PHYSICAL STRUCTURE9
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PE 9211 Analysis of Electrical Machines
Dynamic Characteristics of Permanent Magnet DC Motor
Modes of Dynamic operation
1. Starting from stall
2. Changes in load torque
Condition: The machine supplied from a
constant β voltage source
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Mathematical Model of a PMDC Motor: 9
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This motor consists of two first order differential equation and two
algebraic equation
Armature current equation,
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Speed equation,
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Simulink Model of PMDC Motor
Motor Parameters
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Solving armature current equation
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Solving Speed equation
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Dynamic performance during starting
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Dynamic Characteristics of DC Shunt Motor
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Simulink Model of DC Shunt Motor:
Fig shows the Simulink model of DC Shunt Motor. It is constructed using
subsystems for solving each differential equations (i.e.) armature
current, field current and torque equation.
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Time domain block diagrams and state equations
Shunt connected dc machine
W.K.T
ππ = ππππ + π³π¨π¨ π πππ π
+ π³π¨πππππ β β ββ π
ππ = πππΉπ + π³ππ π ππ
π π β β ββ π
π»π = π»π³ + π± π ππ
π π + π©πππ β ββ β π
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Equations (1),(2) and (3) can be written in terms of its time constants
ππ = ππ π + π³π¨π¨
ππ
π
π π ππ + π³π¨πππππ
ππ = ππ π + ππ π ππ + π³π¨πππππββββββ π
π―πππ, π βΆπ
π π
ππ = πΉπ π + π³ππ
πΉπ
π ππ
ππ = πΉπ π + ππ π ππβββββββ(5)
π»π β π»π³ = ( π©π + π± π) ππ ββ β β π
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ππ βΆ Armature time constant
ππ βΆ Field time constant
πΊππππππ πππ πππππππππ π , π πππ π πππ ππ ,
ππ, πππ ππ πππππ π
ππ =
πππ
πππ + π ππ β π³π¨πππππ β β ββ π
ππ =
ππΉπ
πππ + π ππ β ββ β π
ππ =π
π±π + π©π π»π β π»π³ ββ β β π
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Time domain block diagram of a shunt connected dc machine
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πΊππππππ πππ πππππππππ π , π πππ π πππ π ππ
π π, π ππ
π π
πππ π ππ
π π πππππ π
From (1)
π πππ π
= βππ
π³π¨π¨
ππ β π³π¨π
π³π¨π¨
ππππ + π
π³π¨π¨
ππβ ππ
From (2)
π ππ
π π= β
πΉπ
π³ππ
ππ + π
π³ππ
ππβ ππ
From (3)
π ππ
π π= β
π©π
π±ππ +
π³π¨π
π±ππππ β
π
π±π»π³ β β(ππ)
State equation of shunt dc machine
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π
ππππππ
=
βπΉπ
π³πππ π
πβππ
π³π¨π¨π
π πβπ©π
π±
ππππππ
+
πβπ³π¨πππ
π³π¨π¨
π³π¨πππππ
π±
+
π
π³πππ π
ππ
π³π¨π¨π
π πβπ
π±
ππ
ππ
π»π³
State equations in matrix form or vector matrix form
Note: The second term on the right side contains the product of state
variables causing the system to be nonlinear.
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Permanent Magnet dc Machine
ππ ππ ππππππππππ
π³π¨πππ ππ ππππππππ ππ ππ
ππ ππ π πππππππππ ππ
Strength of the magnetReluctance of the ironNo. of turns in the armature winding
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W.K.T
Above eqns. (1) and (2) can be written in terms of its time constants
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29Time domain block diagram of a permanent magnet DC machine
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State Equation of a permanent magnet DC machine
From (1)
From (2)
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The form in which the state equations are expressed in above eqn.
is called the fundamental form.
OR
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Advantages to using the state space representation compared with other methods.
1.The ability to easily handle systems with multiple inputs and outputs;
2.The system model includes the internal state variables as well as the output variable;
3.The model directly provides a time-domain solution, the matrix/vector modeling is very efficient from a computational standpoint for computer implementation
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404349
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