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In this paper, the method of root locus separation for complex automatic control system is discussed, to illustrate the importance of mathematical analysis methods in the design of automatic control systems. The mathematical method used to solve the separation points of root locus includes heuristic method, Newton residual theorem method, tail quadratic factor method and MATLAB method. This paper introduced the principle of these mathematical methods, analyzed and compared the solution process. The mathematical techniques used to obtain the separation point by heuristics, leaving the item not near the separation point, can make up for the shortcomings of the trial method with great blindness, reduce the number of calculations and increase its applicability. The Newton remainder theorem and the tail two factor method are tedious, but Newton's remainder theorem is more accurate. The Matlab method is faster and simpler. Keywords—separation point of root trajectory, heuristic method, Newton residual theorem, tail second factor method, matlab

Application of Mathematical Analysis Method in the Teaching of Automatic Control Theory