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 shortshunt compound motor:
This figure shows the equivalent circuit for a longshunt compound motor:
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 Steadystate 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
ShortShunt Equations
When Electrical circuit topology is set to
Shortshunt
, the electrical dynamic equations
are:
$$\begin{array}{l}{V}_{s}={R}_{s}{i}_{s}+{L}_{s}\frac{d{i}_{s}}{dt}+{L}_{sp}\frac{d{i}_{p}}{dt}\\ {V}_{p}={R}_{p}{i}_{p}+{L}_{p}\frac{d{i}_{p}}{dt}+{L}_{sp}\frac{d{i}_{s}}{dt}\\ {V}_{emf}={k}_{v}\omega =\left({L}_{sa}{i}_{s}+{L}_{pa}{i}_{p}\right)\omega \\ V={V}_{s}+{V}_{p}\\ {V}_{p}={k}_{v}\omega +{R}_{a}{i}_{a}\\ i={i}_{s}\\ {i}_{a}={i}_{s}{i}_{p}\end{array}$$
These are the mechanical dynamic equations for the shortshunt compound motor:
$$\begin{array}{l}J\dot{\omega}+D\omega ={t}_{e}+{t}_{load}\\ {t}_{e}={k}_{v}{i}_{a}=\left({L}_{sa}{i}_{s}+{L}_{pa}{i}_{p}\right){i}_{a}\end{array}$$
From these dynamic equations, the block obtains the steadystate equations by making the derivatives equal to zero:
$$\begin{array}{l}{V}_{emf}={L}_{sa}{i}_{s}\omega +{L}_{pa}{i}_{p}\omega \\ {t}_{elec}={k}_{v}\left({i}_{s}{i}_{p}\right)={V}_{emf}\frac{{i}_{s}{i}_{p}}{\omega}\\ V={R}_{s}{i}_{s}+{R}_{p}{i}_{p}\\ {R}_{p}{i}_{p}={V}_{emf}+{R}_{a}\left({i}_{s}{i}_{p}\right)\end{array}$$
Then, it computes the steadystate currents and torque as follows:
$$\begin{array}{l}{t}_{elec}\left(\omega ,V\right)=\frac{{V}^{2}\left({L}_{pa}\omega +{L}_{sa}\omega {R}_{p}\right)\left({R}_{a}{L}_{pa}+{R}_{a}{L}_{sa}+{R}_{p}{L}_{sa}\right)}{{\left({R}_{a}{R}_{p}+{R}_{a}{R}_{s}+{R}_{p}{R}_{s}+{L}_{sa}{R}_{p}\omega {L}_{pa}{R}_{s}\omega \right)}^{2}}\\ i={i}_{s}\left(\omega ,V\right)=\frac{V\left({R}_{a}+{R}_{p}{L}_{pa}\omega \right)}{{R}_{a}{R}_{p}+{R}_{a}{R}_{s}+{R}_{p}{R}_{s}+{L}_{sa}{R}_{p}\omega {L}_{pa}{R}_{s}\omega}\end{array}$$
LongShunt Equations
When Electrical circuit topology is set to
Longshunt
, the electrical dynamic equations
are:
$$\begin{array}{l}{V}_{s}={R}_{s}{i}_{s}+{L}_{s}\frac{d{i}_{s}}{dt}+{L}_{sp}\frac{d{i}_{p}}{dt}\\ {V}_{p}={R}_{p}{i}_{p}+{L}_{p}\frac{d{i}_{p}}{dt}+{L}_{sp}\frac{d{i}_{s}}{dt}\\ {V}_{emf}={k}_{v}\omega =\left({L}_{sa}{i}_{s}+{L}_{pa}{i}_{p}\right)\omega \\ V={V}_{p}\\ {V}_{p}={k}_{v}\omega +{R}_{a}{i}_{a}+{V}_{s}\\ i={i}_{s}+{i}_{p}\\ {i}_{a}={i}_{s}\end{array}$$
These are the mechanical dynamic equations for the longshunt compound motor:
$$\begin{array}{l}J\dot{\omega}+D\omega ={t}_{e}+{t}_{load}\\ {t}_{e}={k}_{v}{i}_{a}=\left({L}_{sa}{i}_{s}+{L}_{pa}{i}_{p}\right){i}_{a}\end{array}$$
From these dynamic equations, the block obtains the steadystate equations by making the derivatives equal to zero:
$$\begin{array}{l}{V}_{emf}={L}_{sa}{i}_{s}\omega +{L}_{pa}{i}_{p}\omega \\ {t}_{elec}={k}_{v}{i}_{s}={V}_{emf}\frac{{i}_{s}}{\omega}\\ V={R}_{p}{i}_{p}\\ {R}_{p}{i}_{p}={V}_{emf}+\left({R}_{a}+{R}_{s}\right){i}_{s}\end{array}$$
Then, it computes the steadystate currents and torque as follows:
$$\begin{array}{l}{t}_{elec}\left(\omega ,V\right)=\frac{{V}^{2}\left({R}_{a}{L}_{pa}\omega \right)\left({R}_{a}{L}_{pa}+{R}_{s}{L}_{pa}+{R}_{p}{L}_{sa}\right)}{{R}_{p}^{2}{\left({R}_{a}+{R}_{s}+{L}_{sa}\omega \right)}^{2}}\\ i\left(\omega ,V\right)={i}_{s}+{i}_{p}=\frac{V}{{R}_{p}}+\frac{{R}_{p}V{L}_{pa}V\omega}{{R}_{p}\left({R}_{a}+{R}_{s}+{L}_{sa}\omega \right)}\end{array}$$
Faults
To model a fault in the Compound Motor block, in the Faults section, click the Add fault hyperlink in the parameter that corresponds to the specific fault that you want to model. When the Create Fault window opens, you use it to specify the fault properties. For more information about fault modeling, see Fault Behavior Modeling and Fault Triggering.
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 (timed fault)
When a current limit is exceeded for longer than a specific time interval (behavioral fault)
If you add an armature winding fault, the armature fails at the time specified by the
Trigger fault at time parameter for a timed 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 opencircuit parameter. This
figure illustrates the circuit state behavior and the opencircuit 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.
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 

Longshunt  Hidden 

Visible 
 
Shortshunt  Hidden 

Visible 

Conserving
Parameters
Extended Capabilities
Version History
Introduced in R2021a