Order Transfer Function Research Articles

Dynamic modeling of reversible solid oxide cell stack and control strategy development

Solid oxide cell systems (SOCs) are increasingly being considered for electrical energy storage and as a means to boost the use of renewable energy and improve the grid flexibility by power-to-gas electrochemical conversion. The control of several variables (e.g., local temperature gradients and reactant utilization) is crucial when the stacks are used in dynamic operation with intermittent electrical power sources. In the present work, two 1D models of SOC stacks are established and used to investigate their dynamic behavior and to select and tune a suitable control strategy. Subsequently, safe operating ranges were determined to meet the thermal constraints of the stack by analysing not only the fuel cell (SOFC) and electrolyzer (SOEC) individual modes but also the switching between the two modes when the stack operates reversibly. The dynamic analysis shows that the control loops of our multi-input (reactant molar flow rates), multi-output (reactant utilization and maximum local temperature gradients) control system are strongly decoupled. Therefore, a proportional integral control strategy can be used to prevent dangerous stack operating conditions in dynamic operation. Finally, the controllers were tuned, and their transfer functions were reported. Convective heat transfer via air flow allows controlling the temperature of the solid structure of the cell/stack component, thus avoiding issues related to temperature variation during transient operation. Moreover, the reactant utilization controllers can avoid component fracture or degradation owing to fuel starvation under dynamic operation. The process can be approximated by two first order transfer functions. It can help in the design of more complex control systems in the future if necessary, with embedded process models, such as model predictive control. Results in the simulation environment are preparatory to the programming phase of an actual controller in real-world applications.

Dynamics and Control of Liquid Level in Annular Conical Tank Process: Modelling and Experimental Validation

Objectives: The present work has been carried out to prove the superiority of IMC based PID control strategy over the conventional PID, based on simulation studies and experimental validation on an annular conical tank liquid level nonlinear process. Methods/Statistical Analysis: First principles based Mathematical Model of an annular conical tank liquid level nonlinear process has been developed based on the mass balances and outlet flow hydraulic characteristics. Linearization of the nonlinear model at a specific steady-state operating point led to the theoretical development of state-space and standard first order transfer function models. Open loop and closed loop experimental studies on a computer controlled physical setup were performed to identify the parameters of a FOPDT Model with variable gain and time constant. IMC based PID controller was designed and compared to the conventional PID controller. Findings: The variation in process parameters was attributed to two factors: (a) the variation in annular cross sectional area of the conical tank at different levels, and (b) the variation in outlet flow resistance. The IMC based PID controller has been shown to exhibit superior performance in terms of quantitative performance indices such as ISE, IAE, ITAE, rise time, settling time and percentage overshoot, at four different steady-states. Application/Improvements: Study of Modelling of annular conical tank process and a systematic methodology of process system identification from experimental setup have been reported. The advantages of IMC based PID controller design over the conventional PID tuning method has been experimentally verified. Keywords: Annular Flow Conical tank process, FOPDT model, System Identification, PID controller tuning, IMC based PID.

Tunable and reconfigurable mechanical transmission-line metamaterials via direct active feedback control

Abstract We consider the problem of using active feedback control to create tunable and reconfigurable mechanical metamaterials capable of supporting unconventional wave propagation mechanisms. The nominal system chosen for this analysis is a one-dimensional homogeneous bar having periodically distributed force actuators and subject to longitudinal waves. We note that this system does not make use of local inclusions, instead the actuators are attached directly to the beam and achieve metamaterial properties by means of periodically applied forces. We design control algorithms in order to achieve desired constitutive parameters for the metamaterial in closed loop. In particular, the control system is designed to generate either zero or negative values of the effective properties (i.e. stiffness and mass) to obtain a metamaterial with different dynamic behaviors. Four different regimes of effective properties are considered in this study: single negative or zero, double negative, double zero, double positive. The constitutive parameters achievable via the direct control approach are therefore defined only by the feedback algorithms and are not confined to any particular properties that would otherwise be imposed by local resonators. We model and analyze the system by fractional order transfer functions, which explicitly exhibit the special characteristics of the metamaterial, including the constitutive parameters, dispersion, and transmission and reflection properties. We illustrate the stability and performance of the control system through numerical simulations. Finally we note that, despite the choice of the mechanical system used in this study, the proposed results have general applicability to all those systems described by the second order wave equation in their nominal uncontrolled state.

Dynamic Matrix Control DMC using the Tuning Procedure based on First Order Plus Dead Time for Infant-Incubator

The concept of Model Predictive Control (MPC) is considered as one of the most important controlling strategies. It is used in several fields, such as petrochemical, oil refinery, fertilizer and chemical plants. It is also well spread among the clinicians and in the biomedical fields. In this context, our paper aims to investigate the thermal conditions inside the infant incubator for premature babies. In this study, we propose the Dynamic Matrix Control (DMC) as a control strategy. The most particularity of this strategy is applicable to the Multi-input Multi-output (MIMO) systems. It aims to compare different coupled transfer functions achieved by two identification methods in previous work. Also, a simulation of the air temperature and humidity is achieved inside the unit care. In this work, we focus on the tuning controlling parameters because it is considered as a key step in the successful performance of (DMC). Then, to obtain the (DMC), we have used an analytic tool, which is the Process Reaction Curve (PRC), for higher order transfers function because it needs a lot of work for this purpose. It should be approximated as a low order transfer function with time delay, which is achieved by using the First Order Plus Dead Time (FOPDT) of processing models. Finally, the result of the comparison of the infant-incubator is provided to show an optimal and good performance of the thermal behavior of our propos methodology and prove that a good identification ensures a better performance.

Modeling and Control of Inverter Zero-Voltage-Switching for Inductive Power Transfer System

It's very important to maintain the inverter zero-voltage-switching(ZVS) for inductive power transfer (IPT) system, especially for those high power applications. The ZVS condition can be obtained via regulating the inverter operating frequency of the IPT system. A modeling method based on the energy-amplitude and phase is proposed and corresponding controller is designed to maintain the inverter ZVS condition for IPT. The dynamic model of the ZVS for the half-bridge inverter is developed firstly. To facilitate the dynamic performance analysis and controller design, the original time-variant model is linearized with small-signal method at its operating point, which yields to a 4 order transfer function model. A PI controller which maintains ZVS condition via regulating the inverter operating frequency is designed based on the transfer function. An IPT prototype is built to verify the proposed theory. Experiments show that the controller traces the reference of the ZVS angle within 20 ms under various perturbation, which verifies the correction and effectiveness of the model and controller.

The Integer–Order Approximation of Fractional–Order Systems in The Loewner Framework

Abstract This paper deals with the integer–order (finite–dimensional) approximation of a fractional–order (infinite–dimensional) system using the interpolation approach in the Loewner framework. First given a set of interpolation frequencies and the corresponding values of the original noninteger–order transfer function, a Loewner matrix and a shifted Loewner matrix are created. Then, from these matrices an integer–order model in state–space descriptor form is constructed. Its transfer function matches the original system transfer function at the given frequencies. To avoid singularity problems related to data redundancy, a truncated singular value decomposition may finally be applied. Numerical simulations show that the suggested approach to fractional–order system approximation compares favourably with alternative techniques recently presented in the literature to the same purpose.

FFANN Optimization by ABC for Controlling a 2nd Order SISO System’s Output with a Desired Settling Time

In this study, a control strategy is aimed to ensure the settling time of a 2nd order system’s output value while its input reference value is changed. Here, Feed Forward Artificial Neural Network (FFANN) nonlinear structure has been chosen as a control algorithm. In order to implement the intended control strategy, FFANN’s normalization coefficient (K), learning coefficients (ŋ), momentum coefficients (μ) and the sampling time (Ts) were optimized by Artificial Bee Colony (ABC) but FFANN’s values of weights were chosen arbitrary on start time of control system. After optimization phase, the FFANN behaves as an adaptive optimal discrete time non-linear controller that forces the system output to take the same value with the input reference for a desired settling time (ts). The success of the optimization algorithm was proved with close loop feedback control simulations on Matlab’s Simulink platform based on 2nd order transfer functions. Also, the success was proved with a 2nd order physical system (buck converter) that was structured with power electronics elements on Simulink platform. Finally, the success of the control process was discussed by observing results.

Dynamic analysis and modeling of direct contact membrane distillation for water desalination during startup using linear system theory

The transient performance of direct contact membrane distillation during startup was investigated using experimental data and theoretical modeling. The primary input, inlet hot temperature, caused a minor time delay in the output variable's dynamics because the dynamic of the former is not instantaneous. The minor input, inlet cold temperature, can cause disturbances in the system dynamics if it is not well controlled. Reaction curve methods revealed that the time constant of the outlet permeate temperature varied from 2 to 6 min as the operating temperature increased from 50 to 80 °C. The dynamic of the outlet hot temperature was found to be slower, with the time constant changing from 40 to 16 min under the same operating conditions. Modeling the outlet permeate temperature with a first-order transfer function produced results that closely followed the measured transient response. The lead-lag transfer function was found insufficient for capturing the dynamics of the outlet hot temperature. The choice of a high order transfer function for the hot temperature led to improved tracking of the measured time response. The static version of the transfer functions provided an enhanced prediction of the mass flux at steady state via improved approximation of the bulk temperatures.

CFOA based low pass and high pass fractional step filter realizations

This contribution puts forward a new proposal for Current Feedback Operational Amplifier (CFOA) based Low pass (LP) and High Pass (HP) Fractional Step Filters (FSFs). The proposed filters are designed by approximating the fractional Laplacian operator by an appropriate integer order transfer function. Subsequently, functional block diagram (FBD) approach is used for CFOA based realization of LP and HP FSFs of order (1 + α). Higher order FSFs are realized by cascading FSF of order (1 + α) with higher integer order filters. To illustrate this, CFOA based LP (HP) FSFs of order (5 + α) are obtained by cascading LP (HP) FSFs of order (1 + α) with proposed leapfrog realization of 4th order LP (HP) filter. The proposal is verified through SPICE simulations and experimentation. Stability, sensitivity and non-ideal analyses are also included.

Fractional proportional-resonant current controllers for voltage source converters

This paper proposes a novel fractional proportional-resonant controller, which applies fractional order calculus to the well-known proportional-resonant controllers. The focus of the study is the current control loop of voltage source converters. The main merit of the proposed fractional controller formulation lies into the use of fractional exponents in the integro-derivative parts obtaining a controller with an extra degree of freedom. This degree of freedom allows the phase delay to be improved for a wide frequency range in comparison with the conventional proportional-resonant controllers. Furthermore, the obtained controller results in a lower order transfer function that reduces the computational burden when multiple current frequencies have to be tracked. As fractional integro-derivative exponents are not directly implementable, five mathematical approaches are explored, selecting the Chareff’s approximation for the fractional controller operator’s implementation. A tuning procedure for such a controller is also addressed. The new controller formulation is validated in a 20kVA laboratory set-up based on a silicon-carbide converter, and it is implemented in a DSP. Two AC output converter’s configurations are considered to demonstrate the controllers’ tracking capability; short-circuited (balanced fault) output, and grid-connected operation. This last case is evaluated operating as active filter and delivering fundamental component to a non-ideal grid.

Impact of Load Dynamics on Electromechanical Oscillations of Power Systems

In this paper, the impact of load dynamics on the oscillatory stability of power systems is studied. The well-known composite load model is linearized to yield third order transfer functions for active and reactive power dynamics of loads. It is shown that the third order model exhibits a recovery response that is accompanied by damped oscillations. In studying the impact of loads’ transfer function parameters on the small signal stability of power systems, a resonance is observed between the load and the electromechanical modes of the system that significantly alters the electromechanical modes’ damping. The role of the active and reactive power dynamics, as well as the operating condition of the system on the impact from a dynamic load on electromechanical modes are investigated. For preliminary insights, a single machine infinite bus system (SMIB) is used initially to avoid the unnecessary complexities associated with large grids. The general conclusions drawn from the SMIB studies are then confirmed on a 14 generator model of the Australian grid.

The Identification of Tsunami Height Correlation Model with Earthquake Parameters

Tsunami is an event triggered by earthquake parameters. The earthquake parameters can provide information on the probability of a tsunami even that can be used in estimating the height of a tsunami. By excluding information beyond the earthquake parameters, this research aims to derive a mathematical model that describing the correlation between the height of the tsunami and the parameters of earthquakes. The method used in this research is to apply one of the multivariate methods of time series, namely the transfer function. Based on diagnostic results of Autocorrelation Function plot, Partial Autocorrelation Function and parameter significance, for the strength and depth of the earthquake selected model are ARIMA model (0, 1, 1). Based on the results of the processing of the input-output series model, cross-correlation, and weighting response formed twelve models of possible transfer functions to be modeled relationships between variables Tsunami height (Y), Strength of the earthquake (X1), and Depth of the earthquake (X2). By looking at the minimum AIC values of the model parameters, where the X1 variable is 1679,156 and X2 of 1668,258, we get the order transfer function model is ((0,3,0), (9,0,2), (0,1)), with the mathematical equation model as follows: .

Recursive identification of multiple-input single-output fractional-order Hammerstein model with time delay

This paper deals with identification of the continuous-time Hammerstein systems with time delay using Genetic Algorithm (GA) combined with the Recursive Least-Squares (RLS) method. This model consists of the Radial Basis Function Neural Network (RBFNN) as its nonlinear static part and fractional order transfer function as its dynamic linear part. The fractional orders are identified by GA with an innovative strategy called Modified Genetic Algorithm (MGA). The main innovative idea is the selection and transferring the best characteristics or properties to the next generation. On the other hand, the centers and widths and the weighting parameters of the RBFNN and the transfer function coefficients of the linear dynamic part are updated by the RLS method. Simulation results are applied to illustrate the proposed method accuracy.

Parameterizing Generalized Laguerre Functions to Compute the Inverse Laplace Transform of Fractional Order Transfer Functions

This article concentrates on using generalized Laguerre functions to compute the inverse Laplace transform of fractional order transfer functions. A novel method for selecting the timescale parameter of generalized Laguerre functions in the operator space is introduced and demonstrated on two systems with fractional order transfer functions.

Design and analysis of fractional order seismic transducer for displacement and acceleration measurements

Seismic transducers are widely used for measurement of displacement, velocity, and acceleration. This paper presents the design of seismic transducer in the fractional domain for the measurement of displacement and acceleration. The fractional order transfer function for seismic displacement and acceleration transducer are derived using Grünwald–Letnikov derivative. Frequency response analysis of fractional order seismic displacement transducer (FOSDT) and fractional order seismic acceleration transducer (FOSAT) are carried out for different damping ratio with the different fractional order, and the maximum dynamic measurement range is identified. The results demonstrate that fractional order seismic transducer has increased dynamic measurement range and less phase distortion as compared to the conventional seismic transducer even with a lower damping ratio. Time response of FOSDT and FOSAT are derived analytically in terms of Mittag-Leffler function, the effect of fractional behavior in the time domain is evaluated from the impulse and step response. The fractional order system is found to have significantly reduced overshoot as compared to the conventional transducer. The fractional order seismic transducer design proposed in this paper is illustrated with a design example for FOSDT and FOSAT. Finally, an electrical equivalent of FOSDT and FOSAT is considered, and its frequency response is found to be in close agreement with the proposed fractional order seismic transducer.

An efficient algorithm for low-order direct discrete-time implementation of fractional order transfer functions

Fractional order systems become increasingly popular due to their versatility in modelling and control applications across various disciplines. However, the bottleneck in deploying these tools in practice is related to their implementation on real-life systems. Numerical approximations are employed but their complexity no longer match the attractive simplicity of the original fractional order systems. This paper proposes a low-order, computationally stable and efficient method for direct approximation of general order (fractional order) systems in the form of discrete-time rational transfer functions, e.g. processes, controllers. A fair comparison to other direct discretization methods is presented, demonstrating its added value with respect to the state of art.

Modelling and compensation of dominant thermally induced geometric errors using rotary axes’ power consumption

Thermally induced volumetric errors due to rotary axes’ activity are measured on a five-axis machine tool using a non-contact R-test device with a four-ball uncalibrated artefact and an Invar reference length. The gathered volumetric data allow to estimate intra- and inter-axis machine errors as well as the table expansion via the estimated balls position. Dominant thermal effects are modelled as functions of the measured rotary axes drive power consumption by the superposition of single-input single-output first order transfer functions. The efficiency of the model is validated with different motion sequences and by the compensated machining of a test piece.

Adaptive PI Controller for Slip controlled Belt Continuously Variable Transmission

The control of slip in a belt Continuously Variable Transmission (CVT) has been the subject of many research papers. Optimal control of the belt CVT is of major importance for the efficiency as demonstrated in literature. The challenge in optimizing that efficiency is in the reduction of the necessary clamping forces while the stability of the variable transmission is maintained. Although these problems have already been tackled to a certain extent, mostly fairly complex controllers are proposed. The goal of this paper is to propose a straightforward though effective method to control slip. The main idea of the paper is to use linearized equations of the slip dynamics to update the controller parameters in function of the operating point. This approach allows to reduce the highly nonlinear system to a first order transfer function which is easily controlled with a PI controller. Results based on extensive simulations show that the controller is robust against torque disturbances and speed ratio variations.

PID Controller Design for Controlling Integrating Processes with Dead Time using Generalized Stability Boundary Locus

This paper proposes a method so that all PID controller tuning parameters, which are satisfying stability of any integrating time delay processes, can be calculated by forming the stability boundary loci. Processes having a higher order transfer function must first be modeled by an integrating plus first order plus dead time (IFOPDT) transfer function in order to apply the method. Later, IFOPDT process transfer function and the controller transfer function are converted to normalized forms to obtain the stability boundary locus in (KKcT, KKc(T2 / Ti)), (KKcT, KKcTd) and (KKc(T2/Ti), KKcTd) planes for PID controller design. PID controller parameter values achieving stability of the control system can be determined by the obtained stability boundary loci. The advantage of the method given in this study compared with previous studies in this subject is to remove the need of re-plotting the stability boundary locus as the process transfer function changes. That is, the approach results in somehow generalized stability boundary loci for integrating plus time delay processes under a PID controller. Application of the method has been clarified with examples.

Design of PI Controller using Optimization Method in Fractional Order Control Systems

In control systems, controller preference and design is an important issue for meeting the desired design criteria. In this paper, PI controller design was performed by using optimization method for fractional order systems. First, all the PI controller parameters that make the control system stable are calculated by using the stability boundary locus method. However, each controller parameter selected in the stability region may not be able to optimally control the system. Optimal controller parameters that provide the best control from the PI controller parameters that make the system stable by using the optimization method are obtained. In the optimization process, the optimal PI controller parameters are calculated by using the integral performance criterion based on the error. Simulation studies have been done for closed loop control system including a fractional order transfer function with time delay. It has been shown that the presented method can be successfully applied to fractional order control systems.