First-order Lag Element Research Articles

Scalable Model Predictive Control for Autonomous Mobility-on-Demand Systems

Technological advances in self-driving vehicles will soon enable the implementation of large-scale mobility-on-demand (MoD) systems. The efficient management of fleets of vehicles remains a key challenge, in particular to achieve a demand-aligned distribution of available vehicles, commonly referred to as rebalancing. In this article, we present a discrete-time model of an autonomous MoD system, in which unit capacity self-driving vehicles serve transportation requests consisting of a (time, origin, destination) tuple on a directed graph. Time delays in the discrete-time model are approximated as first-order lag elements yielding a sparse model suitable for model predictive control (MPC). The well-posedness of the model is demonstrated, and a characterization of its equilibrium points is given. Furthermore, we show the stabilizability of the model and propose an MPC scheme that, due to the sparsity of the model, can be applied even to large-scale cities. We verify the performance of the scheme in a multiagent transport simulation and demonstrate that service levels outperform those of the existing rebalancing schemes for identical fleet sizes.

Reset Control of Combustion Oscillation Model

Combustion oscillations occur themselves as pressure and heat release oscillations in lean premixed combustors, and may cause some unexpected damage. This paper proposes a design method of a reset controller to eliminate a combustion oscillation in a lean premixed combustor model. We consider a plant model consisting of a linear system with a nonlinear feedback element and a reset controller using a first-order lag element, which is called a first-order reset element (FORE). We show parameter conditions of the reset controller for which limit cycles are eliminated, using a describing function of the nonlinear element. We apply the proposed design method of the reset controller and a flame describing function to eliminate the combustion oscillation in the lean premixed combustor model and show its effectiveness appropriately.

ダンパを有するPZT精密位置決め装置のモデル化と制御

The authors have researched and developed a highly precise positioning device that uses a piezoelectric element (PZT) and a lever mechanism, which is used to increase the displacement amplitude. Because this device uses elastic deformation of a hinge structure, the resonance peak is very high. Therefore, we attached a damper composed of visco-elastic material (VEM) and a restriction plate to reduce this phenomenon. However, at low range of the frequency response, the gain was reduced by several decibels. We clarified that this damper was the factor to cause an overshoot by identifying a high order model and performing detailed analysis in the previous paper. However, the precision was limited because we modelled a gain reduction area in the first-order phase lag element. In this research, we suggest a method to model the gain reduction part in the high-order phase lag element and demonstrate the effectiveness of the model by experiments. Moreover, we demonstrate the practicality of a simple control system design method for technological advances by experiments on perturbation induced by setting the load mass.

遺伝的アルゴリズムを用いたパラメータ推定による南国果実の熟度判定法

This paper presents a method of maturity detection of the tropical fruits using a smell sensor. We investigate many sensing data of different fruits and find out that the data of the fruits are characterized as a first-order lag element. The first-order lag element has two parameters: gain and time constant. Knowing the gain and time constant of the smell data is useful for detecting the maturity of the fruits. In this paper, we apply a genetic algorithm to identify the gain and time constant parameters for the sensing data. Experiments of the maturity detection for monkey bananas and guavas show good results.

Frequency response model of skeletal muscle and its association with contractile properties of skeletal muscle

The aims of the present study were to develop a mathematical model of the skeletal muscle based on the frequency transfer function, referred to as frequency response model, and to presume the relationship between the model elements and skeletal muscle contractile properties. Twitch force in elbow flexion was elicited by applying a single electrical stimulation to the motor point of biceps brachii muscles, and then analyzed visually by the Bode gain and phase diagram of the force signal. The frequency response model was represented by a frequency transfer function consisting of five basic control elements (proportional element, dead time element, and three first-order lag elements). The model element constants were estimated by best-fitting to the Bode gain and phase diagram of the twitch force signal. The proportional constant and the dead time in the frequency response model correlated significantly with the peak torque and the latency in the actual twitch force, respectively. In addition, the time constants of the three first-order lag elements in the model correlated strongly with the contraction time and the half relaxation time in the actual twitch force. The results suggested a possibility that the individual elements in the frequency response model would reflect the biochemical and biomechanical properties in the excitation–contraction coupling process of skeletal muscle.

Model Based Analysis of Signaling Pathways

Model Based Analysis of Signaling PathwaysThe paper is concerned with application of mathematical modeling to the analysis of signaling pathways. Two issues, deterministic modeling of gene transcription and model-driven discovery of regulatory elements, are dealt with. First, the biological background is given and the importance of the stochastic nature of biological processes is addressed. The assumptions underlying deterministic modeling are presented. Special emphasis is put on describing gene transcription. A framework for including unknown processes activating gene transcription by means of first-order lag elements is introduced and discussed. Then, a particular interferon-β induced pathway is introduced, limited to early events that precede activation of gene transcription. It is shown how to simplify the system description based on the goals of modeling. Further, a computational analysis is presented, facilitating better understanding of the mechanisms underlying regulation of key components in the pathway. The analysis is illustrated by a comparison of simulation and experimental data.

Modeling of dynamic behaviors of friction

This paper deals with modeling of dynamic behaviors of friction in the sliding regime. Using a hydraulic cylinder, friction characteristics are experimentally investigated under various conditions of velocity variation. The friction force of the hydraulic cylinder is measured based on the equation of motion using measured values of the pressures in the cylinder chambers and the acceleration of the hydraulic piston. Comparison between measured unsteady-state friction characteristics and those predicted by the LuGre model shows that the LuGre model cannot simulate the real friction characteristics of hydraulic actuators. In this paper, the LuGre model is modified taking the dynamics of lubricant film formation into consideration. The lubricant film dynamics is approximated by a first-order lag element and its time constant is varied among the acceleration, deceleration and dwell periods. Experiments make clear the dynamic behaviors of the friction of the hydraulic cylinder. It is shown that the modified LuGre model can simulate the real dynamic behaviors of the friction of the hydraulic actuator with a relatively good accuracy.

707 マイクロチャンネルを用いた赤血球形状回復能の計測と評価(J06-2 医療診断のためのマルチスケール血流動態計測と解析(2),ジョイントセッション,21世紀地球環境革命の機械工学:人・マイクロナノ・エネルギー・環境)

In a human body, erythrocytes deform highly and can smoothly pass capillaries of which diameters are narrower than the cells'. Since capillaries connect all organs in a body, decrease in erythrocytes deformability causes several diseases. Therefore it is very important to evaluate the dynamic deformability of the erythrocyte at the microcirculation level. In this research, we produced a micro channel army with a 5μm×5μm square cross section of 100μm in length on the silicon substraight to simulate capillaries. After whole blood was centrifuged and erythrocytes were separated from plasma, the erythrocytes were diluted with autologous plasma by a hematocrit of 10%. This suspension was made to flow through the micro channels. Erythrocyte was observed using a high-speed video camera each day during preservation period. As a result, the time fluctuations of compressive strain of the RBCs agree with the theoretical curve of first-order lag element as a viscoelastic Kelvin model.

A201 マイクロチャンネルを用いた赤血球変形挙動に関する生体外実験

In a human body, erythrocytes deform highly and can smoothly pass capillaries of which diameters are narrower than the cells'. Since capillaries connect all organs in a body, decrease in erythrocytes deformability causes several diseases. Therefore it is very important to evaluate the dynamic deformability of the erythrocyte at the microcirculation level. In this research, we produced a micro channel array with a 5pm×5pm square cross section of 100pm in length on the silicon substraight to simulate capillaries. After whole blood was centrifuged and erythrocytes were separated from plasma, the erythrocytes were diluted with autologous plasma by a hematocrit of 10%. This suspension was made to flow through the micro channels. Erythrocyte was observed using a high-speed video camera each day during preservation period. As a result, the time fluctuations of compressive strain of the RBCs agree with the theoretical curve of first-order lag element as a viscoelastic Kelvin model.

Response of Backflow to Flow Rate Fluctuations

The response of backflow at the inlet of an inducer to the flow rate fluctuation is studied by using three-dimensional numerical calculations based on the k-ϵ turbulence model for the discussion of its effect on cavitation instabilities. It is first shown that the size of the backflow region can be correlated with the angular momentum in the upstream and the phase of the backflow significantly delays behind the quasi-steady response even at a very low frequency. It is then shown that the conservation relation of angular momentum is satisfied with minor effects of the shear stress on the boundary. The supply of the angular momentum by the negative flow is shown to be quasi-steady due to the fact that the pressure difference across the blade causing the backflow is quasi-steady at those frequencies examined. A response function of the angular momentum in the upstream to flow rate fluctuation is derived from the balance of the angular momentum and the results of the numerical calculations. This clearly shows that the backflow responds to the flow rate fluctuation as a first-order lag element. The effects of the backflow cavitation on cavitation instabilities are discussed assuming that the delay of cavity development is much smaller than the delay of the backflow. It was found that the backflow cavitation would destabilize low frequency disturbances due to the effects of the positive mass flow gain factor but stabilize high frequency disturbances due to the effect of the cavitation compliance.

Mechanism and control of electrification in pneumatic conveying of powders

This paper describes the mechanism and control of electrification in pneumatic conveying of powders by both numerical and experimental approaches. A three-dimensional discrete element method (DEM) was used to analyze the particle movement (collision velocity, number of collision, etc.) in a pneumatic conveying process under various operating conditions. A simplified model that assumed the electrification of a single particle to be proportional to the vertical collision velocity and the number of collision against the pipe wall was proposed and the electrification during conveying of powders was numerically computed. The electrification of particles during the pneumatic conveying was also measured and then compared with the calculated results to confirm the validity of the proposed model. A novel electrostatic charge control system comprised corona discharge neutralizer, electrostatic filed strength sensor, and computer control system was developed and applied to the powder pneumatic conveying process. Dynamic characteristics of electrostatic charge and its elimination process through the corona discharge neutralizer were analyzed. Based on these characteristics, a simplified transfer function composed of first-order lag element including dead time was proposed and optimal control parameters for digital PID (proportional-integral-differential) control was determined. Performance of the control system was also investigated experimentally. It was found that the electrostatic charge in the pneumatic conveying process was completely self-controlled.

Chaos in a four-dimensional system consisting of fundamental lag elements and the relation to the system eigenvalues

Abstract A simple system consisting of a second-order lag element (a damped linear pendulum) and two first-order lag elements with piecewise-linear static feedback that has been derived from a power system model is presented. It exhibits chaotic behavior for a wide range of parameter values. The analysis of the bifurcations and the chaotic behavior are presented with qualitative estimation of the parameter values for which the chaotic behavior is observed. Several characteristics like scalability of the attractor and globality of the attractor-basin are also discussed.

A New Adaptive Identification Method of Critical Point Using Frequency Estimator

In this paper, a new adaptive identification method of a frequency response G(jω) that satisfies a phase condition LG(jω) = θ,θ ∊ [–π, –π/2) is proposed. It corresponds to the critical point of a feedback system composed of the plant G(s), a saturation nonlinearity, and a first-order lag element k/(1 + sT) where k is tuned so that a sinusoidal oscillation can continue and T is tuned so that the phase condition can be met at the oscillation frequency. The frequency response is given by G(jω) = – (1 + jωT)/k from the convergent values. In the tuning algorithm, a globally convergent frequency estimator is used for estimating the amplitude and the frequency of the oscillation.

A Design of Minimax Controller for Systems Having Uncertainties. Application to a Tracking Problem of a Two-Link Manipulator.

This paper considers the optimization of systems having uncertain parameters by using minimax strategy. An optimization problem is converted to a minimax problem to treat system design variables as a minimizer which improves a performance index and uncertainties as a maximizer which worsens the same index. The solution of the minimax problem improves the worst case performance most, so the systems designed by the above formulation has robustness to uncertainties. We propose the method which uses the historical information of the optimization process to solve the minimax problems which don't have a saddle point. As a numerical example, we investigate a control system design for a tracking problem of a rigid robot manipulator. In this system, parameters of a first-order lag element between a controller and a actuator have uncertainty, and we design feedback gains of a PD controller. The robustness of the control system design by a proposed method against the uncertainty is demonstrated.

Evaluating the maneuverability of a control stick using electromyography.

This paper proposes maneuverability indexes for a control stick that are based on considerations of muscle characteristics. The indexes are defined on the basis of muscle forces: stiffness of the musculoskeletal system and torque for accelerating the stick. Measuring muscle forces with electromyography, we examine the effectiveness of the proposed indexes experimentally. In a slow tracking operation, the index based on stiffness conforms to the subjective evaluation, but the index based on the torque is inadequate as an index of maneuverability; we therefore use the index based on stiffness as the maneuverability index. In experiments on a step operation, we divided the operation into two phases: moving and holding. The index in the holding operation is in good agreement with the subjective evaluation. In both tracking and step operations the characteristics of the index are appropriate whether or not the controlled object has a first-order lag element. As a result, it is shown that the index can indicate the maneuverability in the low-frequency tracking operation of the stick.

Stability analysis of a controlled-current source-fed induction motor vector control system without a speed sensor

One of the representative vector-controlled induction motor drive systems without a speed sensor is composed of a rotor flux estimator, a PI torque current controller and a conventional vector-controlled current source. However, the stability analysis of this system has not been reported. In this paper, the flux estimator is interpreted as a flux observer. Then a linear model of the system is proposed by deriving the equations of the flux estimator in a synchronously rotating reference frame. By computing the trajectories of the poles and zeros and the transient responses, the following results are obtained. (1) If the rotor flux is estimated using only the stator equations (voltage model), the system becomes unstable when the actuator stator resistance is smaller than the value used by the controller. (2) By choosing a small time constant of the first-order lag element in the flux estimator (reciprocal number of observer gain), the poles and zeros on the imaginary axis move to the stable region. However, another pair of poles has reverse performance. (3) From the viewpoint of stability, the gain of the PI torque current controller should be chosen as large as possible and the stator and rotor resistances in the controller should be set to values smaller than their actual values.

Analysis of Dynamic Characteristics of a Gas Engine Cogeneration System.

Dynamic characteristics of a gas engine cogeneration system are analyzed using a simulation model. DYNAMO(dynamic model) is adopted as a simulation language because it enables an easy and flexible change of model structure and parameters. Dynamic characteristics of each piece of constituent equipment are expressed by using dead time and first-order lag elements. Their parameters are determined so that the simulation results match the measured ones accurately enough. The simulation model of the whole system is created by linking each submodel of constituent equipment. The simulation and measurement results show that the proposed modelling method is a useful tool. As an example of dynamic simulations, it is investigated how the location of measurement points influences the temperature of jacket water for cooling the gas engine.

Digital system for 1/f fluctuation-speed control of a small-fan motor

To produce a comfortable breeze similar to a natural one, a digital open-loop control system was utilized to control the speed of a small fan motor with 1/f fluctuation. The system was modeled as a first-order lag element with a time constant of 1.1 s. The output was controlled by commands and produced 1/f fluctuations, even though it was an open-loop system when the holding time of the data for 1/f fluctuation was set at more than 2 s. >

Comparision of Three Identification Methods for Time-Varying Systems

The aim of the paper is the comparison of three known identification and parameter estimation methods for linear timevarying systems. These three methods are a filter algorithm, a modification of the method of instrumental variables and a correlation method described by the author at the last symposium. With each method tests were carried out on a first-order lag element with stochastically varying gain, as well as a secondorder lag element, also with stochastically varying damping. The time-dependent parametes were changed relative to the system behaviour at low, medium and fast rates. Results of tests performed under equal conditions on these simulated processes with the above-mentioned identification methods permit a comparison of methods for accuracy, time taken for evaluation and necessary a priori information.

Analysis of the Frequency Characteristics of a Three-Phase Induction Motor

In this paper, we discuss the frequency characteristics of a three-phase induction motor theoretically and take up the transfer functions on. the speed variation to the small variation of supply voltage, supply frequency, and load torque. The frequency responses are affected considerably by the electrical time constant at the range of, high signal frequency, but these transfer functions may be approximated by the form of a first-order lag element as the value of mechanical time constant or the slip of a tested induction motor increases.