Against at weak robust and low precision of standard PID,a nonlinear and high precision PID based on repeatable error compensation is put forward in this paper.

The Research of Fuzzy Neural Network on Solving Error Reflection Phenomenon in Machining;

The error reflection phenomenon in machining makes selection of machining parameters mainly depend on worker’s experience because of the complex non-linear relationship among error reflection coefficient and several factors such as feed rate,hardness of work piece and so on.

The error reflection in machining parameters selection mainly depended on workers experience.

Measure and judgement of current transformer s composite error;

Measuring methods of composite errors on current transformer;

The algorithm and realization of a newly developed tester of composite errors including the angle error, ratio error and a harmonic-wave analyzitor are presented.

The paper presents the mathematic modeling of complicated error by optimal knot spline function, which can automatically separate not only the error with secondary low frequency but also the stochastic error from complicated error data.

By minimizing the absolute replication error,the optimal hedging volatility is yielded,namely the adjusted volatility,and then this adjusted volatility with martingale approach is integrated to achieve the optimal portfolio in presence of transaction costs and trading rest.