Roman Voliansky, Nataliya Krasnoshapka, Oleksii Statsenko, Iurii Shramko, Oleksandr Sadovoi, Felix Andika Dwiyanto
The paper deals with the design of methodological backgrounds for studying the perturbed motions of the generalized dynamical plant. These backgrounds are based on the interval methods' usage which makes it possible to define possible boundaries of plant's motions that are not exceeded during plant operations. We offer to determine plant boundary motions by using linear differential equations. The right-hand expressions of these equations depend on plant state variables, control signals, and some coefficients which are defined by plant parameters and nonlinearity boundaries equations factors. To simplify the solution of plant boundary equations we use the matrix Laplace-Carson operator form which gives us the possibility to define plant perturbed motions in a linear-like form. The benefits of the proposed approach are shown by studying the perturbed motion of the simple gravitational pendulum. During our studies, we found that the real plant motion always happens within certain boundaries and never exceeds them. This fact allows us to study the plant whose motions deviate from the desired one due to different parameters and structure, initial conditions, and control signals. The defined perturbed motions equation can be used to plant stability analysis, its dynamic optimization, or its control systems design. © 2022 IEEE.
National Technical University of Ukraine 'Igor Sikorsky Kyiv Polytechnic Institute', Department of Electromechanical Systems Automation and Electric Drives, Kyiv, Ukraine; Dniprovsk State Technical University, Electrical Engineering Department (Of Affiliation), Kamyanske, Ukraine; Dnipro University of Technology, Department of Electric Drive, Dnipro, Ukraine; Universitas Negeri Malang Organization, Department of Electrical Engineering, Malang, Indonesia