제어응용연구실 1 Modeling of Mechanical systems Ⅰ

제어응용연구실 2 CONTENTS ▶ Equations of Mechanical System ▶ Modeling of Mechanical System Elements

제어응용연구실 3 Introduction Point Point 1. 선형 / 비선형 모형과 시변 / 시불변 모형의 형태와 물리적인 의 미를 학습 2.Translational motion, Rotation Motion 의 운동 해석

제어응용연구실 4 Modeling of Mechanical System Elements

제어응용연구실 5 Translational Motion Translational Motion Modeling of Mechanical System Elements Mass Mass : An element that stores the kinetic energy of translational motion ▶ ( g is the gravitational acceleration constant ) ※ Mass inductance ※ Mass is analogous to inductance of electric networks

제어응용연구실 6 Modeling of Mechanical System Elements ※ Conversion Table

제어응용연구실 7 ※ Conversion Table Modeling of Mechanical System Elements

제어응용연구실 8 Modeling of Mechanical System Elements Force : 1 N = lb (force) = oz (force) Mass : 1kg = 1000g = lb (mass) = oz (mass) = slug Distance : 1 m = ft = in. 1 in. = 25.4 mm 1 ft = m Figure. Force-mass system M y (t) f (t)f (t) The force equation ――― ―――

제어응용연구실 9 Modeling of Mechanical System Elements Linear Spring Linear Spring ( K : the spring constant, or simply stiffness ) Figure. Force-spring system The force equation : An element that stores potential energy ※ Linear Spring capacitor ※ Linear Spring is analogous to a capacitor in electric networks

제어응용연구실 10 Modeling of Mechanical System Elements Friction Friction ― Viscous Friction Figure. Dashpot for viscous friction The force equation : A retarding force that is a linear relationship between the applied force and velocity. ( B : Viscous frictional coefficient )

제어응용연구실 11 Modeling of Mechanical System Elements ― Static Friction : A retarding force that tends to prevent motion from beginning. ― Coulomb Friction : A retarding force that has a constant amplitude with respect to the change of velocity.

제어응용연구실 12 Modeling of Mechanical System Elements Rotational Motion Rotational Motion Inertia Inertia : An element that stores the kinetic energy of rotational motion Figure. Torque-inertia system For instance, the inertia of a circular disk or shaft about its geometric axis is given by The torque equation

제어응용연구실 13 Modeling of Mechanical System Elements ― ― ― ―

제어응용연구실 14 Modeling of Mechanical System Elements Torsional Spring Torsional Spring Figure. Torque-torsional spring system The torque equation Friction for Rotational Motion Friction for Rotational Motion

제어응용연구실 15 Modeling of Mechanical System Elements Conversion ( Between Translational and Rotational Motions ) Conversion ( Between Translational and Rotational Motions ) Figure. Rotary-to-linear motion Control system ( lead screw) A load may be controlled to move along a straight line through a rotary motor-and-screw assembly.

제어응용연구실 16 Figure. Rotary-to-linear motion Control system ( rack and pinion) Modeling of Mechanical System Elements Figure. Rotary-to-linear motion Control system ( belt and pulley) A similar situation in which a rack -and-pinion is used as a mechanical linkage. The control of a mass through a pulley by a rotary motor, such as the control of a printwheel in an electric typewriter.

제어응용연구실 17 Modeling of Mechanical System Elements Gear Trains, Levers, and Timing Belts Gear Trains, Levers, and Timing Belts Figure. Gear train

제어응용연구실 18 Modeling of Mechanical System Elements Figure. Gear train with friction and inertia 1. The torque equation for gear 2 2. The torque equation on the side of gear 1 Example of torque equation Example of torque equation

제어응용연구실 19 Modeling of Mechanical System Elements 3. Converte ※ The following quantities are obtained when reflecting from gear 2 to gear 1 :

제어응용연구실 20 Equations of Mechanical System

제어응용연구실 21 Equations of Mechanical System Equations of Mechanical System Equations of Mechanical System Figure. Mass-spring-friction systemFigure. Free-body diagram Example of Mechanical system Example of Mechanical system

제어응용연구실 22 Equations of Mechanical System

제어응용연구실 23 Example of Mechanical system Example of Mechanical system Equations of Mechanical System

제어응용연구실 24 Equations of Mechanical System ― Force equations for the system ― State variables

제어응용연구실 25 Equations of Mechanical System ― State equations ― Output equations

제어응용연구실 26 Equations of Mechanical System ― State diagram

제어응용연구실 27 Equations of Mechanical System ― Applying the gain formula to the state diagram

제어응용연구실 28 Example of Mechanical system Example of Mechanical system ▲▲▲▲▲▲▲▲▲▲ ▲▲▲▲▲▲▲▲ Figure. Motor-load system Equations of Mechanical System

제어응용연구실 29 Equations of Mechanical System ― Torque equations for the system

제어응용연구실 30 Equations of Mechanical System ― State equations ― State diagram

제어응용연구실 31 Equations of Mechanical System ― Applying the gain formula to the state diagram