Compound Motor

Compound motor model with electrical and torque characteristics and fault modeling

Since R2021a

Libraries:
Simscape / Electrical / Electromechanical / Brushed Motors

Description

The Compound Motor block represents the electrical and torque characteristics of a compound motor. This figure shows the equivalent circuit for a short-shunt compound motor:

Short-shunt compound motor model

This figure shows the equivalent circuit for a long-shunt compound motor:

Long-shunt compound motor model

where:

i is the total current.
i_s is the series field winding current.
i_p is the parallel field winding current.
i_a is the armature current.
V is the total voltage.
V_s is the series field winding voltage.
V_p is the parallel field winding voltage.
V_a is the armature voltage.
ω is the angular velocity.
t_e is the torque.

If you set the Steady-state parameterization parameter to By equivalent circuit parameters, you can specify the equivalent circuit parameters for this model:

R_a — Armature resistance, Ra
R_s — Series field winding resistance, Rs
R_p — Shunt field winding resistance, Rp
L_sa — Series field winding to armature back EMF constant, Lsa
L_pa — Shunt field winding to armature back EMF constant, Lpa

Short-Shunt Equations

When Electrical circuit topology is set to Short-shunt, the electrical dynamic equations are:

$\begin{array}{l} V_{s} = R_{s} i_{s} + L_{s} \frac{d i_{s}}{d t} + L_{s p} \frac{d i_{p}}{d t} \\ V_{p} = R_{p} i_{p} + L_{p} \frac{d i_{p}}{d t} + L_{s p} \frac{d i_{s}}{d t} \\ V_{e m f} = k_{v} ω = (L_{s a} i_{s} + L_{p a} i_{p}) ω \\ V = V_{s} + V_{p} \\ V_{p} = k_{v} ω + R_{a} i_{a} \\ i = i_{s} \\ i_{a} = i_{s} - i_{p} \end{array}$

These are the mechanical dynamic equations for the short-shunt compound motor:

$\begin{array}{l} J \dot{ω} + D ω = t_{e} + t_{l o a d} \\ t_{e} = k_{v} i_{a} = (L_{s a} i_{s} + L_{p a} i_{p}) i_{a} \end{array}$

From these dynamic equations, the block obtains the steady-state equations by making the derivatives equal to zero:

$\begin{array}{l} V_{e m f} = L_{s a} i_{s} ω + L_{p a} i_{p} ω \\ t_{e l e c} = k_{v} (i_{s} - i_{p}) = V_{e m f} \frac{i_{s} - i_{p}}{ω} \\ V = R_{s} i_{s} + R_{p} i_{p} \\ R_{p} i_{p} = V_{e m f} + R_{a} (i_{s} - i_{p}) \end{array}$

Then, it computes the steady-state currents and torque as follows:

$\begin{array}{l} t_{e l e c} (ω, V) = \frac{- V^{2} (L_{p a} ω + L_{s a} ω - R_{p}) (R_{a} L_{p a} + R_{a} L_{s a} + R_{p} L_{s a})}{{(R_{a} R_{p} + R_{a} R_{s} + R_{p} R_{s} + L_{s a} R_{p} ω - L_{p a} R_{s} ω)}^{2}} \\ i = i_{s} (ω, V) = \frac{V (R_{a} + R_{p} - L_{p a} ω)}{R_{a} R_{p} + R_{a} R_{s} + R_{p} R_{s} + L_{s a} R_{p} ω - L_{p a} R_{s} ω} \end{array}$

Long-Shunt Equations

When Electrical circuit topology is set to Long-shunt, the electrical dynamic equations are:

$\begin{array}{l} V_{s} = R_{s} i_{s} + L_{s} \frac{d i_{s}}{d t} + L_{s p} \frac{d i_{p}}{d t} \\ V_{p} = R_{p} i_{p} + L_{p} \frac{d i_{p}}{d t} + L_{s p} \frac{d i_{s}}{d t} \\ V_{e m f} = k_{v} ω = (L_{s a} i_{s} + L_{p a} i_{p}) ω \\ V = V_{p} \\ V_{p} = k_{v} ω + R_{a} i_{a} + V_{s} \\ i = i_{s} + i_{p} \\ i_{a} = i_{s} \end{array}$

These are the mechanical dynamic equations for the long-shunt compound motor:

$\begin{array}{l} J \dot{ω} + D ω = t_{e} + t_{l o a d} \\ t_{e} = k_{v} i_{a} = (L_{s a} i_{s} + L_{p a} i_{p}) i_{a} \end{array}$

From these dynamic equations, the block obtains the steady-state equations by making the derivatives equal to zero:

$\begin{array}{l} V_{e m f} = L_{s a} i_{s} ω + L_{p a} i_{p} ω \\ t_{e l e c} = k_{v} i_{s} = V_{e m f} \frac{i_{s}}{ω} \\ V = R_{p} i_{p} \\ R_{p} i_{p} = V_{e m f} + (R_{a} + R_{s}) i_{s} \end{array}$

Then, it computes the steady-state currents and torque as follows:

$\begin{array}{l} t_{e l e c} (ω, V) = \frac{V^{2} (R_{a} - L_{p a} ω) (R_{a} L_{p a} + R_{s} L_{p a} + R_{p} L_{s a})}{R_{p}^{2} {(R_{a} + R_{s} + L_{s a} ω)}^{2}} \\ i (ω, V) = i_{s} + i_{p} = \frac{V}{R_{p}} + \frac{R_{p} V - L_{p a} V ω}{R_{p} (R_{a} + R_{s} + L_{s a} ω)} \end{array}$

Faults

The Compound Motor block allows you to model three types of faults:

Armature winding fault — The armature winding fails and becomes open circuit.
Series field winding fault — The series field winding fails and becomes open circuit.
Shunt field winding fault — The shunt field winding fails and becomes open circuit.

The block can trigger fault events:

At a specific time (temporal fault)
When a current limit is exceeded for longer than a specific time interval (behavioral fault)

You can enable or disable these trigger mechanisms separately.

You can choose whether to issue an assertion when a fault occurs by using the Reporting when a fault occurs parameter. The assertion can take the form of a warning or an error. By default, the block does not issue an assertion.

If you set the Enable armature winding open-circuit fault parameter to On, the armature fails at the time specified by the Simulation time for armature winding fault event parameter for a temporal fault, or when the winding currents exceeds the value of the Maximum permissible armature winding current parameter for a behavioral fault. When the armature fails, the voltage source connected to this block observes an open circuit for a fraction of the total motor revolution, specified by the Fraction of revolution during which armature is open-circuit parameter. This figure illustrates the circuit state behavior and the open-circuit state (rev_faulted) for a revolution period:

Model Thermal Effects

You can expose thermal ports to model the effects of losses that convert power to heat. To expose the thermal ports, set the Modeling option parameter to either:

No thermal port — The block does not contain thermal ports.
Show thermal port — The block contains thermal conserving ports for the series field winding, the shunt field winding, and the armature.

For more information about using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.

Examples

Compound Motor Design Optimization

Find design parameters that optimize a compound motor torque-speed curve to match the desired curve.

Open Model

Ports

The type, visibility, and location of the block ports depend on how you configure the Electrical circuit topology parameter in the Configuration tab, and if you expose the thermal ports:

Electrical circuit topology	Thermal ports	Block
`Long-shunt`	`Hidden`
`Long-shunt`	`Visible`
`Short-shunt`	`Hidden`
`Short-shunt`	`Visible`

Conserving

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+ — Positive terminal
electrical

Electrical conserving port associated with the compound motor positive terminal.

- — Negative terminal
electrical

Electrical conserving port associated with the compound motor negative terminal.

C — Motor case
mechanical

Mechanical rotational conserving port associated with the compound motor case.

R — Motor rotor
mechanical

Mechanical rotational conserving port associated with the compound motor rotor.

Hs — Series field winding thermal port
thermal

Thermal conserving port associated with the series field winding. For more information, see Model Thermal Effects.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Hp — Shunt field winding thermal port
thermal

Thermal conserving port associated with the shunt field winding.. For more information, see Model Thermal Effects.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Ha — Armature thermal port
thermal

Thermal conserving port associated with the armature. For more information, see Model Thermal Effects.

Dependencies

To enable this port, set Modeling option to Show thermal port.

Parameters

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Modeling option — Whether to enable thermal ports
`No thermal port` (default) | `Show thermal port`

Whether to enable the thermal ports of the block and model the effects of losses that convert power to heat.

Configuration

Electrical circuit topology — Topology of electrical circuit
`Long-shunt` (default) | `Short-shunt`

Topology of the electrical circuit.

Shunt winding polarity — Shunt winding polarity
`Cumulative` (default) | `Differential`

Magnetic orientation of the shunt winding.

Steady-State

Steady-state parameterization — Block parameterization
`By equivalent circuit parameters` (default) | `By rated, stall, and no-load datasheet parameters`

Select one of the following methods for block parameterization:

By equivalent circuit parameters — Provide electrical parameters for an equivalent circuit model of the motor.
By rated, stall, and no-load datasheet parameters — Provide current and speed parameters that the block converts to an equivalent circuit model of the motor.

Armature resistance, Ra — Armature resistance
`1.68` `Ohm` (default) | positive scalar

Resistance of the conducting portion of the motor.

Dependencies

To enable this parameter, set Steady-state parameterization to By equivalent circuit parameters.

Series field winding resistance, Rs — Series field winding resistance
`1.68` `Ohm` (default) | positive scalar

Resistance of the series field winding.

Dependencies

To enable this parameter, set Steady-state parameterization to By equivalent circuit parameters.

Shunt field winding resistance, Rp — Shunt field winding resistance
`303` `Ohm` (default) | positive scalar

Resistance of the shunt field winding.

Dependencies

To enable this parameter, set Steady-state parameterization to By equivalent circuit parameters.

Series field winding to armature back EMF constant, Lsa — Series field winding to armature back EMF constant
`0.69` `H` (default) | positive scalar

Series field winding to armature back EMF constant.

Dependencies

To enable this parameter, set Steady-state parameterization to By equivalent circuit parameters.

Shunt field winding to armature back EMF constant, Lpa — Shunt field winding to armature back EMF constant
`0.64` `H` (default) | positive scalar

Shunt field winding to armature back EMF constant.

Dependencies

To enable this parameter, set Steady-state parameterization to By equivalent circuit parameters.