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Figure 2.1 a. Block diagram representation of a system; b. block diagram representation of an interconnection of subsystems. Table 2.1 Laplace transform table. Table 2.2 Laplace transform theorems. Figure 2.2 Block diagram of a transfer function.

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## Figure 2.1 a. Block diagram representation of a system; b. block diagram representation of an interconnection of subsy

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**Figure 2.1 a.Block diagramrepresentation of a system;b.**block diagramrepresentationof aninterconnectionof subsystems ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Table 2.1Laplace transform table**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Table 2.2Laplace transform theorems**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.2 Block diagram of a transfer function**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Table 2.3Voltage-current, voltage-charge, and impedance**relationships for capacitors, resistors, and inductors ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.3RLC network**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.4Block diagram of series RLC electrical network**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.5Laplace-transformednetwork**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.6a. Two-loop electricalnetwork;b.**transformedtwo-loop electricalnetwork;c. block diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.7Block diagram of the network of Figure 2.6**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.8Transformednetwork readyfor nodal analysis**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.9Three-loopelectrical network**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.10a. Operationalamplifier;b. schematic for**aninverting operationalamplifier; c. inverting operational amplifier configured for transfer function realization. Typically, the amplifier gain, A, is omitted. ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.11Inverting operationalamplifier circuit for**Example 2.14 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.12General noninvertingoperational amplifiercircuit**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.13Noninvertingoperational amplifiercircuit**forExample 2.15 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.14Electric circuit forSkill-AssessmentExercise 2.6**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Table 2.4Force-velocity, force-displacement, and impedance**translational relationshipsfor springs, viscous dampers, and mass ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.15a. Mass, spring, and damper system; b. block**diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.16a. Free-body diagram of mass, spring, and damper**system;b. transformed free-body diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.17a. Two-degrees-of-freedom**translationalmechanicalsystem8;b. block diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.18a. Forces on M1 due only to motion of M1b. forces**on M1 due only to motion of M2c. all forces on M1 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.19a. Forces on M2 due only to motion of M2;b.**forces on M2due only to motionof M1;c. all forces on M2 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.20Three-degrees-of-freedomtranslationalmechanical**system ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.21Translationalmechanical systemfor**Skill-AssessmentExercise 2.8 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Table 2.5Torque-angular velocity, torque-angular**displacement, and impedancerotational relationships for springs, viscous dampers, and inertia ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.22a. Physical system; b. schematic; c. block**diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.23a. Torques on J1due only to themotion of J1b.**torques on J1due only to themotion of J2c. final free-bodydiagram for J1 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.24a. Torques on J2due only to themotion of J2;b.**torques on J2due only to themotion of J1c. final free-bodydiagram for J2 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.25Three-degrees-of-freedom rotationalsystem**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.26Rotational mechanical system for**Skill-AssessmentExercise 2.9 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.27A gear system**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.28Transfer functions for a. angular displacement in**lossless gears and b. torque in lossless gears ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.29a. Rotationalsystem drivenby gears;b. equivalent**system at the output after reflection of input torque;c. equivalent system at the inputafter reflection ofimpedances ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.30a. Rotational mechanical system with gears;b.**system after reflection of torques and impedances to the output shaft;c. block diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.31Gear train**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.32a. System using a gear train;b. equivalent system**at the input;c. block diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.33Rotational mechanical system with gears for**Skill-Assessment Exercise 2.10 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.34NASA flightsimulatorrobot arm**withelectromechanicalcontrol systemcomponents © Debra Lex. ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.35DC motor:a. schematic12;b. block diagram**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.36Typical equivalentmechanical loading on a motor**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.37DC motor driving a rotational mechanical load**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.38Torque-speed curves with an armature voltage,**ea,as a parameter ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.39a. DC motor and load;b. torque-speed curve;c.**block diagram ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.40Electromechanical system forSkill-Assessment**Exercise 2.11 ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.41Development ofseries analog:a. mechanical**system;b. desired electricalrepresentation;c. series analog;d. parameters forseries analog ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.42Series analog of mechanical system of Figure**2.17(a) ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.43Development ofparallel analog:a. mechanical**system;b. desired electricalrepresentation;c. parallel analog;d. parameters forparallel analog ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.44Parallel analog ofmechanical systemof Figure**2.17(a) ©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e**Figure 2.45a. Linear system;b. nonlinear system**©2000, John Wiley & Sons, Inc. Nise/Control Systems Engineering, 3/e

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