Analysis and control of micro-stepping characteristics of ultrasonic motor

Micro-stepping motion of ultrasonic motors satisfies biomedical applications, such as cell operation and nuclear magnetic resonance, which require a precise compact-structure non-magnetization positioning device. When the pulse number is relatively small, the stopping characteristics have a non-negligible effect on the entire stepwise process. However, few studies have been conducted to show the rule of the open-loop stepwise motion, especially the shutdown stage. In this study, the modal differences of the shutdown stage are found connected with amplitude and velocity at the turn-off instant. Changes of the length in the contact area and driving zone as well as the input currents, vibration states, output torque, and axial pressure are derived by a simulation model to further explore the rules. The speed curves and vibration results in functions of different pulse numbers are compared, and the stepwise motion can be described by a two-stage two-order transfer function. A test workbench based on the Field Programmable Gate Array is built for acquiring the speed, currents, and feedback voltages of the startup–shutdown stage accurately with the help of its excellent synchronization performances. Therefore, stator vibration, rotor velocity, and terminal displacements under different pulse numbers can be compared. Moreover, the two-stage two-order model is identified on the stepwise speed curves, and the fitness over 85% between the simulation and test verifies the model availability. Finally, with the optimization of the pulse number, the motor achieves 3.3 µrad in clockwise and counterclockwise direction.

THEORY AND APPLICATION OF FRACTIONAL STEP CHARACTERISTIC FINITE DIFFERENCE METHOD IN NUMERICAL SIMULATION OF SECOND ORDER ENHANCED OIL PRODUCTION

A kind of second-order implicit fractional step characteristic finite difference method is presented in this paper for the numerically simulation coupled system of enhanced （chemical） oil production in porous media. Some techniques, such as the calculus of variations, energy analysis method, commutativity of the products of difference operators, decomposition of high-order difference operators and the theory of a priori estimates are introduced and an optimal order error estimates in l^2 norm is derived. This method has been applied successfully to the numerical simulation of enhanced oil production in actual oilfields, and the simulation results ate quite interesting and satisfactory.

Characteristic fractional step finite difference method for nonlinear section coupled system

For the section coupled system of multilayer dynamics of fluids in porous media, a parallel scheme modified by the characteristic finite difference fractional steps is proposed for a complete point set consisting of coarse and fine partitions. Some tech- niques, such as calculus of variations, energy method, twofold-quadratic interpolation of product type, multiplicative commutation law of difference operators, decomposition of high order difference operators, and prior estimates, are used in theoretical analysis. Optimal order estimates in 12 norm are derived to show accuracy of the second order approximation solutions. These methods have been used to simulate the problems of migration-accumulation of oil resources.

CONVERGENCE ANALYSIS OF MIXED VOLUME ELEMENT-CHARACTERISTIC MIXED VOLUME ELEMENT FOR THREE-DIMENSIONAL CHEMICAL OIL-RECOVERY SEEPAGE COUPLED PROBLEM

The physical model is described by a seepage coupled system for simulating numerically three-dimensional chemical oil recovery, whose mathematical description includes three equations to interpret main concepts. The pressure equation is a nonlinear parabolic equation, the concentration is defined by a convection-diffusion equation and the saturations of different components are stated by nonlinear convection-diffusion equations. The transport pressure appears in the concentration equation and saturation equations in the form of Darcy velocity, and controls their processes. The flow equation is solved by the conservative mixed volume element and the accuracy is improved one order for approximating Darcy velocity. The method of characteristic mixed volume element is applied to solve the concentration, where the diffusion is discretized by a mixed volume element method and the convection is treated by the method of characteristics. The characteristics can confirm strong computational stability at sharp fronts and it can avoid numerical dispersion and nonphysical oscillation. The scheme can adopt a large step while its numerical results have small time-truncation error and high order of accuracy. The mixed volume element method has the law of conservation on every element for the diffusion and it can obtain numerical solutions of the concentration and adjoint vectors. It is most important in numerical simulation to ensure the physical conservative nature. The saturation different components are obtained by the method of characteristic fractional step difference. The computational work is shortened greatly by decomposing a three-dimensional problem into three successive one-dimensional problems and it is completed easily by using the algorithm of speedup. Using the theory and technique of a priori estimates of differential equations, we derive an optimal second order estimates in 12 norm. Numerical examples are given to show the effectiveness and practicability and the method is testified as a powerful tool to solve the important problems.

Direct Digital Frequency Control Based on the Phase Step Change Characteristic between Signals

We present a new digital phase lock technology to achieve the frequency control and transformation through high precision multi-cycle group synchronization between signals without the frequency transformation circuit. In the case of digital sampling, the passing zero point of the phase of the controlled signal has the phase step characteristic, the phase step of the passing zero point is monotonic continuous with high resolution in the phase lock process, and using the border effect of digital fuzzy area, the gate can synchronize with the two signals, the quantization error is reduced. This technique is quite different from the existing methods of frequency transformation and frequency synthesis, the phase change characteristic between the periodic signals with different nominal is used. The phase change has the periodic phenomenon, and it has the high resolution step value. With the application of the physical law, the noise is reduced because of simplifying frequency transformation circuits, and the phase is locked with high precision. The regular phase change between frequency signals is only used for frequency measurement, and the change has evident randomness, but this randomness is greatly reduced in frequency control, and the certainty of the process result is clear. The experiment shows that the short term frequency stability can reach 10-12/s orders of magnitude.

Simple PID Parameter Tuning Method Based on Outputs of the Closed Loop System

Most of the existing PID parameters tuning methods are only effective with pre-known accurate system models, which often require some strict identification experiments and thus infeasible for many complicated systems. Actually, in most practical engineering applications, it is desirable for the PID tuning scheme to be directly based on the input-output response of the closed-loop system. Thus, a new parameter tuning scheme for PID controllers without explicit mathematical model is developed in this paper. The paper begins with a new frequency domain properties analysis of the PID controller. After that, the definition of characteristic frequency for the PID controller is given in order to study the mathematical relationship between the PID parameters and the open-loop frequency properties of the controlled system. Then, the concepts of M-field and θ-field are introduced, which are then used to explain how the PID control parameters influence the closed-loop frequency-magnitude property and its time responses. Subsequently, the new PID parameter tuning scheme, i.e., a group of tuning rules, is proposed based on the preceding analysis. Finally, both simulations and experiments are conducted, and the results verify the feasibility and validity of the proposed methods. This research proposes a PID parameter tuning method based on outputs of the closed loop system.

A Mixed-finite Volume Element Coupled with the Method of Characteristic Fractional Step Difference for Simulating Transient Behavior of Semiconductor Device of Heat Conductor And Its Numerical Analysis

The mathematical system is formulated by four partial differential equations combined with initial- boundary value conditions to describe transient behavior of three-dimensional semiconductor device with heat conduction. The first equation of an elliptic type is defined with respect to the electric potential, the successive two equations of convection dominated diffusion type are given to define the electron concentration and the hole concentration, and the fourth equation of heat conductor is for the temperature. The electric potential appears in the equations of electron concentration, hole concentration and the temperature in the formation of the intensity. A mass conservative numerical approximation of the electric potential is presented by using the mixed finite volume element, and the accuracy of computation of the electric intensity is improved one order. The method of characteristic fractional step difference is applied to discretize the other three equations, where the hyperbolic terms are approximated by a difference quotient in the characteristics and the diffusion terms are discretized by the method of fractional step difference. The computation of three-dimensional problem works efficiently by dividing it into three one-dimensional subproblems and every subproblem is solved by the method of speedup in parallel. Using a pair of different grids （coarse partition and refined partition）, piecewise threefold quadratic interpolation, variation theory, multiplicative commutation rule of differential operators, mathematical induction and priori estimates theory and special technique of differential equations, we derive an optimal second order estimate in L2-norm. This numerical method is valuable in the simulation of semiconductor device theoretically and actually, and gives a powerful tool to solve the international problem presented by J. Douglas, Jr.