Compound motor model with electrical and torque characteristics and fault modeling
Simscape / Electrical / Electromechanical / Brushed Motors
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
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:
$$\begin{array}{l}{t}_{elec}\left(\omega ,V\right)=\frac{{V}^{2}\left({L}_{pa}\omega +{L}_{sa}\omega {R}_{p}\right)\left({R}_{a}{L}_{pa}+{R}_{a}{L}_{sa}+{R}_{p}{L}_{sa}\right)}{{\left({R}_{a}{R}_{p}+{R}_{a}{R}_{s}+{R}_{p}{R}_{s}+{L}_{sa}{R}_{p}\omega {L}_{pa}{R}_{s}\omega \right)}^{2}}\\ i={i}_{s}\left(\omega ,V\right)=\frac{V\left({R}_{a}+{R}_{p}{L}_{pa}\omega \right)}{{R}_{a}{R}_{p}+{R}_{a}{R}_{s}+{R}_{p}{R}_{s}+{L}_{sa}{R}_{p}\omega {L}_{pa}{R}_{s}\omega}\end{array}$$
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:
$$\begin{array}{l}{t}_{elec}\left(\omega ,V\right)=\frac{{V}^{2}\left({R}_{a}{L}_{pa}\omega \right)\left({R}_{a}{L}_{pa}+{R}_{s}{L}_{pa}+{R}_{p}{L}_{sa}\right)}{{R}_{p}^{2}{\left({R}_{a}+{R}_{s}+{L}_{sa}\omega \right)}^{2}}\\ i\left(\omega ,V\right)={i}_{s}+{i}_{p}=\frac{V}{{R}_{p}}+\frac{{R}_{p}V{L}_{pa}V\omega}{{R}_{p}\left({R}_{a}+{R}_{s}+{L}_{sa}\omega \right)}\end{array}$$
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 opencircuit fault parameter to
Yes
, the armature fails at the time specified by the
Time at which armature winding fault is triggered 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
opencircuit parameter. This figure illustrates the circuit state
behavior and the opencircuit state (rev_faulted
) for a
revolution period:
The block has three optional thermal ports that are hidden by default. To expose the thermal ports, rightclick the block, and from the context menu select Simscape > Block choices > Show thermal port.
Use the thermal ports to simulate the effects of copper resistance losses that convert electrical power to heat. For more information on using thermal ports in actuator blocks, see Simulating Thermal Effects in Rotational and Translational Actuators.
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 
