Control Step Size Research Articles

Small-block frequency estimators to control step size in phase-shifting interferometry

We derive an estimator for the step size in phase-shifting interferometry. Using a minimum of five samples, it avoids the occasional indeterminate results that afflict the traditional Carré step-size estimate. The estimator can be understood as a generalization of the modified-covariance frequency estimator for a real-valued sinusoid with an unknown mean. We describe its use in the NRC Gauge Block Interferometer for monitoring the motion of a phase-shifting mirror mount.

Dual-Branch-UNet: A Dual-Branch Convolutional Neural Network for Medical Image Segmentation

In intelligent perception and diagnosis of medical equipment, the visual and morphological changes in retinal vessels are closely related to the severity of cardiovascular diseases (e.g., diabetes and hypertension). Intelligent auxiliary diagnosis of these diseases depends on the accuracy of the retinal vascular segmentation results. To address this challenge, we design a Dual-Branch-UNet framework, which comprises a Dual-Branch encoder structure for feature extraction based on the traditional U-Net model for medical image segmentation. To be more explicit, we utilize a novel parallel encoder made up of various convolutional modules to enhance the encoder portion of the original U-Net. Then, image features are combined at each layer to produce richer semantic data and the model’s capacity is adjusted to various input images. Meanwhile, in the lower sampling section, we give up pooling and conduct the lower sampling by convolution operation to control step size for information fusion. We also employ an attention module in the decoder stage to filter the image noises so as to lessen the response of irrelevant features. Experiments are verified and compared on the DRIVE and ARIA datasets for retinal vessels segmentation. The proposed Dual-Branch-UNet has proved to be superior to other five typical state-of-the-art methods.

Derivation of the Reduction Formula of Sixth Order and Seven Stages Runge-Kutta Method for the Solution of an Ordinary Differential Equation

This paper is describing in detail the way we define the equations which give the formulas in the methods Runge-Kutta 6th order 7 stages with the incorporated control step size in the numerical solution of Ordinary Differential Equations (ODE). The purpose of the present work is to construct a system of nonlinear equations and then by solving this system to find the values of all set parameters and finally the reduction formula of the Runge-Kutta (6,7) method (6th order and 7 stages) for the solution of an Ordinary Differential Equation (ODE). Since the system of high order conditions required to be solved is complicated, all coefficients are found with respect to 7 free parameters. These free parameters, as well as some others in addition, are adjusted in such a way to furnish more efficient R-K methods. We use the MATLAB software to solve several of the created subsystems for the comparison of our results which have been solved analytically. Some examples for five different choices of the arbitrary values of the systems are presented in this paper.

Optimal path crossing the orientation exclusion zone of a robot with offset wrist

AbstractAn unexpected path reversal is discovered for a serial robot with an offset-axis wrist over a finite range of proximity to the wrist singularity. This is replicated by a kinematic model. A prior spherical-wrist method transits the singularity with limited joint rate and acceleration under a constant rate of tool traversal. Accurate position is maintained by controlling a small deviation in orientation. Extensions to the method for an offset wrist (1) find the least-maximum deviation, (2) identify and locate where a path reversal occurs, and (3) use this point to control step size in a high-order predictor-correction path following procedure.

Adaptive Step Size Control of Extended/Unscented Kalman Filter Using Event Handling Concept

This paper presents a novel (Extended/Unscented) Kalman Filter by augmenting the event handling procedure of Ordinary Differential Equation (ODE) solvers with the predictor-corrector scheme of Extended/Unscented discrete Kalman Filter (EKF/UKF) introducing a variable step size Kalman Filter. This innovation allows a new quality of precision while operating Kalman Filters. The original Kalman Filter is based on a time-discrete predictor-corrector scheme considering fixed step size. The main new idea is to introduce and control step size handling not introduced before. Step size control of EKF/UKF will increase the performance when applied to switching/stiff systems. The step size is controlled based on the current performance (EKF/UKF innovation) and is adapted during the estimation procedure based on an event handling algorithm. The proposed event handling algorithm consists of two parts: relaxing sample time and restricting sample time (ST). Relaxing procedure is used to avoid high computational time when no rapid change exists in system dynamics. Restricting procedure is considered to improve the estimation performance by decreasing the EKF/UKF step size in the case of fast dynamical behavior (switching/stiff behavior). Effectiveness of the proposed approach is verified considering the well-known Van der Pol oscillator as a common example of stiff systems.

Control proximal gradient algorithm for image $$\ell _1$$ ℓ 1 regularization

We consider a control proximal gradient algorithm (CPGA) for solving the minimization of a nonsmooth convex function. In particular, the convex function is an $$\ell _1$$ regularized least squares function derived by the discretized $$\ell _1$$ norm models arising in image processing. This proximal gradient algorithm with the control step size is attractive due to its simplicity. However, this method is also known to converge quite slowly. In this paper, we present a fast control proximal gradient algorithm by adding Nesterov step. It preserves the computational simplicity of proximal gradient methods with a convergence rate $$1/k^2$$ . It is proven to be better than the existing methods both theoretically and practically. The initial numerical results for performing the image deblurring demonstrate the efficiency of CPGA when it is compared to the existing fast iterative shrinkage-thresholding algorithms.

Improved Black Hole Algorithm Based on Golden Sine Operator and Levy Flight Operator

The black hole (BH) algorithm is a new type of natural heuristic algorithm inspired by the movement law of the “black hole” celestial body in the universe. BH algorithm has received extensive attention due to its advantages such as fewer parameters, simple algorithm structure and strong exploitation. For the shortcomings of poor exploaration and premature convergence of BH algorithm, the improved golden sine (G-S) operator is introduced into BH algorithm to greatly improve the exploaration. Then the Levy flight operator with controlled step size has become a better local search operator from the global search operator, so the improved Levy flight operator is introduced to further improve the exploitation of BH algorithm. Ultimately, the golden sine operator and Levy flight operator based black hole (GSLBH) algorithm is able to balance the exploaration with exploitation. GSLBH, BH, Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WAO), Firefly Algorithm (FA), Golden Sine Algorithm (Gold-SA) were adopted to carry out the simulation experiments with 17 benchmark functions, respectively, and the statistical data results are analyzed and compared. Finally, it can be concluded that the proposed improved black hole algorithm has better exploaration, and the convergence speed and accuracy of the algorithm have been further improved.

State feedback control and variable step size MPPT algorithm of three-level grid-connected photovoltaic inverter

In this paper, the state feedback linearization control technique is applied for controlling the power factor of a grid-connected multi-level photovoltaic inverter. By applying this technique, the nonlinear state model of three-level inverter – in the d–q reference frame – will be transformed into two equivalent linear subsystems. Hence, the pole placement linear control loops can be applied on these linear subsystems in order to separately control the grid power factor and the dc link voltage of the inverter. The control system includes also a Maximum Power Point Tracker (MPPT) based on variable step size incremental conductance algorithm. Compared with conventional fixed step size method, the variable step MPPT improves the speed and the tracking accuracy. It has been shown that the three-level inverter allows reduction of the THD of grid voltage and current as well as the reduction of the blocking voltage of the inverter switches.

Performance analysis of a distributed fixed-step power control algorithm via window concept in cellular mobile systems

In cellular mobile systems, the received carrier-to-interference ratio (CIR) can be maintained within the desirable range provided that the path gain remains approximately constant over a number of consecutive power control steps. However, when channels suffer short-term fading, it is not clear whether existing power control algorithms remain convergent. This paper proposes a distributed fixed-step power control algorithm with binary feedback via window concept for cellular mobile systems. The essence of the proposed algorithm is that the power control step size can be regulated by window size. The performance of the proposed scheme is analyzed in short-term fading channels. A sufficient condition for system stability is derived using a simple received CIR model and a power control window. It is shown herein that the bound of the received CIR of each user varies as a function of the target CIR, the size of the power control step and the link gain. The analysis and simulation results show that if the step size is properly set according to the window size, the proposed algorithm can achieve a small convergence region and a fast convergence rate.

Maneuvering control simulation of underwater vehicle based on combined discrete-event and discrete-time modeling

When designing or acquiring underwater vehicles such as submarines and torpedoes, it is necessary to predict their performance precisely and perform tests repeatedly using modeling and simulation at both the engineering level and the tactical engagement level. For simulation performed for analysis purposes at the engineering level, which requires a considerable amount of computation power, a discrete-time system simulation that computes significant values at every single unit time using the established mathematical model or engineering model is mainly employed. To simulate a complex or complicated task such as a traffic analysis or tactical measure of effectiveness (MOE) analysis at the engagement level, it is appropriate to use a discrete-event system simulation that causes transition between model states through the triggering of events on the basis of the passing of messages between simplified mathematical models coupled in various ways. In this paper, we studied a maneuvering control of underwater vehicle from the perspective of a combined discrete-event and discrete-time system simulation; the simulation model is established on the basis of discrete-event system specification (DEVS) formalism, which is a representative modeling formalism of a discrete-event system simulation. In detail, the simulation includes DEVS modeling implementations of simulation execution time control and discrete-time step size control in real time at the time of performing a discrete-time system simulation for the purpose of three-dimensional visualization or carrying out a performance analysis using the DEVS model. This hybrid approach makes possible to build a simulation-based expert system which supports the decision making for the acquisition of an underwater vehicle.

Input output feedback linearization control and variable step size MPPT algorithm of a grid-connected photovoltaic inverter

In this paper, the power factor of a grid-connected photovoltaic inverter is controlled using the input output Feedback Linearization Control (FLC) technique. This technique transforms the nonlinear state model of the inverter in the d–q reference frame into two equivalent linear subsystems, and then applies a pole placement linear control loops on this subsystem in order to separately control the grid power factor and the dc link voltage of the inverter. Maximum Power Point Tracker (MPPT) that allows extraction of maximum available power from the photovoltaic (PV) array has been included. This MPPT is based on variable step size incremental conductance method. Compared with conventional fixed step size method, the variable step MPPT improves the speed and the accuracy of the tracking.

Variable step size initial value algorithm for singular perturbation problems using locally exact integration

We consider quasilinear singular perturbation problems of the form ε y ″ + p ( x ) y ′ + q ( x , y ) = h ( x ) , x ∈ [ 0 , 1 ] ; y ( 0 ) = α , y ( 1 ) = β with a boundary layer at one end point. The original problem is reduced to an asymptotically equivalent linear first order initial-value problem (IVP). Then, a variable step size initial value algorithm is applied to solve this (IVP). The algorithm is based on the locally exact integration of quadratic linearized problem coefficients on a non-uniform mesh. Two term-recurrence relation with controlled step size is obtained. Several problems are solved to demonstrate the applicability and efficiency of the algorithm. It is observed that the present method approximates the exact solution very well.

Computational aspects of continuous–discrete extended Kalman-filtering

This paper elaborates how the time update of the continuous---discrete extended Kalman-filter (EKF) can be computed in the most efficient way. The specific structure of the EKF-moment differential equations leads to a hybrid integration algorithm, featuring a new Taylor---Heun-approximation of the nonlinear vector field and a modified Gauss---Legendre-scheme, generating positive semidefinite solutions for the state error covariance. Furthermore, the order of consistency and stability behavior of the outlined procedure is investigated. The results are incorporated into an algorithm with adaptive controlled step size, assuring a fixed numerical precision with minimal computational effort.

Novel artificial neural network with simulation aspects for solving linear and quadratic programming problems

In this paper linear and quadratic programming problems are solved using a novel recurrent artificial neural network. The new model is simpler and converges very fast to the exact primal and dual solutions simultaneously. The model is based on a nonlinear dynamical system, using arbitrary initial conditions. In order to construct an economy model, here we avoid using analog multipliers. The dynamical system is a time dependent system of equations with the gradient of specific Lyapunov energy function in the right hand side. Block diagram of the proposed neural network model is given. Fourth order Runge–Kutta method with controlled step size is used to solve the problem numerically. Global convergence of the new model is proved, both theoretically and numerically. Numerical simulations show the fast convergence of the new model for the problems with a unique solution or infinitely many. This model converges to the exact solution independent of the way that we may choose the starting points, i.e. inside, outside or on the boundaries of the feasible region.

Convergence analysis of distributed fixed‐step power control algorithm for cellular mobile systems

AbstractPower control plays a vital role in the operation of cellular systems. It has been shown that a power control mechanism with distributed fixed‐step control algorithm using a single bit can maintain the received carrier‐to‐interference ratio (CIR) within a desired range in long‐term fading channels. However, as far as the short‐term fading is concerned, whether such a power control algorithm remains convergent is not clear. In this work, a simple received CIR model is adopted to derive the condition that ensures system stability for short‐term fading channels. The bounds of the received CIR are also obtained. Furthermore, the effects of the power control step size and the time required for convergence are also analyzed. Copyright © 2007 John Wiley & Sons, Ltd.

Consecutive transmit power control ratio aided adaptive power control for UMTS

An adaptive power control algorithm is proposed to minimise power control errors at mobile speeds from 0 to 80 km/h in a UMTS system. The proposed algorithm adjusts its power control step size based on a new parameter called consecutive transmit power control ratio. Simulations of the proposed algorithm show that it outperforms fixed-step algorithms without any requirements for additional knowledge such as Doppler estimations.

Signaled Step Size for Downlink Power Control of Dedicated Channels in UTRA TDD

This paper discusses downlink inner loop power control of dedicated channels in UTRA TDD. The current UTRA TDD downlink power control is similar to one in UTRA FDD mode, that comprises of closed inner loop and quality based outer loop. However, due to the time division feature and associated fexibility with asymmetry of TDD, the inner loop can not react as fast as in FDD and it is affected by rapid changes in environment. Therefore, the effect of the inner loop algorithm to the performance of UTRA TDD network is studied in this paper. Especially, the use of asymmetric step sizes for "power up" and "power down" commands is evaluated in contrast to the conventional symmetric power adjustment. Since it would be beneficial for the downlink inner loop power control to reach the target SIR as fast as possible, the power control step size based on the difference between the UE measured SIR and target SIR would be the most desirable power adjustment. Since the effectiveness of this type of an algorithm depends on available signaling bandwidth that is used, a study is carried out to find the tradeoff between the signaling bandwidth and related network performance.

Nanostructuring surfaces by ion sputtering

Surface etching by ion sputtering can be used to patternsurfaces. Recent studies using the high-spatial-resolutioncapability of the scanning tunnelling microscope revealed in factthat ion bombardment produces repetitive structures at nanometrescale, creating peculiar surface morphologies ranging fromself-affine patterns to `fingerprint'-like and even regularstructures, for instance waves (ripples), chequerboards orpyramids. The phenomenon is related to the interplay between ionerosion and diffusion of adatoms (vacancies), which inducessurface re-organization. The paper reviews the use of sputteretching to modify `in situ' surfaces and thin films, producingsubstrates with well defined vertical roughness, lateralperiodicity and controlled step size and orientation.

Analysis of an up/down power control algorithm for the CDMA reverse link under fading

We analyze the performance of a code division multiple access (CDMA) reverse link a with an up/down power control algorithm in the presence of fading. We derive a stochastic nonlinear feedback control system model for the power controlled reverse link, and study the power control performance based on the nonlinear model using the technique of statistical linearization. We provide a general analysis framework that allows us to study the effect of mobile speed, power control step size, and fading channel parameters such as correlation coefficient and rate of fading on power control errors. Numerical results show excellent accuracy of our analysis, which can be used to design and optimize the system parameters without going through lengthy simulations. For example, in the presence of shadow fading, it is seen that a power control step size in the range of 0.5-1.3 dB is sufficient to keep power control errors near a minimum. In the case of Rayleigh fading, the standard deviation of power control errors grows quickly even at moderate mobile speeds.

Accurate and economical solution of the pressure-head form of Richards' equation by the method of lines

The pressure-head form of Richards' equation (RE) is difficult to solve accurately using standard time integration methods. For example, mass balance errors grow as the integration progresses unless very small time steps are taken. Further, RE may be solved for many problems more economically and robustly with variable-size time steps rather than with a constant time-step size, but variable step-size methods applied to date have relied upon empirical approaches to control step size, which do not explicitly control temporal truncation error of the solution. We show how a differential algebrain equation implementation of the method of lines can give solutions to RE that are accurate, have good mass balance properties, explicitly control temporal truncation error, and are more economical than standard approaches for a wide range of solution accuracy. We detail changes to a standard integrator, DASPK, that improves efficiency for the test problems considered, and we advocate the use of this approach for both RE and other problems involving subsurface flow and transport phenomena.