DISCRETE APPROXIMATION OF CONTINUOUS OBJECTS WITH MATLAB

This work is dedicated to the study of various discrete approximation methods for continuous links, which is theobligatory step in the digital control systems synthesis for continuous dynamic objects and the guidelines development for performing these opera-tions using the MATLAB programming system. The paper investigates such sampling methods as pulse-, step-, and linearly invariant Z-transformations, substitution methods based on the usage of numerical integration various methods and the zero-pole correspond-ence method. The paper presents examples of using numerical and symbolic instruments of the MATLABto perform these opera-tions, offers an m-function improved version for continuous systems discretization by the zero-pole correspondence method, which allows this method to approach as step-invariant as linearly invariant Z-transformations; programs for continuous objects discrete approximation in symbolic form have been developed, which allows to perform comparative analysis of sampling methods and sys-tems synthesized with their help and to study quantization period influence on sampling accuracy by analytical methods. A compari-son of discrete transfer functions obtained by different methods and the corresponding reactions in time to different signalsis per-formed. Usingof the developed programs it is determined that the pulse-invariant Z-transformationcan be usedonly when the input of a continuous object receives pulse signals, and the linear-invariant transformation should be used for intermittentsignals at the input. The paper also presents an algorithm for applying the Tustin method, which corresponds to the replacement of analogueinte-gration by numerical integrationusingtrapezoidal method. It is shown that the Tustin method is the most suitable for sampling of first-order regulators with output signal limitation. The article also considers the zero-pole correspondence method and shows that it has the highest accuracy among the roughmethods of discrete approximation.Based on the performed research, recommendations for the use of these methods in the synthesis of control systems for continuous dynamic objects are given.