20.6.9.1. PMDC

The PMDC machine block implements a permanent magnet excited DC motor.

Figure 20.136 PMDC Motor

Dialog Box

Figure 20.137 PMDC dialog box

Table 20.73 Electrical Parameter

Parameter Name	Signal	Description
Voltage Constant	\(K_e\)	Back electromotive force (BEMF) constant. In DC Motor it is same as Torque constant. You can find the value of Voltage Constant or the Torque Constant in the datasheet.
Pole Pair Number		The number of pole pairs. It means how many pairs of Field Pole there are.
Armature Resistance	\(R_a\)	The armature resistance between the armature terminal A+ and A-. You can find the value of Armature Resistance in the datasheet. [Ohms]
Armature Inductance	\(L_a\)	The armature inductance between the armature terminal A+ and A-. You can find the value of Armature Inductance in the datasheet. [H]
Armature Initial Current	\(A\)	Initial value of armature current. Set this value to ‘0’ if you don`t know it.

Table 20.74 Mechanical Parameter

Parameter Name	Signal	Description
Exclude Rotor/Include Rotor		Select the type of Motor between Exclude Rotor and Include Rotor. The more detail explanation of two types is in the Equation of PMDC.
Rotor Inertia	\(J\)	Inertia of rotor. This parameter don`t need on the Rotor Speed Type. You can find the inertia of rotor in the datasheet. [kg*m^2]
Friction Gain	\(B\)	Viscous friction gain between motor and load. When you apply the friction between the motor and the load in your dynamic model, you have to set this value to ‘0’. [Nms]
Friction Offset	\(T_f\)	Viscous friction Offset between motor and load (\(B\omega+ offset\)). When you apply the friction between the motor and the load in your dynamic model, you have to set this value to ‘0’. [Nm]
Rotor Initial Speed	\(\omega\)	Initial value of rotor speed. Set this value to ‘0’ if you don`t know it. [rad/s]

20.6.9.1.1. Input and Output of PMDC

Exclude Rotor (RD Cosim) Type

Figure 20.138 Input Port and Output Port of Rotor Speed Type

Table 20.75 Input Signals

Port	Input Signal		Description
1st Port	Rotor Angle	\(\theta\)	The Rotor Angle. [rad]
	Rotor Speed	\(\omega\)	The Rotor Angular Speed. This value is a differential of Rotor Angl. [rad/s]
2nd Port	Armature Voltage	\(V_q\)	The Armature Voltage. [V]

Table 20.76 Output Signals

Port	Output Signal		Description
1st Port	Rotor Angle	\(\theta\)	The Rotor Angle. [rad]
	Rotor Speed	\(\omega\)	The Rotor Angular Speed. [rad/s]
	Armature Current	\(I_a\)	The Armature Current. [A]
	Electrical Torque	\(T_e\)	The Generated electrical torque. [N.m]
2nd Port	Control Signals		This signal is used when you control the motor use the PMDC Drive block. When you use the PMDC Machine block, this port does not export any signal.
3rd Port	Driving Torque	\(T_d\)	The driving torque \({{T}_{d}}\) subtracts the viscous friction of rotor from the electrical torque \({{T}_{e}}\). The more detail explanation of this is in the Rotor Speed part of the Equation of PMDC. [N.m]

Example

Figure 20.139 Example of Rotor Speed Type

Include Rotor (Standalone) Type

Figure 20.140 Input Port and Output Port of Load Torque Type

Table 20.77 Input Signals

Port	Input Signal		Description
1st Port	Load Torque	\(T_L\)	The Load Torque. This value is used to calculate the Driving Torque in the Load Torque Type. [N]
2nd Port	Armature Voltage	\(V_a\)	The Armature Voltage. [V]

Table 20.78 Output Signals

Port	Output Signal		Description
1st Port	Rotor Angle	\(\theta\)	The Rotor Angle. [rad]
	Rotor Speed	\(\omega\)	The Rotor Angular Speed. [rad/s]
	Armature Current	\(I_a\)	The Armature Current. [A]
	Electrical Torque	\(T_e\)	The Generated electrical torque. [N.m]
2nd Port	Control Signals		This signal is used when you control the motor use the PMDC Driver block. When you use the PMDC Machine block, this port does not export any signal.
3rd Port	Rotational Velocity		Rotor Rotational Velocity. [rad/s]

Example

Figure 20.141 Example of Load Torque Type

20.6.9.1.2. Equation of PMDC

Electrical Part

The voltage equations of PMDC are as follows.

\({{V}_{a}}={{R}_{a}}{{I}_{a}}+{{L}_{a}}\frac{d{{I}_{a}}}{dt}+E\)

where,

\({{V}_{a}}\) is the input armature voltage.

\({{R}_{a}}\) is the armature resistance.

\({{L}_{a}}\) is the armature inductance.

\({{I}_{a}}\) is the armature current.

\(E\) is the back electromotive force.

The armature winding is connected to the outside terminal. This block is very similar to a shunt connected DC motor. A back electromotive force (BEMF) by magnet, which is generated between the armature terminals, is proportional to the machine speed.

\(E={{K}_{E}}{{\omega }_{m}}\)

where,

\({{K}_{E}}\) is the voltage (BEMF) constant

\({{\omega }_{m}}\) is the mechanical angular speed.

The electrical torque, which is developed by PMDC motor, is proportional to the armature current \({{I}_{a}}\).

\({{T}_{e}}={{K}_{E}}{{I}_{a}}={{K}_{T}}{{I}_{a}}\)

The torque constant \({{K}_{T}}\) is equal to the voltage (BEMF) constant \({{K}_{E}}\).

When the machine is in generator mode, the sign of torque is positive. In motor mode, the sign of torque is negative.

Mechanical Part

• Exclude Rotor

  The driving torque \({{T}_{d}}\) subtracts the viscous friction of rotor from the electrical torque \({{T}_{e}}\).

  \({{T}_{d}}={{T}_{e}}-sign({{\omega }_{m}})(B\left| {{\omega }_{m}} \right|+{{T}_{f}})\)

  where,

  \(B\) is the viscous friction gain.

  \({{T}_{f}}\) is the viscous friction offset.

• Include Rotor

  The mechanical dynamics of the rotor is governed by the equation.

  \({{T}_{e}}=J\frac{d{{\omega }_{m}}}{dt}+sign({{\omega }_{m}})(B\left| {{\omega }_{m}} \right|+{{T}_{f}})+{{T}_{L}}\)

  where,

  \(J\) is the inertia of rotor.

  \(B\) is the viscous friction gain.

  \({{T}_{f}}\) is the viscous friction offset.

  \({{T}_{L}}\) is the load torque.