Error Change Rate Research Articles

Systematic design of membership functions for fuzzy logic control of variable speed refrigeration system

The systematic design of membership functions (MFs) for the fuzzy logic control (FLC) of a variable speed refrigeration system (VSRS) is presented in this paper to reduce trial and error as well as dependence on expert knowledge. In particular, the influence of MFs on the error and error change rate of controlled variables is investigated in detail to verify the validity of the designed MFs. To this end, the range of MFs obtained based on the control accuracy and experimental data for the static and dynamic states of the VSRS were used as the criterion values. Two different values from the criterion were then used to compare the control performance through simulations and experiments. Some simulations and real experiments for the VSRS were conducted to verify the validity of the designed MFs. The experimental results showed good agreement with the simulation results. The error change rate and sampling time strongly affected the control performance of the VSRS in the transient state. Moreover, the desired control accuracy at steady-state, an essential element in the design specifications, was successfully achieved using the proposed approach. The suggested method can be applied using the control accuracy and simple experimental results from the static and dynamic states of the target system without depending on iterative work when designing MFs, which will be helpful for beginners.

Dynamic analysis of gear system under fractional-order PID control with the feedback of meshing error change rate

Based on the fractional-order proportional-integral-derivative (PID) control of the feedback of change rate of gear meshing error, the nonlinear dynamics problem of a spur gear pair is investigated. A model is established including backlash, time-varying stiffness, internal and external excitations and other factors, where the fractional-order PID control terms are also considered. The periodic solution is obtained based on the incremental harmonic balance method, and it is verified by the numerical solution. The effects of the coefficients and the orders of the fractional-order PID controller are analyzed in detail. The control performances of fractional-order PID controller and integer-order PID controller are compared. The results show that the fractional-order PID controller has good control performance for the gear meshing system. By changing the parameters of the controller, the resonance amplitude of the gear meshing system can be suppressed, and the resonance frequency of the gear meshing system can also be adjusted.

The Passive Series Stiffness That Optimizes Torque Tracking for a Lower-Limb Exoskeleton in Human Walking.

This study uses theory and experiments to investigate the relationship between the passive stiffness of series elastic actuators and torque tracking performance in lower-limb exoskeletons during human walking. Through theoretical analysis with our simplified system model, we found that the optimal passive stiffness matches the slope of the desired torque-angle relationship. We also conjectured that a bandwidth limit resulted in a maximum rate of change in torque error that can be commanded through control input, which is fixed across desired and passive stiffness conditions. This led to hypotheses about the interactions among optimal control gains, passive stiffness and desired quasi-stiffness. Walking experiments were conducted with multiple angle-based desired torque curves. The observed lowest torque tracking errors identified for each combination of desired and passive stiffnesses were shown to be linearly proportional to the magnitude of the difference between the two stiffnesses. The proportional gains corresponding to the lowest observed errors were seen inversely proportional to passive stiffness values and to desired stiffness. These findings supported our hypotheses, and provide guidance to application-specific hardware customization as well as controller design for torque-controlled robotic legged locomotion.

Human eye ocular component analysis for refractive state and refractive surgery.

To analyze the clinical factors influencing the human vision corrections via the changing of ocular components of human eye in various applications; and to analyze refractive state via a new effective axial length. An effective eye model was introduced by the ocular components of human eye including refractive indexes, surface radius (r1, r2, R1, R2) and thickness (t, T) of the cornea and lens, the anterior chamber depth (S1) and the vitreous length (S2). Gaussian optics was used to calculate the change rate of refractive error per unit amount of ocular components of a human eye (the rate function M). A new criterion of myopia was presented via an effective axial length. For typical corneal and lens power of 42 and 21.9 diopters, the rate function Mj (j=1 to 6) were calculated for a 1% change of r1, r2, R1, R2, t, T (in diopters) M1=+0.485, M2=-0.063, M3=+0.053, M4=+0.091, M5=+0.012, and M6=-0.021 diopters. For 1.0 mm increase of S1 and S2, the rate functions were M7=+1.35, and M8=-2.67 diopter/mm, respectively. These rate functions were used to analyze the clinical outcomes in various applications including laser in situ keratomileusis surgery, corneal cross linking procedure, femtosecond laser surgery and scleral ablation for accommodation. Using Gaussian optics, analytic formulas are presented for the change of refractive power due to various ocular parameter changes. These formulas provide useful clinical guidance in refractive surgery and other related procedures.

Correlation Between Multiple Electric Arc Furnace Operations and Unscheduled Power Flows in the Interconnection Lines at the Eastern Cross Border of ENTSO-E

In this paper, the correlation between unscheduled power flows in the interconnection lines at the eastern cross border of the European Network of Transmission System Operators for Electricity (ENTSO-E) and multiple electric arc furnace (EAF) operations in Turkey has been assessed. Turkey is interconnected to ENTSO-E at the eastern cross border via Greece and Bulgaria, with a 400-MW export and a 550-MW import agreement. In order to determine the degree of the relationship between the unscheduled power exchange between Turkey and Europe, and the multiple high-power EAF operations, Pearson correlation method has been employed. For this purpose, time-synchronized data of active power consumption have been collected from 17 major EAF plants during 1 week with a time resolution of 3 s, by using custom-design, synchronized power-quality (PQ) analyzers. A total peak-power consumption of nearly 1.5 GW of multiple EAF loads has been recorded. The results obtained have been evaluated by the use of the National Power Quality Monitoring System of Turkey, which continuously monitors the power flows in the interconnection lines of the ENTSO-E by PQ analyzers. The rate of change in total EAF power consumptions higher than 200 MW in less than 15 s against the rate of change in area control error (ACE) index is found to be closely correlated to each other, with a Pearson correlation coefficient (CC) of 0.8. Since the response of the frequency restoration reserve of power plants is much slower, such rapid fluctuations in the power consumption of multiple EAFs collectively result in uncontrollable power flows in the interconnection lines at the eastern cross border of ENTSO-E.

Temperature control for a vehicle climate chamber using chilled water system

The effective temperature control of a vehicle climate chamber was investigated. The temperature was regulated by electrical heater power and valve opening in the chilled water system. Cooling load and water flow rate through the adjusting valve were studied based on the distributed parameter model developed in a previous article. In order to ensure the flow capacity and increase linearity between the cooling side control output and the air temperature, two equal percentage valves were applied. The climate chamber has characteristics of large thermal inertia and non-linearity. Performance of a proportional–integral–derivative (PID) controller used in the existing system was not satisfactory, so a fuzzy self-tuning PID controller was designed. The PID gains were tuned online according to temperature error, error change rate, and air velocity using fuzzy logic. Model predictions showed that the fuzzy PID control stabilized the air temperature in a shorter time and with smaller overshoot and undershoot. The time averaged temperature error was reduced from 0.37°C to 0.09°C in the high temperature test, and that of the low temperature test was reduced from 0.42°C to 0.18°C.

Gain Scheduling of PID Controller Based on Fuzzy Systems

This paper aims to utilize fuzzy rules and reasoning to determine the controller parameters and the PID controller generates the control signal. The objective of this study is to simulate the proposed scheme on various processes and arrive at results providing better response of the system when compared with best industrial auto-tuning technique: Ziegler-Nichols. The proposed scheme is based upon the Ultimate Gain (Ku) and the Period (Tu) of the system. The error and rate of change in error gains are tuned manually to get the desired response using LabVIEW. This can also be done with various optimization techniques. A thumb rule for choosing the ranges for Kc, Kd and Ki has been obtained experimentally.

Dynamic optimization for robust path planning of horizontal oil wells

This paper considers the three-dimensional path planning problem for horizontal oil wells. The decision variables in this problem are the curvature, tool-face angle and switching points for each turn segment in the path, and the optimization objective is to minimize the path length and target error. The optimal curvatures, tool-face angles and switching points can be readily determined using existing gradient-based dynamic optimization techniques. However, in a real drilling process, the actual curvatures and tool-face angles will inevitably deviate from the planned optimal values, thus causing an unexpected increase in the target error. This is a critical challenge that must be overcome for successful practical implementation. Accordingly, this paper introduces a sensitivity function that measures the rate of change in the target error with respect to the curvature and tool-face angle of each turn segment. Based on the sensitivity function, we propose a new optimization problem in which the switching points are adjusted to minimize target error sensitivity subject to continuous state inequality constraints arising from engineering specifications, and an additional constraint specifying the maximum allowable increase in the path length from the optimal value. Our main result shows that the sensitivity function can be evaluated by solving a set of auxiliary dynamic systems. By combining this result with the well-known time-scaling transformation, we obtain an equivalent transformed problem that can be solved using standard nonlinear programming algorithms. Finally, the paper concludes with a numerical example involving a practical path planning problem for a Ci-16-Cp146 well.

A Variable Universe Self-Tuning Fuzzy-PI Speed Controller for Induction Motor with DTC-SVM

In the paper, To control the speed of induction motor drive with DTC-SVM, A variable universe self-tuning fuzzy-PI(VUFPI) controller was designed based on the concept of variable universe to generate the torque reference value, Two inputs of the fuzzy controller are speed error and error change rate, the output of the fuzzy controller are adjustment parameters (,) of PI controller parameters (Kp, Ki), the input and output variable universe of fuzzy controller were regulated by scale factor which is calculated according to error grade, The simulation results show that the proposed method has fast response speed and lower torque ripple.

Fuzzy logic controller design with unevenly-distributed membership function for high performance chamber cooling system

Fuzzy logic controller adopting unevenly-distributed membership function was presented with the purpose of enhancing performance of the temperature control precision and robustness for the chamber cooling system. Histogram equalization and noise detection were performed to modify the evenly-distributed membership functions of error and error change rate into unevenly-distributed membership functions. Then, the experimental results with evenly and unevenly distributed membership functions were compared under the same outside environment conditions. The experimental results show that the steady-state error is reduced around 40% and the noise disturbance is rejected successfully even though noise range is 60% of the control precision range. The control precision is improved by reducing the steady-state error and the robustness is enhanced by rejecting noise disturbance through the fuzzy logic controller with unevenly-distributed membership function. Moreover, the system energy efficiency and lifetime of electronic expansion valve (EEV) installed in chamber cooling system are improved by adopting the unevenly-distributed membership function.

A Satellite Ephemeris Correction Calculating Algorithm Based on the Hill Differential Equation

The Hill differential equation is used to describe the change characteristic of the ephemeris prediction error in order to calculate the satellite broadcast ephemeris error and the error change rate. After the ECEF coordinate system converses the satellite inertial coordinate system, both the satellite ephemeris correction and the correction accuracy can be calculated by the Kalman filter. When the GEO, IGSO and MEO satellites move over the China, the calculation algorithms based on the weighted least square, the velocity model of the Kalman filter and the Hill differential equation are compared in the computing performance of the ephemeris corrections by using the reference date of IGS website. The simulation results show that: the ephemeris correction solver value based on the Hill differential equation can accurately reflect the ephemeris error characteristics at the current time. And it is able to correctly reflect the perturbation impact for the satellite ephemeris error. The Hill differential equation method is more suitable at the master station for engineering application about the MEO, IGSO and GEO satellites.

Fuzzy PID Control for Valve-Controlled Cylinder Hydraulic System

A valve-controlled cylinder hydraulic system is used widely in engineering. The principle of the valve-controlled cylinder hydraulic system is presented. The fuzzy PID controller of valve-controlled cylinder hydraulic system is designed, and the simulation model is built. Based on the model, simulation analysis is carried out. The results show that the PID controller parameters can change with the variations of control error and control-error change rate according to fuzzy reasoning, the response error of valve-controlled cylinder is kept in a range of -0.06～0.1cm, and the required control accuracy can be obtained.

AC Position Servo System Controller of Aircraft Simulator Based on Genetic Algorithm Optimization

This paper analyzes nonlinear and uncertainties factors caused by the friction and clearance of ac servo system. a Fuzzy-PID controller based on Genetic Algorithm was designed. Adjust the three parameters of PID controller based on the error and error change rate ; Adjust the various parameters of the fuzzy-PID controller using genetic algorithm optimization; This method has better control effect on the AC of Meter systems than traditional PID controller. And both dynamic and steady performances were improved evidently

Research and Application of Human-Simulated Intelligent Controller

The principle of human-simulated intelligent controller (HSIC) and the application in industrial control have been discussed. The improved HSIC compensates and consumes the system according to different conditions combined by error and error change rate. Because the parameter tuning of HSIC is completed in programmable logic controller, the control strategy of HSIC is simple than that of PID algorithm and the system response speed is more quickly. The author suggests that the parameters of HSIC should be optimized to decrease the complex degree of parameter tuning process and to reduce system overshoot dramatically.

Accuracy of a GFR Estimating Equation Over Time in People With a Wide Range of Kidney Function

Change in glomerular filtration rate (GFR) is important for clinical decision making. GFR estimates from serum creatinine level provide an unbiased but imprecise estimate of GFR at single time points. However, the accuracy of estimated GFR over time is not well known. Longitudinal study of diagnostic test accuracy. 4 clinical trials with longitudinal measurements of GFR and serum creatinine on the same day, including individuals with and without kidney disease with a wide range of kidney function, diverse racial backgrounds, and varied clinical characteristics. GFR estimated using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation. GFR measured using urinary clearance of (125)I-iothalamate. Data included 19,735 GFR measurements in 3,531 participants during a mean follow-up of 2.6 years. Mean values at baseline for measured and estimated GFR and error (measured GFR - estimated GFR) were 73.1 (95% CI, 71.6 to 74.5), 72.7 (95% CI, 71.5 to 74.0), and 0.14 (95% CI, -0.35 to 0.63) mL/min/1.73 m(2), respectively. Mean rates of change in measured and estimated GFR and error were -2.3 (95% CI, -2.4 to -2.1), -2.2 (95% CI, -2.4 to -2.1), and -0.09 (95% CI, -0.24 to 0.05) mL/min/1.73 m(2) per year (P < 0.001, P < 0.001, and P = 0.2, respectively). Variability (ie, standard deviation) among participants in rate of change in measured GFR, estimated GFR, and error was 4.3, 3.4, and 3.3 mL/min/1.73 m(2) per year, respectively. Only 15% of participants had a rate of change in error >3 mL/min/1.73 m(2) per year, and only 2% had a rate of change in error >5% per year. Participants' characteristics were not available over time. The accuracy of GFR estimates did not change over time. Clinicians should interpret changes in estimated GFR over time as reflecting changes in measured GFR rather than changes in errors in the GFR estimates in most individuals.

Incremental Error Analysis of 3D Polygonal Model through MAYA API

Generally applications in computer graphics use very high detailed models. These models are too compound for the limited hardware capacity and take much time to render and to transmit. Related fields can benefit from simplification of complex polygonal models. This introduces errors in the models during the process of simplification. It is require to judge when to stop the simplification process as rate of error change in the model is not same in every step of simplification process. It is required to measure the error in the model during simplification to judge the quality of the 3D model at every stage. It is proposed to measure the error in the model at every stage and analyze the rate of change of error in the model as a valuable tool for managing data complexity. This algorithm is implemented on 4 different sets of models. Each set contains models at different number of polygon levels. Experiments are repeated to measure error on them at each level. In order to gain in both memory and speed, VC++ API is developed and created a MLL (Maya link library) to load as a plug-in in Maya.

Input vector optimization of feed-forward neural networks for fitting ab initio potential-energy databases

The variation in the fitting accuracy of neural networks (NNs) when used to fit databases comprising potential energies obtained from ab initio electronic structure calculations is investigated as a function of the number and nature of the elements employed in the input vector to the NN. Ab initio databases for H(2)O(2), HONO, Si(5), and H(2)C[Double Bond]CHBr were employed in the investigations. These systems were chosen so as to include four-, five-, and six-body systems containing first, second, third, and fourth row elements with a wide variety of chemical bonding and whose conformations cover a wide range of structures that occur under high-energy machining conditions and in chemical reactions involving cis-trans isomerizations, six different types of two-center bond ruptures, and two different three-center dissociation reactions. The ab initio databases for these systems were obtained using density functional theory/B3LYP, MP2, and MP4 methods with extended basis sets. A total of 31 input vectors were investigated. In each case, the elements of the input vector were chosen from interatomic distances, inverse powers of the interatomic distance, three-body angles, and dihedral angles. Both redundant and nonredundant input vectors were investigated. The results show that among all the input vectors investigated, the set employed in the Z-matrix specification of the molecular configurations in the electronic structure calculations gave the lowest NN fitting accuracy for both Si(5) and vinyl bromide. The underlying reason for this result appears to be the discontinuity present in the dihedral angle for planar geometries. The use of trigometric functions of the angles as input elements produced significantly improved fitting accuracy as this choice eliminates the discontinuity. The most accurate fitting was obtained when the elements of the input vector were taken to have the form R(ij) (-n), where the R(ij) are the interatomic distances. When the Levenberg-Marquardt procedure was modified to permit error minimization with respect to n as well as the weights and biases of the NN, the optimum powers were all found to lie in the range of 1.625-2.38 for the four systems studied. No statistically significant increase in fitting accuracy was achieved for vinyl bromide when a different value of n was employed and optimized for each bond type. The rate of change in the fitting error with n is found to be very small when n is near its optimum value. Consequently, good fitting accuracy can be achieved by employing a value of n in the middle of the above range. The use of interparticle distances as elements of the input vector rather than the Z-matrix variables employed in the electronic structure calculations is found to reduce the rms fitting errors by factors of 8.86 and 1.67 for Si(5) and vinyl bromide, respectively. If the interparticle distances are replaced with input elements of the form R(ij) (-n) with n optimized, further reductions in the rms error by a factor of 1.31 to 2.83 for the four systems investigated are obtained. A major advantage of using this procedure to increase NN fitting accuracy rather than increasing the number of neurons or the size of the database is that the required increase in computational effort is very small.

PID제어기와 신경회로망 제어기를 이용한 유도전동기의 속도제어에 관한 연구

산업 자동화의 고정밀도에 따라 직류서보 전동기는 강인제어가 요구되고 있다. 하지만 PID 제어기를 갖는 전동기 제어 시스템이 부하 외란의 영향을 받게되면 제어 시스템의 강인제어는 어렵게 된다. 이에 대한 보완적인 한 방법으로 본 논문에서는 전동기 제어시스템을 위한 PID-신경망 복합형 제어기법을 제시하였다. 신경망 제어기의 출력은 부하 외란 인가시에 발생되는 오차와 오차 변화율에 의해서 결정된다. 신경망 제어기를 이용한 직류서보 전동기의 강인제어는 시뮬레이션에 의하여 확인하였다. Robust control for DC servo motor is needed according to the highest precision of industrial automation. However, when a motor control system with PID controller has an effect of load disturbance, it is very difficult to guarantee the robustness of control system. As a compensation method solving this problem, in this paper, PID-neural network hybrid control method for motor control system is presented. The output of neural network controller is determined by error and rate of error change occurring in load disturbance. The robust control of DC servo motor using neural network controller is demonstrated by computer simulation.

CMET and Refractive Error Progression in Children

To assess whether genetic variation in cMET is associated with refractive error or change in refractive error over time. Cohort study. Discovery set (Set 1: N = 579 children; 403 cases, 176 controls). Confirmatory set (Set 2: N = 547 children; 338 cases, 209 controls). Children in the discovery set were genotyped for a panel of genetic markers within cMET. Markers that were found to be significantly associated with the presence of refractive error or more rapid change in refractive error were then genotyped in the confirmatory set. Presence or absence of myopia and the rate of change in refractive error over a 3-year follow-up period. Carriage of the variant cMET +110703 A allele was found to associate with increased susceptibility to myopia. The variant was also found to associate with a faster rate of change in refractive error in both the discovery set and the confirmatory cohort regardless of the initial refractory ability (School 1; chi(2) for trend P = 0.014) (Schools 2 and 3; chi(2) for trend = 5.42, P = 0.020) (combined N = 1126, overall chi(2) for trend = 10.90, P = 9.6 x 10(-4)). Carriage of the variant allele was also found to be significantly overrepresented in children within the fastest changing quartile (Q4: mean change of -3.01 D over 3 years) compared with the slowest (Q1: mean change of -0.28 D over 3 years) (P(Set1) = 0.004, P(Set2) = 0.02, Combined N = 559, P = 3.0 x 10(-4)). Our data implicate the involvement of cMET in the pathogenesis of myopia in general, as well as more rapid progression in refractive error regardless of the initial refractory ability. These results underline the importance of eye growth genes in the development of common myopia.

Hierarchical fuzzy controllers for an astronomical telescope tracking

The paper presents an application of fuzzy logic controller (FLC) with hierarchically structured rule base for a two-link direct drive Celestron telescope. The hierarchical fuzzy logic controller (HFLC) is implemented, as nonlinear blocks used in a control system, for supervision of PID controller for position tracking of the telescope driven by electric motors. The HFLC is composed of two FLC stages connected in cascade. The input variables, for the first stage, of the HFLC are the position error and the rate of change in the position error. Then the output from the first stage and the position error integral are used as input variables for the second stage of the HFLC PID. The simulation results of the proposed HFLC PID, when the telescope is subjected to a unit step in reference position, are compared with the PID controller. The dynamic responses of the HFLC PID improve the rise time, damping factor and settling time compared with the PID controller. Also, the proposed techniques, hierarchical fuzzy PID controller, reduce the computation time due to reduction of rule base. The simulation results show the effectiveness of the proposed HFLC PID controller scheme as a promising technique.