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The article proposes new methodological directions, models and methods of effective digital proportional-integral-differential (PID) control. The theoretic multiple models of the digital PID controller based on the discretization of the continuum model are proposed, differing in the component composition that significantly influences the dynamics of regulation. Mathematical models of digital control with the replacement of the integral in the continuum model by the Simpson's rule are proposed,doi:10.1088/1742-6596/1333/4/042027 fatcat:gigaz4slzbfdrptxzurf4rkd7a