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Load on Motor

Load on Motor. The mechanical part of the motor equations is derived using Newton's law, which states that the inertial load J times the derivative of angular rate equals the sum of all the torques about the motor shaft. The result is this equation,.

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Load on Motor

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  1. Load on Motor The mechanical part of the motor equations is derived using Newton's law, which states that the inertial load J times the derivative of angular rate equals the sum of all the torques about the motor shaft. The result is this equation, Where is a linear approximation for viscous friction

  2. Transient Electrical Equation Finally, the electrical part of the motor equations can be described by :

  3. Transient behavior of Motor This sequence of equations leads to a set of two differential equations that describe the behavior of the motor, the first for the induced current, and the second for the resulting angular rate,

  4. Example Listed below are nominal values for the various parameters of a DC motor. R= 2.0 ; %Ohms L= 0.5 ; % Henrys Km = .015; % torque constant Kb = .015; % emf constant Kf = 0.2; % Nms J= 0.02; % kg.m^2/s^2

  5. DC Machines • Shunt-connected DC Machine

  6. DC Machines • The dynamic equations (assuming rfext=0) are: Where Lff = field self-inductance Lla= armature leakage inductance Laf = mutual inductance between the field and rotating armature coils ea = induced voltage in the armature coils (also called counter or back emf )

  7. DC Machines

  8. DC Machines - Shunt DC Machine • Time-domain block diagram • The machine equations are solved for:

  9. DC Machines - Shunt DC Machine • Time domain block diagram + - Va ia G2 if Vf G1 Laf X + - Vf G3 ia X if

  10. DC Machines - Shunt DC Machine • State-space equations Let ; Re-writing the dynamic equations,

  11. DC Machines - Permanent Magnet The field flux in the Permanent Magnet machines is produced by a permanent magnet located on the stator. Therefore, Lsfif is a constant determined by the strength of the magnet, the reluctance of the iron, and the number of turns of the armature winding.

  12. DC Machines - Permanent Magnet • Dynamic equations of a Permanent Magnet Machine

  13. DC Machines - Permanent Magnet • Dynamic equations,

  14. DC Machines - Permanent Magnet • Time domain block diagram • The equations are solved by,

  15. DC Machines - Permanent Magnet • Time domain block diagram Va + - r Te ia + - ea Kv G2 G1 TL Kvr Kv

  16. DC Machines - Permanent Magnet • State-space equations • re-writing the equations as function of states,

  17. DC Machines - Permanent Magnet • In a matrix form,

  18. DC Machines - Permanent Magnet • Transfer Function, • Let

  19. DC Machines - Permanent Magnet • The, we will have • Re-arranging the equation,

  20. DC Machines - Permanent Magnet • In a matrix representation,

  21. DC Machines - Permanent Magnet • Solving for ia

  22. DC Machines - Permanent Magnet • Let m be, • The equation is then reduced to,

  23. DC Machines - Permanent Magnet

  24. DC Machines - Permanent Magnet

  25. DC Machines - Permanent Magnet • The characteristic equation (or force-free equation) of the system is as shown below,

  26. DC Machines - Permanent Magnet • If  < 1 , the roots are a conjugate complex pair, and the natural response consists of an exponentially decaying sinusoids. • If  > 1, the roots are real and the natural response consists of two exponential terms with negative real exponents.

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