Second-order Transfer Function Research Articles

An Analytical Approach to Integral Resonant Control of Second-Order Systems

Systems with colocated sensor-actuator pairs exhibit the interesting property of pole-zero interlacing. Integral resonance control (IRC) exploits this property by changing the pole-zero interlacing to zero-pole interlacing. The unique phase response of this class of systems enables a simple integral feedback controller to add substantial damping. Over the past few years, IRC has proven to be extremely versatile and has been applied to a wide variety of systems whose dominating dynamics of interest can be accurately modeled by second-order transfer functions. To date, a manual approach has been employed to determine the parameters of the IRC scheme, namely the feed-through term and the integral gain. In this paper, the relationship between the feed-through term, integral gain, and achievable damping is derived analytically for undamped/lightly damped second-order systems. The relationship between damping controller and an outer servo loop is also derived. These results add to the current understanding of colocated systems and automate the design of IRC controllers with a specified damping and tracking bandwidth. The presented results are applied to design and implement a damping and tracking controller for a piezoelectric nanopositioning stage.

Measurement-Based Load Modeling Using Transfer Functions for Dynamic Simulations

Measurement-based load modeling is a promising approach to reliably represent load behavior in dynamic simulations of large power systems. This paper presents a methodology that starts with the acquisition of voltages and currents from power quality monitoring systems and highlights the issues associated with selecting, processing and resampling the data to estimate the relationship between the power deviations as a function of the voltage deviations. The load model mathematical structure chosen is a second-order transfer function, whose parameters are estimated using a genetic algorithm (GA) as the optimization technique that minimizes the error between the real data that are measured and the data that are simulated with the proposed models. Some insights were achieved regarding the appropriate search space choice.

Optimisation of wavelengths selection used for the multi-spectral temperature measurement by ordinary least squares method of surfaces exhibiting non-uniform emissivity

In this paper, a method based on the ordinary least squares method for optimising the wavelength selection used for the multi-spectral temperature measurement of surfaces exhibiting non-uniform temperature-depending emissivity is presented. The goal consists of minimising the standard deviation of the estimated temperature (optimal design experiment). Two methods for wavelengths selection are presented – sequential and global with or without constraints – on the spectral range. Then, the estimated temperature results obtained by two different models taking into account a second-order polynomial transfer function including the emissivity and for different number of parameters and wavelengths are compared. The first model is based on Wien’s approximation and fluxes ratio (as done in the bicolour temperature technique) and the other is based on the fluxes (Planck’s law but without fluxes ratio). Different selection criteria are presented. These points are treated from theoretical, numerical and experimental points of view.

Study on a Novel Modeling Method for the Electromagnetic Flywheel Systems

This study proposes a new modeling method for nonlinear systems based on a genetic algorithm (GA). Through this method, the transfer functions of the above unidentified systems can be identified. This method would well help the nonlinear systems to find out their optimal solutions in controls. First, the physical input-output data pairs of the unidentified system should be collected. Next, the coefficients of the first second-order transfer function can be identified by GA. Last, based on the errors between the physical data pair and the first second-order transfer function; similarly the second second-order transfer functions can be identified by GA.So far as known, electromagnetic flywheel (EF) systems are with many uncertainties, such as nonlinear electromechanical coupling and electromagnetic saturation, etc. They are difficult to accurately modeling by traditional mathematic ways that restrict the control and application of them. In order to confirm the effectiveness and feasibility of this proposed method, an EF system is setup for this study. By assessing the results of calculations and experiments shows that the proposed method is possible to be applied for any nonlinear systems.

A Novel Method of Transfer-Function Identification for Unknown Systems

This study proposes a new modeling method for unknown systems. Through this method, the transfer functions can be identified. First, the input-output data pairs of the unidentified system should be collected. Then, the transfer function’s coefficients can be identified based on the errors via the derivative-free search methods such as GA etc. Here, a second-order transfer function is used in this study. For a second-order transfer function is difficult to approach each system, a plurality of transfer functions may be used depending on the precise requirement. Finally, following the previous steps, the other transfer function can be found in succession. In order to confirm the effectiveness of this proposed method, an electromagnetic flywheel (EF) system is used in this study. Such kinds of systems are always with many uncertainties as nonlinear electromechanical coupling and electromagnetic saturation, etc. They are difficult to modeling via traditional mathematic ways. In this study, the data pairs of EF system is collected by experiments. By assessing the results of the proposal and experimental data shows that this method is feasible to any unknown systems. system, achieve more saving energy and high efficiency control purposes.

PID tuning under uncertain conditions: robust LMI design for second-order plus time-delay transfer functions

This paper proposes a systematic method for design of PID controllers for continuous time systems subjected to time-delay. An appropriate Lyapunov-Krasovskii functional is proposed yielding delay dependent conditions that guarantee a prescribed H∞ performance for the closed-loop system. The controller design is carried out by means of convex optimization problems written in the form of linear matrix inequalities. The innovative aspect is that robustness issues associated with time-delay are investigated by assuming that it can vary within prescribed bounds. Numerical experiments are provided to illustrate the advantages.

Tuning of <i>PI</i> <sup>λ</sup> Controllers Based on Gain and Phase Margins and its Application in Water Tank

This paper discusses the parameters tuning of fractional-order controller satisfying the desired gain-margin and phase-margin specifications in terms of a stability equation method applicable to fractional-delay systems. The tuning procedure is then applied to the level control of double water tank, which is modeled as a second-order transfer function with time-delay. The Matlab simulations and the experiments on the water tank device show the effectiveness of the tuning and the benefits of using fractional-order controllers.

Online Set Point Modulation to Enhance Microgrid Dynamic Response: Theoretical Foundation

The need for higher degree of infrastructure utilization of the electric power system inevitably results in its operation closer to the limits. This in turn places the burden on control and protection strategies to ensure the constraints are not violated. This is especially imperative in microgrids in which resources are more limited and constraints are tighter. This paper presents an adaptive control strategy to augment the existing controllers and enhance their performance. This strategy monitors the response of a controlled device and temporarily modulates its control set point to achieve close tracking of the set point in the presence of disturbances. A detailed analytical derivation for the case that the overall behavior of the system (the devices and its controller) is approximated with a second-order transfer function is presented to confirm the viability of this strategy and its ability in designing a response with limited over- or undershoot.

Modeling the Pilot Detection of Time-Varying Aircraft Dynamics

T HE human pilot is typically required to control aircraft in which the dynamics of the vehicle vary with time. This variation may occur naturally as the aircraft changes flight condition, it can be deliberately induced by changes in the stability and command augmentation system (SCAS), or it may result from airframe damage or control system failures. The means by which the pilot is able to accommodate these changes has led to studies describing the “adaptive human pilot,” (e.g., [1–3]). The work in [4] used a simplified pursuit-control model of the human operator derived from the more complete structural pilot model of [5]. The simplification in [4] allowed implementation of an adaptive control structure in computer simulation of control tasks with time-varying controlledelement dynamics as reported in [6]. It is desirable to hypothesize the manner in which the more complete structural model might be employed to explain human pilot detection of time-varying vehicle dynamics. The structural pilot model is shown in Fig. 1 in a form suitable for a simple single-axis task, such as an aircraft/rotorcraft pitch-attitude tracking task. The pilot model includes three feedback loops defined as visual, vestibular, and proprioceptive. For the purposes of this initial discussion, the vestibular loop will be ignored (K _ m 0). A detailed description of each of the elements in the model is given in [5]. Here, with the exception of the element YPF, the elements will only be briefly described. In themajority of applications, the element Ye is a simple gain. The time delay 0 is set to 0.2 s. YNM is a simple second-order transfer function representing the neuromuscular dynamics in the particular limb that is driving the cockpit inceptor (e.g., control stick or rudder pedals). The element YFS represents the cockpit inceptor force/feel system dynamics. Yc represents the vehicle dynamics in the control axis in question (i.e., the transfer function between vehicle pitch attitude and longitudinal control inceptor input ). The proprioceptive feedback element YPF is assumed to be of the form such that

Closed-Loop Identification of Second-Order Plus Time Delay (SOPTD) Model of Multivariable Systems by Optimization Method

The closed-loop identification of second-order plus time delay (SOPTD) transfer function models of multivariable systems is presented based on optimization method using the combined step-up and step-down responses. The need for combined step up and step down changes in the set point is brought out for the convergence of the model parameters. A standard nonlinear least-squares optimization method is used to obtain the parameters of the SOPTD model transfer function matrix by minimizing the sum of squared errors between the closed-loop responses of the model and the actual process responses. A simple method is proposed to obtain the initial guess values of SOPTD transfer function model parameters from the main and interaction responses of the actual process. This method was applied to two-input two-output (TITO) second-order plus time delay (SOPTD), higher order and 3 × 3 SOPTD transfer function models of multivariable systems. The proposed method considerably reduces the computational time for the optimiza...

Concept for the integration of geometric and servo dynamic errors for predicting volumetric errors in five-axis high-speed machine tools: an application on a XYC three-axis motion trajectory using programmed end point constraint measurements

A modelling approach for volumetric error prediction taking into account geometric and servo dynamic errors in a five-axis high-speed machine tool is proposed in this paper. Polynomial functions are used to represent and then predict the geometric errors. A simple second-order transfer function model is used to model and predict the servo dynamic error. The servo dynamic errors are added to the axis position geometric errors and propagated to the tool and workpiece using matrix transformations. The validity of the error integration concept is tested for a XYC three-axis motion trajectory. Two experimental setups are used. The first experimental test used the KGM grid encoder instrument to estimate the parameters of the servo dynamic error models of the X- and Y-axes. The second experimental test used a programmed end point constraint procedure with measurement of the 3D volumetric positioning errors between a point on the tool holder and another fixed to the machine table. The tests involve maintaining the nominal coincidence of these two points whilst exercising the three axes. These last tests are used to estimate the geometric error parameters and also to validate the prediction performance of the integrated geometric and dynamic model. The result shows the effectiveness of the error integration concept.

System Identification and Closed-Loop Control of End-Tidal CO<formula formulatype="inline"><tex Notation="TeX">$_{\bf 2}$</tex></formula> in Mechanically Ventilated Patients

This paper presents a systematic approach to system identification and closed-loop control of end-tidal carbon dioxide partial pressure (PETCO2) in mechanically ventilated patients. An empirical model consisting of a linear dynamic system followed by an affine transform is proposed to derive a low-order and high-fidelity representation that can reproduce the positive and inversely proportional dynamic input-output relationship between PETCO2 and minute ventilation (MV) in mechanically ventilated patients. The predictive capability of the empirical model was evaluated using experimental respiratory data collected from eighteen mechanically ventilated human subjects. The model predicted PETCO2 response accurately with a root-mean-squared error (RMSE) of 0.22+/-0.16 mmHg and a coefficient of determination (r2) of 0.81+/-0.18 (mean+/-SD) when a second-order rational transfer function was used as its linear dynamic component. Using the proposed model, a closedloop control method for PETCO2 based on a proportionalintegral (PI) compensator was proposed by systematic analysis of the system root locus. For the eighteen mechanically ventilated patient models identified, the PI compensator exhibited acceptable closed-loop response with a settling time of 1.27+/- 0.20 min and a negligible overshoot (0.51+/-1.17%), in addition to zero steady-state PETCO2 set point tracking. The physiologic implication of the proposed empirical model was analyzed by comparing it with the traditional multi-compartmental model widely used in pharmacological modeling.

Delay modeling of high-speed distributed interconnect for the signal integrity prediction

A relevant modeling-method of distributed interconnect line for the high-speed signal integrity (SI) application is introduced in this paper. By using the microwave and transmission line (TL) theory, the interconnect lines are assumed as its distributed RLC-model. Then, based on the transfer matrix analysis, the second-order global transfer function of the interconnect network comprised of the TL driven by voltage source including its internal resistance and the impedance load is expressed. Thus, mathematical analysis enabling the physical SI-parameters’ extraction was established by using the transient response of the loaded line. To verify the relevance of the developed model, RC- and RLC-lines excited by square-wavepulse with 10-Gbits/s-rate were investigated. So, comparisons with SPICE-computations were performed. As results, transient responses perfectly well correlated to the reference SPICE-models were evidenced. As application of the introduced model, evaluations of rise-/fall-times, propagation delays, signal attenuations and even the settling times were realized for different values of TL-parameters. Compared to other methods, the computation execution time and data memory consumed by the program implementing the proposed delay modeling-method algorithm are much better.

Dynamics Simulation of Beam-Carried Cranes Based on Virtual Prototyping

Firstly this paper introduces the flexibility theory of virtual prototyping. Secondly a virtual prototype of rigid-flexible coupling model for beam-carried cranes is built, based on collaborative simulation platform by using the software of UG, ADAMS and ANSYS. Finally the response curves of the displacement for the girder’s centroid with step load and different frequency sine load were analyzed by virtual prototyping simulation. And the corresponding second-order system transfer function is given through the system identification. The result of simulation provided some theory basis for the structure design and optimization of beam-carried cranes.

A straightforward determination of fluid viscosity and density using microcantilevers: From experimental data to analytical expressions

Vibrating microcantilevers are used to measure the density and the viscosity of surrounding fluids. The classical procedure involves experimental acquisition of the deflection spectrum of the beam, but a systematic calibration step is mandatory for obtaining viscosity and density. In the present study, a method is proposed to facilitate these measurements for Newtonian fluids with only one calibration step in air during the cantilever lifetime. Our approach relies on a complete theoretical analysis allowing to approximate semi-analytically the deflection spectrum with a second-order transfer function and to determine an analytical relationship between viscosity, density and the parameters of the transfer function. Fluid parameter determination results are shown for validation and discussed.

다중모델추정기법을 이용한 HEV/EV용 리튬이온전지의 잔존충전용량 추정

This paper presents a new state of charge(SOC) estimation of large capacity of Li-ion battery (LIB) based on the multiple model adaptive estimation(MMAE) method. We first introduce an equivalent circuit model of LIB. The relationship between the terminal voltage and the open circuit voltage(OCV) is nonlinear and may vary depending on the changes of temperature and C-rate. In this paper, such behaviors are described as a set of multiple linear time invariant impedance models. Each model is identified at a temperature and a C-rate. These model set must be obtained a priori for a given LIB. It is shown that most of impedances can be modeled by first-order and second-order transfer functions. For the real time estimation, we transform the continuous time models into difference equations. Subsequently, we construct the model banks in the manner that each bank consists of four adjacent models. When an operating point of cell temperature and current is given, the corresponding model bank is directly determined so that it is included in the interval generated by four operating points of the model bank. The MMAE of SOC at an arbitrary operating point (T o C, Ibat(A)) is performed by calculating a linear combination of voltage drops, which are obtained by four models of the selected model bank. The demonstration of the proposed method is shown through simulations using DUALFOIL.

Dynamic Modeling of Terahertz Quantum Cascade Lasers

In this paper, the influence of the simplifications made in the four-equation-based set of rate equations describing the dynamic behavior of a quantum cascade laser (QCL) is studied. Numerical simulations based on the set of four rate equations has been developed, enabling the theoretical study of the influence of different parameters on the direct modulation response of the laser. These equations have been then linearized in order to deduce a set of state system equations, which was written in a matrix formalism. Finally, an approximate second-order transfer function has been derived with the linearized dependence of its times constant.

DESIGN AND STABILITY ANALYSIS OF MIXED-MODE FILTERS CONTAINING ONLY GROUNDED CAPACITORS

In this paper, three dual-mode (mixed-mode) analog filters using only grounded capacitors and two to three second-generation current conveyors (CCIIs) are presented. The first proposed filter can provide a transimpedance-mode (TIM) second-order filter transfer function (TF), and is free from passive component matching constraints, which is advantageous in integrated circuit (IC) design. Other two mixed-mode filters having the property of tunability are derived from the first proposed filter. However, the developed filters in this work, like other active filters, suffer from nonidealities such as nonideal gain and parasitic impedance effects which increase the order of the filter TFs; accordingly, stability problem may arise. In this study, stability analysis using gain and phase margins is accomplished. To explain the claimed ideas, several computer simulations and an experimental test are performed.

Zone Model Predictive Control: A Strategy to Minimize Hyper- and Hypoglycemic Events

Development of an artificial pancreas based on an automatic closed-loop algorithm that uses a subcutaneous insulin pump and continuous glucose sensor is a goal for biomedical engineering research. However, closing the loop for the artificial pancreas still presents many challenges, including model identification and design of a control algorithm that will keep the type 1 diabetes mellitus subject in normoglycemia for the longest duration and under maximal safety considerations. An artificial pancreatic beta-cell based on zone model predictive control (zone-MPC) that is tuned automatically has been evaluated on the University of Virginia/University of Padova Food and Drug Administration-accepted metabolic simulator. Zone-MPC is applied when a fixed set point is not defined and the control variable objective can be expressed as a zone. Because euglycemia is usually defined as a range, zone-MPC is a natural control strategy for the artificial pancreatic beta-cell. Clinical data usually include discrete information about insulin delivery and meals, which can be used to generate personalized models. It is argued that mapping clinical insulin administration and meal history through two different second-order transfer functions improves the identification accuracy of these models. Moreover, using mapped insulin as an additional state in zone-MPC enriches information about past control moves, thereby reducing the probability of overdosing. In this study, zone-MPC is tested in three different modes using unannounced and announced meals at their nominal value and with 40% uncertainty. Ten adult in silico subjects were evaluated following a scenario of mixed meals with 75, 75, and 50 grams of carbohydrates (CHOs) consumed at 7 am, 1 pm, and 8 pm, respectively. Zone-MPC results are compared to those of the "optimal" open-loop preadjusted treatment. Zone-MPC succeeds in maintaining glycemic responses closer to euglycemia compared to the "optimal" open-loop treatment in te three different modes with and without meal announcement. In the face of meal uncertainty, announced zone-MPC presented only marginally improved results over unannounced zone-MPC. When considering user error in CHO estimation and the need to interact with the system, unannounced zone-MPC is an appealing alternative. Zone-MPC reduces the variability of control moves over fixed set point control without the need to detune the controller. This strategy gives zone-MPC the ability to act quickly when needed and reduce unnecessary control moves in the euglycemic range.

Over- and under-convergent step responses in fractional-order transfer functions

In this paper we highlight a remarkable difference between the step responses of a classical second-order transfer function and its fractional-order counterpart. It can be easily shown that the step response of a stable classical second-order transfer function crosses its final value infinitely over time. In contrast, it is illustrated here that the step responses of a fractional-order counterpart of the classical second-order model possess only a finite number of such crossovers. In other words, for such a system one can find a specific time instant after which the step response is over or under-convergent to its final value. This property interprets some phenomena observed in the real-world and should be considered during the design of the control system.