07 Electro-Mechanical Systems
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Department of Mechanical Engineering, NTU National Taiwan University ENGINEERING Mechatronic and Robotic Systems Laboratory System Dynamics Yu-Hsiu Lee 7. Electro-Mechanical Systems
Transcript of 07 Electro-Mechanical Systems
Department of Mechanical Engineering, NTU
National Taiwan UniversityENGINEERINGMechatronic and Robotic Systems Laboratory
System Dynamics
Yu-Hsiu Lee
7. Electro-Mechanical Systems
11/18/2021 2Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Outline
• Energy converter
Force on a current-carrying wire and Lenz’s law
Working principle of brushed DC motor
• Geared motor and loads
Geared motor
Motor with load
• Motor control
Open-loop speed control
Closed-loop speed control
Closed-loop position control
Energy Converter
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Electromechanical Energy Conversion
• Current-carrying wire within a magnetic field
Straight wire
• Wire moving within a magnetic field (Lenz’s law)
Straight wire
Also called back emf
11/18/2021 5Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Schematic of a DC motor [KB07] • Motor torque
• Back emf
• Motor constant
[KB07] Kulakowski, Bohdan T., John F. Gardner, and J. Lowen Shearer. Dynamic modeling and control of engineering systems. Cambridge University Press, 2007.
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11/18/2021 6Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Schematic of a DC motor [KB07] • KVL circuit analysis
• Torque balance
• Laplace transform
[KB07] Kulakowski, Bohdan T., John F. Gardner, and J. Lowen Shearer. Dynamic modeling and control of engineering systems. Cambridge University Press, 2007.
Notice the coupling/interaction betweenelectrical and mechanical elements
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11/18/2021 7Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Schematic of a DC motor [KB07] • Laplace transform
• Current
• Transfer function
[KB07] Kulakowski, Bohdan T., John F. Gardner, and J. Lowen Shearer. Dynamic modeling and control of engineering systems. Cambridge University Press, 2007.
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11/18/2021 8Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Simulink block diagram
11/18/2021 9Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Simscape block diagram
11/18/2021 10Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Schematic of a DC motor [KB07] • Transfer function
[KB07] Kulakowski, Bohdan T., John F. Gardner, and J. Lowen Shearer. Dynamic modeling and control of engineering systems. Cambridge University Press, 2007.
First-order dynamics+
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11/18/2021 11Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Schematic of a DC motor [KB07] • Transfer function
In steady-state
[KB07] Kulakowski, Bohdan T., John F. Gardner, and J. Lowen Shearer. Dynamic modeling and control of engineering systems. Cambridge University Press, 2007.
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11/18/2021 12Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Schematic of a DC motor [KB07] In steady-state
Motor curves
[KB07] Kulakowski, Bohdan T., John F. Gardner, and J. Lowen Shearer. Dynamic modeling and control of engineering systems. Cambridge University Press, 2007.
No loadspeed
Stalltorque
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11/18/2021 13Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Brushed DC Motor
• Schematic of a DC motor [KB07] • Simplified transfer function model
Speed output
Position output
[KB07] Kulakowski, Bohdan T., John F. Gardner, and J. Lowen Shearer. Dynamic modeling and control of engineering systems. Cambridge University Press, 2007.
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Geared Motor and Loads
11/18/2021 15Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Geared Motor
• Schematic
1) KVL
2) Torque balance
• Combing 1) & 2):
• If there are N such actuators:
11/18/2021 16Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Geared Motor with Loads: Robot Manipulators
• Recall rigid body dynamics of a robot manipulator
• Combining actuator dynamics with rigid body dynamics
• Combing 1) & 2):
• If there are N such actuators:
Motor Robot
11/18/2021 17Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Geared Motor with Loads: Robot Manipulators
• Recall rigid body dynamics of a robot manipulator
• Combining actuator dynamics with rigid body dynamics
When gear ratios are large
• Combing 1) & 2):
• If there are N such actuators:
Only actuator dynamics remain
11/18/2021 18Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Example
• Schematic
• Load side
• Motor side
• Complete dynamics
Correspondence
11/18/2021 19Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Example
• Schematic
• Load side
• Motor side
• Open-loop velocity under small constant voltage
Less sensitive to gravitational effect.But the static gain is decreased.
Motor Control
11/18/2021 21Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
Open-Loop Speed Control
• Schematic
First-order model
Characteristics
Velocity change under unittorque disturbance.
11/18/2021 22Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Schematic
KVL with velocity feedback
Torque balance
Closed-Loop Speed Control
After substitution
Characteristics
Tachometer
Control
Smaller, but can be scaled
Faster response
Less affectedby disturbance
11/18/2021 23Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Schematic
• Block diagram
Closed-Loop Speed Control
Transfer function
Root locus
Tachometer
Control
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Re
Im
Increasing gain
11/18/2021 24Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Schematic
• Block diagram
Closed-Loop Speed Control
Transfer function
Root locus
Tachometer
Control
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UnstableRegion
11/18/2021 25Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Block diagram
Closed-Loop Speed Control
After substitution
Characteristics
Smaller, but can be scaled
Faster response
Less affectedby disturbance
11/18/2021 26Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Simulation results
Closed-Loop Speed Control
After substitution
Characteristics
Smaller, but can be scaled
Faster response
Less affectedby disturbance
11/18/2021 27Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Schematic
KVL with position feedback
Torque balance
Closed-Loop Position Control
After substitution
Characteristics
Control
Encoder
Asymptotically stable
Servo compliance
11/18/2021 28Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Schematic
• Block diagram
Closed-Loop Position Control
Transfer function
Root locus
Control
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Re
Im
Encoder
11/18/2021 29Mechatronic and Robotic Systems Laboratory, Department of Mechanical Engineering, NTU
• Schematic
• Block diagram
Closed-Loop Position Control
Transfer function
Root locus
Control
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Encoder
UnstableRegion
