DC Machine

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Introduction to Feedback Control of
Electromechanical Systems
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Introduction to Feedback Control of
Electromechanical Systems

• Proportional (P), proportional integral (PI),
  proportional integral derivative (PID) control
  algorithms are widely used in electromechanical
  systems.
• The objective is to solve practical problems
  using PID type control algorithms for solving
  the motion control problems for non linear
  electromechanical systems.
• To understand the basic foundations in control of
  electric machines.
• Transfer function of analog and digital PID
  controllers are employed to find mathematical
  models of closed loop systems, to analyze and
  study closed loop systems.

3
Continuous time electromechanical systems and
analog PID controllers

• The closed loop system in the time and s-domain
  with the negative unit loop gain are presented
  below

4
Continuous time electromechanical systems and
analog PID controllers

• The majority of electromechanical motion devices
  should be considered as continuous time systems.
• To attain the performance limits of
  electromechanical systems, one must remain up to
  date on design methods and control algorithms.
• The simplest control algorithms available, which
  the designer should study first, are the PID type
  controllers.
• The linear analog PID control law

Derivative feedback gain
Proportional feedback gain
Integral feedback gain
5
Continuous time electromechanical systems and
analog PID controllers

• is the error
  between the reference signal and the system
  output
• Block diagram of PID controller
• Using the Laplace transform for the most general
  case
• The transfer function for PID controllers

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TUNING THE PID CONTROLLER

• 
  Ziegler-Nichols Tuning Rules
• 1. SET KP. Starting with KP0, KI0 and KD0,
  increase KP until the output starts overshooting
  and ringing significantly.
• 2. SET KD. Increase KD until the overshoot is
  reduced to an acceptable level.
• 3. SET KI. Increase KI until the final error is
  equal to zero.

Gain 0.6 Ku Integral Pu/2 Derivative
Pu/8
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TUNING THE PID CONTROLLER
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Unit step response of a 2nd order underdamped
system
9
Analog control of permanent magnet DC Motor

• Permanent magnet DC Motor are widely used in
  servo systems.
• Figure Schematic diagram of rotating table
  actuated by permanent magnet motor

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Analog control of permanent magnet DC Motor

• The angular displacement of the positioning table
  the output equation
• To control the motor angular velocity wr, as well
  as angular displacement ?r, and rotating table
  kgear ?r, one regulates the armature voltage
  applied to the motor winding ua.
• To guarantee the stability, to attain the desired
  accuracy, to ensure tracking and disturbance
  attenuation of the servo system, one should
  design the control algorithm, and the coefficient
  of PID controller must be found.
• Find the transfer function. Obtained using
  differential equations that describe the system
  dynamics.
• Induced emf

Back emf constant
angular velocity
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Analog control of permanent magnet DC Motor

• Using KVL
• Applied Newtonian mechanics to find the
  differential equations for mechanical systems.
• Using Newtons second law
• Electromagnetic torque developed by permanent
  magnet DC motor
• Viscous torque
• Load torque TL

equivalent moment of inertia
Torque constant Back emf constant
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Analog control of permanent magnet DC Motor

• Using Newtons second law
• Dynamics of rotor angular displacement
• The derived three first order differential
  equations are rewritten in the s-domain

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Analog control of permanent magnet DC Motor

• Block diagram of closed loop the permanent magnet
  DC motor

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Analog control of permanent magnet DC Motor

• The controller should be designed, and the output
  equation
• Using this output equation, as well as
• Block diagram of open loop servo actuated by
  permanent magnet DC motor

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Analog control of permanent magnet DC Motor

• Using the linear PID controller
• Block diagram of closed loop servo actuated by
  permanent magnet DC motor with the linear PID
  controller

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Analog control of permanent magnet DC Motor
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Analog control of permanent magnet DC Motor
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QUIZ 2