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Modeling Electromechanical Systems: Problem Analysis and Mathematical Formulations

This document presents a comprehensive analysis of three modeling problems in electromechanical systems. Each problem requires the establishment of mathematical models organized in matrix form using generalized variables and inputs. Problem 1 involves energy equations for a motor, while Problem 2 explores the effects of a movable inductor core on inductance, and Problem 3 requires modeling with variable inputs. Each section encourages readers to engage in formulating solutions and clicking for provided answers, making it an interactive learning resource.

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Modeling Electromechanical Systems: Problem Analysis and Mathematical Formulations

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  1. HOMEWORK 07 Modeling of Electromechanical Systems Problem 1: Problem 2: Problem 3:

  2. z1 By 4 3 Jm , Bm JL 2 1 2 + Vk K2 Motor - z2 Ra , La Ki , Kb Problem 1: Energy equations considered in example 7.1 are given below; Input : Vk Generalized variables: qa, θm, θL Establish the mathematical model of the system and organize in matrix form. Click for answer.

  3. R L(x) x(t) Vk - + m k b Problem 2: In the system shown above, core of inductor is movable and the change of inductance via x is given below. Establish the mathematical model of the system. x(t) ve q(t) are the generalized variables, Vk(t) is the input. Click for answer.

  4. R2 R1 k2 k1 fk b L(x1) m1 C(x2) Vk - + m2 x1 x2 Problem 3: In the electromechanical system fk(t) and Vk(t) are the inputs. q(t), x1(t) and x2(t) are the generalized variables. Establish the mathematical model of the system. Click for answer.

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