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A kind derivative algorithm is discussed and the difference of numerical derivative and physical derivative is analyzed. What is more important is that the first step error problem is proposed and its bad affection to the system stability is shown by using a first order system as an example. Also the reason for unstable phenomenon is analyzed by using differential method. At last, detailed numerical simulation is given to shown the rightness of the proposed main conclusion. Introduction The design problem of differentiator is always a difficult and hot issue in the field of control[1-4]. For linear differential, Kahlil (1994) designed a linear high gain tracking differentiator, provides a signal to derivative, but the differentiator in each layer may contain the disturbance, so the anti interference performance is poor [5]. Wang Xinhua analyzed the high order linear tracking [6] with multiple integral chain structure in 2010 and the nature and limitations of Ibrir [7] in 2004 for linear derivative tracking. This paper is based on the above reasons, the physical and digital differential difference is studied, especially the first step error of the derivative, and the error influence on the stability of the system is analyzed. Although the first-order system simple is taken as an example, but the results are of general significance and can be extended to general system. Model Description To make the main result more easy to understand, the below first order system is taken as an example to show the whole analysis process. u x x + = 3  (1) And the control objective is to design a control law such that the system state x can trace the desired value d x . But the main purpose of this paper is to show the realization of derivative algorithm and all possible problems that will cause the system unstable. Analysis of Difference between Numerical Derivative and Physical Derivative with Different First Step Value Define a new variable as d x x e − = , then it holds: 3 3 d e e u x = + +  (2) Design a PD control law as below: 6 3 u e e = − −  (3) Then it can be substitute into the original system as 3 3 4 4 d e e x − = +  (4) And according to above design, the system should be stable, but in fact the system is unstable in real simulation, which can see below figures. 2nd International Conference on Advances in Mechanical Engineering and Industrial Informatics (AMEII 2016) © 2016. The authors Published by Atlantis Press 1608 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 -10 -8 -6 -4 -2 0 2 4 x 10 304

Difference between Numerical Derivative and Physical Derivative Realization and Its Affection to Stability Analysis