ELG 4152 Modern Control

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ELG 4152 Modern Control
Professor Riadh Habash

• Team Member
• Min Shi, 3150752
• Yuxiang Chen, 3481495
• Yichen Fan, 3588950
• Peng Liang, 3520871

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Introduction

• Hybrid Control over induction servo motor.
• Application manipulators.
• Automobile industry
• Ship building industry
• Aerospace industry
• Other fields needs heavy lifting by any
  manipulators.
• Induction Servo Motor Characteristics
• Heavy duty, good torque
• Fast acceleration
• Accurate positioning
• Low armature inductance, low electrical time
  constant
• Often seen with brushed
• Commutation required
• Regular maintenance
• Highly non-linear, controller needed
• Higher cost

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Reference

• R.J. Wai, C.-M. Lin and C.-F. Hsu Hybrid Control
  for Induction Servo Motor (IEEE Proc. Control
  Theory Appl, Vol 149, No. 6, pp.555-561 November
  2002)
• Rong-Jong Wai Robust Control for Induction Servo
  Motor Drive (Department of Electrical
  Engineering Yuan Ze University,2001)
• F.-J. Lin, R.-J.Wai Hybrid controller using a
  neural network for a PM synchronous servo motor
  drive (IEEE Proc. Control Theory Appl, Vol 145,
  No. 3,pp.223-229, May 1998)
• Rong-Jong Wai, Kuo-Min Lin, and Chung-You Lin
  Total Sliding-Mode Speed Control of
  Field-Oriented Induction Motor Servo Drive
  (Department of Electrical Engineering, Yuan Ze
  University, Chung-Shan Institute of Science and
  Technology)
• R. Firoozian, T. J. Lim COMPARISON OF PID AND
  ACTIVE CONTROL TECHNIQUES FOR ELECTRO-HYDRAULIC
  SERVO MOTORS (Department of Mechanical Process
  Engineering, Univemity of Sheffield)
• Rong-Jong Wai Development of Intelligent
  Position Control System Using Optimal Design
  Technique (IEEE TRANS INDUSTRIAL ELECTRONICS,
  VOL. 50, pp.219-231, FEBRUARY 2003)
• http//www.hansen-motor.com/servo-motors.htm

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Induction Servo Motor

• The induction servomotor we used in our project
  is a 3phase Y-connected four-pole 800 W 60 Hz 120
  V/5.4 A type motor.
• The mechanical equation of the induction
  servomotor drive can be represented as
• Where ? is the motor position U(t) is the
  control effort. An, Bn are given
• An-B/J -1.1172 (srad)-1
  BnKt/J101.4854 (As2)-1
• B,J,Kt are constant for servo motor
• Kt0.4851Nm/A J0.00478 Nms2B0.00534
  Nms/rad

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Objective

• Our objective is to control a induction servo
  motor position with 2 different hybrid controls
  from Robust Control, Computed Torque and
  Sliding Surface controlling methods.
• Figures and graphics will be shown for each
  controlling methods and also for Hybrid methods
  for comparison.

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Solution(1)---PID

• PID controller, the most conventional method.
• However, the performance of PID controller can be
  significantly compromised when the controlled
  system is highly nonlinear (as servo motors), and
  has large uncertainty (i.e. external torque).

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Solution (2)---other methods

• The following methods are the most common ones
  for induction servo motors controlling
• Robust
• Computed torque
• Sliding mode

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Advanced Control

• Besides the methods we mentioned above, there are
  two advanced control methods that are commonly
  adopted by the industry.
• Fuzzy logic feed back control system
• Neural network control system
• But due to their complexity for testing and
  implementation, we are not going to use these two
  methods in our control system.

Hybrid Control

• Hybrid 1 Adding Sliding surface before error
  goes into Robust Control
• Hybrid 2 Adding Computed Torque into Robust
  Control

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Robust Mode

• Advantages
• The error caused by uncertainties will be
  compensated.
• Insensitive to the uncertainties variation.
• Disadvantages
• More sensitive to the external force compare to
  Sliding Surface method.
• Large control effort (expenditure) compare to
  Computed Torque method.
• More complex electric circuit.

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Robust

• Simulink Diagram

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Robust

• Robust Control Law

• Xp is defined as Xp? ?T
• ? rotor position
• ? rotor speed

• The equation for

• The equation for K

• Ec is defined as Ec
• e is equivalent to ?e

• The equation for

• is the pseudo inverse of

1.25 1.25

• R is the desired input

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Graphic results with no uncertainties (external
torque)

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position follows the reference model quite
  well
• Control effort is larger than computed torque but
  smaller than sliding mode.
• Error is from -0.3 to 0.3.

Control Effort

• Error

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Results with external load disturbance of 0.5Nm
occurring at 5s

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position still quite follows the reference
  model, but is worse than sliding mode.
• Control effort jumped to 1 at 5s.
• An Error change at 6s.

• Control Effort

Error
END CYX
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Sliding Mode

• Advantages
• Improve performance based on computed torque
• Insensitive to the uncertainties variation
• Disadvantages
• Very large control effort

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Sliding Mode

• Simulink diagram

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Sliding Mode

• Sliding mode law

• Control law for Ueq

• Control law for Uvs

• Where s(t) is the output of sliding surface,
  which is defined as follow

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Results with no uncertainties

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position follows the reference model quite
  well
• Control effort is larger than computed torque
• Error is from -0.1 to 0.1

Control Effort

• Error

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Results with external load disturbance of 0.5Nm
occurring at 5s

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position still quite follows the reference
  model with uncertainties
• Control effort very large but still around zeros.
  
• Error is from -0.1 to -.02, but keep steady

• Control Effort

Error
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Computed Torque

• Advantages
• Conventional
• Relatively Lowest control effort
• High performance if no uncertainties
• Disadvantages
• The stability will be destroyed when
  uncertainties occur

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Computed Torque

• Simulink Diagram

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Computed Torque

• Computed torque law

- ?e is the tracking error, defined as
?e ?- ?d
-K1, and K2 should match with the Hunuitz
polynomial equation, that is the roots of the
following eqution lie open left-half of complex
plane.
Here, we choose K116, K264
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Results with no uncertainties

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position follows the reference model quite
  well
• Control effort is relatively low
• Error is from -0.15 to 0.15

• Control Effort

• Error

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Results with external load disturbance of 0.5Nm
occurring at 5s

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• System stability of rotor position control failed
• Control effort jumped to 1 at 5s
• Error jumped to -1.5 at 5s without changing the
  P-P value

• Control Effort

Error
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Midstage Summary
Controller Error Computation effort Application 2 different Hybrid Control System will be presented in the coming part
Robust Control plants with a bit more expensive but better behavior over external conditions 2 different Hybrid Control System will be presented in the coming part
Computed Torque Fields where motor will not experience any obvious external torque 2 different Hybrid Control System will be presented in the coming part
Sliding Mode With a strong budget, this controlling method gives best error resistance 2 different Hybrid Control System will be presented in the coming part
Best Medium Worst Best Medium Worst Best Medium Worst Best Medium Worst Best Medium Worst
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Improvement

• All the three methods has significant drawbacks.
• The tracking error still too large for all these
  methods.
• The performance and control effort can be further
  improved by using hybrid control system.

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Hybrid 1 RobustSliding surfance

• Advantages
• The best performance for both with and without
  uncertainties.
• Less insensitive to the variation of parameters.
• Disadvantages
• Control effort is relatively large.

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Hybrid 1

• Simulink Diagram

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Hybrid1

• Control law
• The sliding surface is added before the tracking
  error ?e goes into the Robust control.
• Sliding surface

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Results with no uncertainties

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position almost the same as the reference
  model
• Control effort is relatively large.
• Error is from -0.022 to 0.028.

Control Effort

• Error

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Results with external load disturbance of 0.5Nm
occurring at 5s

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position still very close to the reference
  model
• Control effort jumped to 1 at 5s.
• An Error change at 6s, but the error is still
  very small.

• Control Effort

Error
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Hybrid 2 RobustComputed Torque

• Advantages
• The better performance without uncertainties.
• Very small control effort for both with and
  without uncertainties.
• Disadvantages
• Performance gets bad with uncertainties, but will
  compensate later on.

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Hybrid 2

• Simulink Diagram

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Hybrid 2

• Control law
• The control effort is defined as
• U(t)Ua(t)Ub(b)
• Ua(t) is the control effort from the robust.
• Ub(t) is the control effort from the computed
  torque.

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Results with no uncertainties

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position almost the same as the reference
  model
• Control effort is very small.
• Error is from -0.033 to 0.04.

Control Effort

• Error

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Results with external load disturbance of 0.5Nm
occurring at 5s

• rotor position vs reference model
• (Dash line for reference model)

• Simulink results
• Rotor position affect by the uncertainty, but
  compensates later on.
• Control effort has no change.
• An Error change at 6s, but is getting smaller
  gradually.

• Control Effort

Error
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Comparison

• Common improvement
• Both hybrid control systems improve the
  performance significantly.
• Trade-off
• Hybrid control 1 has better performance and less
  sensitive to external torque, but with a larger
  control effort.
• Hybrid control 2 has less control effort, but
  with a larger tracking error, especially with
  external torque.

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Final Conclusion

• Our new hybrid control systems decreases the
  tracking error at both conditions.
• But Our new methods has a trade-off in error
  tracking and control effort.
• Although we did not optimize every part, our two
  new methods are the better choice, and one of the
  hybrid control may be recommend to meet the
  specification requirement.

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• Thank you very much!
• ??!
• merci beaucoup!
• Any Questions?