earthquake loading with rate-dependent behavior. A loading assembly with multiple actuators is required to impose realistic boundary conditions on physical specimens. However, such a testing system is expected to exhibit significant dynamic coupling of the actuators and suffer from time lags that are associated with the dynamics of the servo-hydraulic system, as well as control-structure interaction (CSI). One approach to reducing experimental errors considers a multi-input, multi-output (MIMO) controller design, yielding accurate reference tracking and noise rejection. In this paper, a framework for multi-axial real-time hybrid simulation (maRTHS) testing is presented. The methodology employs a real-time feedback-feedforward controller for multiple actuators commanded in Cartesian coordinates. Kinematic transformations between actuator space and Cartesian space are derived for all six-degrees-offreedom of the moving platform. Then, a frequency domain identification technique is used to develop an accurate MIMO transfer function of the system. Further, a Cartesian-domain model-based feedforward-feedback controller is implemented for time lag compensation and to increase the robustness of the reference tracking for given model uncertainty. The framework is implemented using the 1/5th-scale Load and Boundary Condition Box (LBCB) located at the University of Illinois at Urbana- Champaign. To demonstrate the efficacy of the proposed methodology, a single-story frame subjected to earthquake loading is tested. One of the columns in the frame is represented physically in the laboratory as a cantilevered steel column. For realtime execution, the numerical substructure, kinematic transformations, and controllers are implemented on a digital signal processor. Results show excellent performance of the maRTHS framework when six-degrees-of-freedom are controlled at the interface between substructures.

Inversion-based robust feedforward–feedback two-degree-of-freedom control approach for multi-input multi-output systems with uncertainty

In this study, an inversion-based robust feedforward–feedback two-degree-of-freedom (2DOF) control approach is proposed to improve the tracking performance and robustness for multi-input multi-output (MIMO) systems with uncertainty. The proposed approach enhances trajectory tracking precision by robust-inversion feedforward control and combats the adverse effects caused by system uncertainty, coupling and disturbance by H∞ mixed sensitivity robust MIMO feedback control. The main contributions of this paper are as follows: (i) a combination of robust diagonal dominance-based static pre-compensation and inversion-based robust feedforword–feedback 2DOF control, (ii) extending the single-input single-output (SISO) robust-inversion-based feedforward control to MIMO system by introducing the optimal coefficients which not only consider the uncertainties of diagonal transfer functions, but also take the non-diagonal elements in MIMO transfer function matrix into account, (iii) a systematic integration of H∞ mixed sensitivity robust feedback control and inversion feedforward control. A numerical example and simulation results illustrate a better performance obtained by the proposed control approach compared with H∞ mixed sensitivity robust feedback control and 2DOF control approach combined with the regular SISO robust-inversion-based feedforward control and robust feedback control.

Version 8 of the Matlab System Identification Toolbox

Version 8.0 of MATLAB's System Identification toolbox is released with version R2012a of MATLAB in the spring of 2012. This release presents a re-engineered implementation of the code using the new MATLAB object-oriented programming. Two main features are (1) that the toolbox commands and plots are seamlessly integrated with the other MATLAB toolboxes that deal with linear dynamic systems and (2) several new features and model objects. The toolbox now supports multi-input–multi-output (MIMO) systems across all model objects, and more emphasis is placed on continuous-time models. Also a new model object, idtf covers MIMO transfer function models in both continuous and discrete time.

On the Ultimate Limits of Chaos-Based Asynchronous DS-CDMA—I: Basic Definitions and Results

The ultimate limits of chaos-based asynchronous direct-sequence code-division multiple access systems are investigated using the concept of capacity taken from information theory. To this aim, we model the spreading at the transmitter and the sampling of the incoming signal at the receiver with a unique linear multi-input multi-output transfer function. We then assume the existence of a coding/decoding pair that is able to transmit information through this channel with a vanishing error probability. The capacity of the system is then identified with the maximum rate at which such an errorless link may operate. The capacity is a random quantity depending on the spreading sequences and, due to the asynchronism, on the users relative delays and phases. We then compare different spreading strategies [classical m and Gold codes, independent identically distributed (i.i.d.) and chaos-based codes] in terms of expected performance as well as of the probability that one method outperforms another. To ease further analytical investigations that should cope with expectations of logarithms, we measure capacity not only in bits per use but also in codewords per use. Some formal results along with extensive numerical evidence show that this does not alter the performance ranking. Such a ranking shows that chaos-based spreading always outperforms i.i.d. spreading and those trying to mimic it. This aligns with and complements what was already known about the ability of chaos-based techniques of minimizing multiple access interference.

On the Ultimate Limits of Chaos-Based Asynchronous DS-CDMA—II: Analytical Results and Asymptotics

The ultimate limits of chaos-based asynchronous direct-sequence code-division multiple access systems are investigated using the concept of capacity taken from information theory. To this aim, we model the spreading at the transmitter and the sampling of the incoming signal at the receiver with a unique linear multi-input multi-output transfer function depending on spreading sequences and on the users relative delays and phases. The capacity can be computed using a known formula and is a random quantity depending on the process generating the spreading codes and on the delays and phases that are random in asynchronous environments. In the companion paper, we show that chaos-based spreading is able to outperform classical spreading in most cases. We delve here into analytical investigations aimed at clarifying such phenomena and show that chaos-based spreading is actually able to reach the absolute maximum performance in the classical two-user case as well as when the number of users and the spreading factor grow to infinity. Under suitable conditions, and in complete analogy with what happens for suboptimal receivers dominated by multiple-access interference, maximum capacity is attained by spreading sequences whose auto-correlation profile is well approximated by an exponential trend with rate r-=-2+/spl radic/3.

Identification of multiinput-multioutput transfer function and noise model of a blast furnace from closed-loop data

A procedure is described for the identification of multiinput-multioutput transfer function and the disturbance model from closed-loop data. The basic step of the identification procedure is to obtain a multivariate time series model for the input and the output series. A new method-viz., the method of successive orthogonalization is given for the modeling of multiple time series. Real data on closed-loop operation of a blast furnace are analyzed.