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3. Consider the following DC servomotor problem: La lell Fixed field llle R. O (t) Ja v, (t) e (t) Output angle 0,(t), Ba Ni B1 Figure 1 Servomotor plant schematic

3. Consider the following DC servomotor problem: La lell Fixed field llle R. O (t) Ja v, (t) e (t) Output angle 0,(t), Ba Ni B1 Figure 1 Servomotor plant schematic

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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3. Consider the following DC servomotor problem: La lell Fixed field R. O (t) v, (t) e (t) Ja Output angle 0,(t), Ba Ni B1 Figure 1 Servomotor plant schematic elll
Transcribed Image Text:3. Consider the following DC servomotor problem: La lell Fixed field R. O (t) v, (t) e (t) Ja Output angle 0,(t), Ba Ni B1 Figure 1 Servomotor plant schematic elll
For the system parameters given below, find the transfer function from the input voltage to the shaft position Quanser SRV-02 System datasheet parameters: Armature resistance Ra = 2.6 N • Armature inductance La = 0.18 × 10-3 H • Back emf constant Km = 7.68 x 10 -3 V/(rad/s) N. Low-gear gear ratio K, = N = 14 The induced motor torque that is delivered to the load is reduced by the motor rotational loss inefficiency and the gearbox inefficiency: Tm = NmN,K;ia, where • Ideal motor torque constant K, = 7.68 x 10 -3 N-m/A • Motor efficiency due to rotational loss 7m = 0.69 • Internal gearbox efficiency ng = 0.90 • Net motor torque constant K, = NmNgK, = 4.77 x 10-³ N-m/A The total motor armature inertia is the sum of the rotor inertia and the tachometer inertia: • Rotor inertia Jrotor = 3.90 x 10-7 kg-m? • Tachometer inertia Jrach = 7.06 x 10-8 kg-m? Armature inertia Ja = Jrotor + Jrach = 4.606 x 10 -7 kg-m? Equivalent low-gear load inertia Jz = 2.08 x 10-5 kg-m² Load-side equivalent low-gear viscous damping coefficient: Beg.ioad N2 Ba + B2 = 1.5 x 10-3 N-m/(rad/s)
Transcribed Image Text:For the system parameters given below, find the transfer function from the input voltage to the shaft position Quanser SRV-02 System datasheet parameters: Armature resistance Ra = 2.6 N • Armature inductance La = 0.18 × 10-3 H • Back emf constant Km = 7.68 x 10 -3 V/(rad/s) N. Low-gear gear ratio K, = N = 14 The induced motor torque that is delivered to the load is reduced by the motor rotational loss inefficiency and the gearbox inefficiency: Tm = NmN,K;ia, where • Ideal motor torque constant K, = 7.68 x 10 -3 N-m/A • Motor efficiency due to rotational loss 7m = 0.69 • Internal gearbox efficiency ng = 0.90 • Net motor torque constant K, = NmNgK, = 4.77 x 10-³ N-m/A The total motor armature inertia is the sum of the rotor inertia and the tachometer inertia: • Rotor inertia Jrotor = 3.90 x 10-7 kg-m? • Tachometer inertia Jrach = 7.06 x 10-8 kg-m? Armature inertia Ja = Jrotor + Jrach = 4.606 x 10 -7 kg-m? Equivalent low-gear load inertia Jz = 2.08 x 10-5 kg-m² Load-side equivalent low-gear viscous damping coefficient: Beg.ioad N2 Ba + B2 = 1.5 x 10-3 N-m/(rad/s)
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