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Data Acquisition Part 7

Tham khảo tài liệu 'data acquisition part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Minimum Data Acquisition Time for Prediction of Periodical Variable Structure System 171 necessary in case of changes of integration step only. It is more convenient to use methods for discretisation where state transient matrix exp A.t can be expressed in semi-symbolic form using numerical technique Mann 1982 . Unlike the expansion of the matrix into Taylor series these methods need a numerical calculation of characteristic numbers and their feature is the calculation with negligible residual errors. So if the linear system is under investigation its behaviour during transients can be predicted. This is not possible or sufficient for linearised systems with periodically variable structure. Although the use of numerical solution methods and computer simulation is very convenient some disadvantages have to be noticed system behaviour nor local extremes of analysed behaviours can not be determined in advance the calculation can not be accomplished in arbitrary time instant as the final values of the variables from the previous time interval have to be known the calculations have to be performed since the beginning of the change up to the steady state very small integration step has to be employed taking numerical non- stability into account it means the step of about 10-6 s for the stiff systems with determinant of very low value. It follows that system solution for desired time interval lasts for a relatively long time. The whole calculation has to be repeated for many times for system parameters changes and for the optimisation processes. This could be unsuitable when time is an important aspect. That is why a method eliminating mentioned disadvantages using simple mathematics is introduced in the following sections. 2.1 Analytical method of a transient component separation under periodic nonharmonic supply Linear dynamic systems responses can also be decomposed into transient and steady-state components of a solution Mayer et al. 1978 Mann 1982 x t Xp t xu t 4 The