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Figure P4.17 shows the free-body diagrams for planetary

Control Systems Engineering | 7th Edition | ISBN: 9781118170519 | Authors: Norman J. Nise ISBN: 9781118170519 162

Solution for problem 69 Chapter 4

Control Systems Engineering | 7th Edition

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Control Systems Engineering | 7th Edition | ISBN: 9781118170519 | Authors: Norman J. Nise

Control Systems Engineering | 7th Edition

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Problem 69

Figure P4.17 shows the free-body diagrams for planetary gear components used in the variable valve timing (VVT) system of an internal combustion engine (Ren, 2011). Here an electric motor is used to drive the carrier. Analysis showed that the electric motor with planetary gear load (Figure P4.17) may be represented by the following equation: cs GesEas GmsTcams where cs is the output carrier angular speed in rad/s, Ea(s) is the input voltage applied to the armature, and Tcamsis the input load torque. The voltage input transfer function, Ge(s), is Ges K RmJs D KKm 45 0:2s 1 and the load torque input transfer function, Gm(s), is Gms Rmk RmJs D KKm 5 0:2s 1 Find an analytical expression for the output carrier angular speed, ct, if a step voltage of 100 volts is applied at t = 0 followed by an equivalent load torque of 10 N-m, applied at t = 0.4 sec.

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Textbook: Control Systems Engineering
Edition: 7
Author: Norman J. Nise
ISBN: 9781118170519

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Figure P4.17 shows the free-body diagrams for planetary