Remove brushed motor distinction

appendices/classical-control-theory/laplace-domain-analysis/do-flywheels-need-pd-control.tex

@@ -33,7 +33,7 @@ \subsection{Do flywheels need PD control?}
 \end{align}
 
 For an explanation of where these equations come from, read section
-\ref{sec:dc_brushed_motor}.
+\ref{sec:dc_motor}.
 
 First, we'll solve for $\frac{d\omega}{dt}$ in terms of $V$.
 
@@ -107,14 +107,14 @@ \subsection{Do flywheels need PD control?}
 armature, the response timescales increase and the inductance matters even less.
 \begin{bookfigure}
   \begin{minisvg}{2}{build/figs/highfreq_unstable_step}
-    \caption{Step response of second-order DC brushed motor plant augmented with
+    \caption{Step response of second-order DC motor plant augmented with
       position ($L = 230$ μH)}
     \label{fig:cs_tf_highfreq_unstable_step}
   \end{minisvg}
   \hfill
   \begin{minisvg}{2}{build/figs/highfreq_stable_step}
-    \caption{Step response of first-order DC brushed motor plant augmented with
-      position ($L = 0$ μH)}
+    \caption{Step response of first-order DC motor plant augmented with position
+      ($L = 0$ μH)}
     \label{fig:cs_tf_highfreq_stable_step}
   \end{minisvg}
 \end{bookfigure}

appendices/classical-control-theory/laplace-domain-analysis/steady-state-error.tex

@@ -1,9 +1,9 @@
 \subsection{Steady-state error}
 \index{steady-state error!classical}
 
-To demonstrate the problem of \gls{steady-state error}, we will use a DC brushed
-motor controlled by a velocity PID controller. A DC brushed motor has a transfer
-function from voltage ($V$) to angular velocity ($\dot{\theta}$) of
+To demonstrate the problem of \gls{steady-state error}, we will use a DC motor
+controlled by a velocity PID controller. A DC motor has a transfer function from
+voltage ($V$) to angular velocity ($\dot{\theta}$) of
 \begin{equation}
   G(s) = \frac{\dot{\Theta}(s)}{V(s)} = \frac{K}{(Js+b)(Ls+R)+K^2}
 \end{equation}

appendices/classical-control-theory/transfer-functions/transfer-functions-in-feedback.tex

@@ -104,8 +104,8 @@ \subsubsection{DC motor transfer function}
 unmodeled high frequency, nonlinear dynamics, but they can be safely ignored
 depending on the operating regime.
 
-To demonstrate this, consider the transfer function for a second-order DC
-brushed motor (a CIM motor) from voltage to velocity.
+To demonstrate this, consider the transfer function for a second-order DC motor
+(a CIM motor) from voltage to velocity.
 \begin{equation*}
   G(s) = \frac{K}{(Js + b)(Ls + R) + K^2}
 \end{equation*}
@@ -134,14 +134,14 @@ \subsubsection{DC motor transfer function}
 similar for low frequency operating regimes.
 \begin{bookfigure}
   \begin{minisvg}{2}{build/figs/highfreq_unstable_step}
-    \caption{Step response of second-order DC brushed motor plant augmented with
+    \caption{Step response of second-order DC motor plant augmented with
       position ($L = 230$ μH)}
     \label{fig:tf_highfreq_unstable_step}
   \end{minisvg}
   \hfill
   \begin{minisvg}{2}{build/figs/highfreq_stable_step}
-    \caption{Step response of first-order DC brushed motor plant augmented with
-      position ($L = 0$ μH)}
+    \caption{Step response of first-order DC motor plant augmented with position
+      ($L = 0$ μH)}
     \label{fig:tf_highfreq_stable_step}
   \end{minisvg}
 \end{bookfigure}

fundamentals-of-control-theory/control-system-basics/why-feedback-control.tex

@@ -1,6 +1,6 @@
 \section{Why feedback control?}
 
-Let's say we are controlling a DC brushed motor. With just a
+Let's say we are controlling a DC motor. With just a
 \glslink{model}{mathematical model} and knowledge of all current \glspl{state}
 of the \gls{system} (i.e., angular velocity), we can predict all future
 \glspl{state} given the future voltage \glspl{input}. Why then do we need

modern-control-theory/continuous-state-space-control/elevator.tex

@@ -1,8 +1,8 @@
 \section{Elevator}
 \label{sec:ss_model_elevator}
 
-This elevator consists of a DC brushed motor attached to a pulley that drives a
-mass up or down.
+This elevator consists of a DC motor attached to a pulley that drives a mass up
+or down.
 \begin{bookfigure}
   \input{figs/elevator-system-diagram}
   \caption{Elevator system diagram}

modern-control-theory/continuous-state-space-control/flywheel.tex

@@ -1,7 +1,7 @@
 \section{Flywheel}
 \label{sec:ss_model_flywheel}
 
-This flywheel consists of a DC brushed motor attached to a spinning mass of
+This flywheel consists of a DC motor attached to a spinning mass of
 non-negligible moment of inertia.
 \begin{bookfigure}
   \input{figs/flywheel-system-diagram}
@@ -236,7 +236,7 @@ \subsection{Do flywheels need PD control?}
 \end{align}
 
 For an explanation of where these equations come from, read section
-\ref{sec:dc_brushed_motor}.
+\ref{sec:dc_motor}.
 
 First, we'll solve for $\frac{d\omega}{dt}$ in terms of $V$.
 
@@ -300,14 +300,14 @@ \subsection{Do flywheels need PD control?}
 armature, the response timescales increase and the inductance matters even less.
 \begin{bookfigure}
   \begin{minisvg}{2}{build/figs/highfreq_unstable_step}
-    \caption{Step response of second-order DC brushed motor plant augmented with
+    \caption{Step response of second-order DC motor plant augmented with
       position ($L = 230$ μH)}
     \label{fig:cs_ss_highfreq_unstable_step}
   \end{minisvg}
   \hfill
   \begin{minisvg}{2}{build/figs/highfreq_stable_step}
-    \caption{Step response of first-order DC brushed motor plant augmented with
-      position ($L = 0$ μH)}
+    \caption{Step response of first-order DC motor plant augmented with position
+      ($L = 0$ μH)}
     \label{fig:cs_ss_highfreq_stable_step}
   \end{minisvg}
 \end{bookfigure}

modern-control-theory/continuous-state-space-control/single-jointed-arm.tex

@@ -1,8 +1,8 @@
 \section{Single-jointed arm}
 \label{sec:ss_model_single-jointed_arm}
 
-This single-jointed arm consists of a DC brushed motor attached to a pulley that
-spins a straight bar in pitch.
+This single-jointed arm consists of a DC motor attached to a pulley that spins a
+straight bar in pitch.
 \begin{bookfigure}
   \input{figs/single-jointed-arm-system-diagram}
   \caption{Single-jointed arm system diagram}

modern-control-theory/continuous-state-space-control/what-is-a-dynamical-system.tex

@@ -7,16 +7,16 @@ \section{What is a dynamical system?}
 integrals. You can define reasonably accurate linear \glspl{model} for pretty
 much everything you'll see in FRC with just those relations.
 
-But let's say you have a DC brushed motor hooked up to a power supply and you
-applied a constant voltage to it from rest. The motor approaches a steady-state
-angular velocity, but the shape of the angular velocity curve over time isn't a
-line. In fact, it's a decaying exponential curve akin to
+But let's say you have a DC motor hooked up to a power supply and you applied a
+constant voltage to it from rest. The motor approaches a steady-state angular
+velocity, but the shape of the angular velocity curve over time isn't a line. In
+fact, it's a decaying exponential curve akin to
 \begin{equation*}
   \omega = \omega_{max}\left(1 - e^{-t}\right)
 \end{equation*}
 
 where $\omega$ is the angular velocity and $\omega_{max}$ is the maximum angular
-velocity. If DC brushed motors are said to behave linearly, then why is this?
+velocity. If DC motors are said to behave linearly, then why is this?
 
 Linearity refers to a \gls{system}'s equations of motion, not its time domain
 response. The equation defining the motor's change in angular velocity over time
@@ -33,12 +33,11 @@ \section{What is a dynamical system?}
 
 Also of note is that the relation between the input voltage and the angular
 velocity of the output shaft is a linear regression. You'll see why if you model
-a DC brushed motor as a voltage source and generator producing back-EMF (in the
-equation above, $bV$ corresponds to the voltage source and $-a\omega$
-corresponds to the back-EMF). As you increase the input voltage, the back-EMF
-increases linearly with the motor's angular velocity. If there was a friction
-term that varied with the angular velocity squared (air resistance is one
-example), the relation from input to output would be a curve. Friction that
-scales with just the angular velocity would result in a lower maximum angular
-velocity, but because that term can be lumped into the back-EMF term, the
-response is still linear.
+a DC motor as a voltage source and generator producing back-EMF (in the equation
+above, $bV$ corresponds to the voltage source and $-a\omega$ corresponds to the
+back-EMF). As you increase the input voltage, the back-EMF increases linearly
+with the motor's angular velocity. If there was a friction term that varied with
+the angular velocity squared (air resistance is one example), the relation from
+input to output would be a curve. Friction that scales with just the angular
+velocity would result in a lower maximum angular velocity, but because that term
+can be lumped into the back-EMF term, the response is still linear.

modern-control-theory/discrete-state-space-control/linear-quadratic-regulator.tex

@@ -172,7 +172,7 @@ \subsection{Bryson's rule}
 \subsection{Pole placement vs LQR}
 
 This example uses the following continuous second-order \gls{model} for a CIM
-motor (a DC brushed motor).
+motor (a DC motor).
 \begin{align*}
   \mat{A} = \begin{bmatrix}
     -\frac{b}{J} & \frac{K_t}{J} \\

modern-control-theory/nonlinear-control/differential-drive.tex

@@ -1,9 +1,8 @@
 \section{Differential drive}
 \label{sec:ss_model_differential_drive}
 
-This drivetrain consists of two DC brushed motors per side which are chained
-together on their respective sides and drive wheels which are assumed to be
-massless.
+This drivetrain consists of two DC motors per side which are chained together on
+their respective sides and drive wheels which are assumed to be massless.
 \begin{bookfigure}
   \begin{bookminifig}{2}
     \input{figs/differential-drive-fbd}

system-modeling/newtonian-mechanics-examples.tex

@@ -21,14 +21,14 @@ \chapter{Newtonian mechanics examples}
 servo mechanisms (it's just the flywheel \gls{model} augmented with a position
 \gls{state}).
 
-These \glspl{model} assume all motor controllers driving DC brushed motors are
-set to brake mode instead of coast mode. Brake mode behaves the same as coast
-mode except where the applied voltage is zero. In brake mode, the motor leads
-are shorted together to prevent movement. In coast mode, the motor leads are an
-open circuit.
+These \glspl{model} assume all motor controllers driving DC motors are set to
+brake mode instead of coast mode. Brake mode behaves the same as coast mode
+except where the applied voltage is zero. In brake mode, the motor leads are
+shorted together to prevent movement. In coast mode, the motor leads are an open
+circuit.
 
 \renewcommand*{\chapterpath}{\partpath/newtonian-mechanics-examples}
-\input{\chapterpath/dc-brushed-motor}
+\input{\chapterpath/dc-motor}
 \input{\chapterpath/elevator}
 \input{\chapterpath/flywheel}
 \input{\chapterpath/single-jointed-arm}

system-modeling/newtonian-mechanics-examples/dc-brushed-motor.tex → system-modeling/newtonian-mechanics-examples/dc-motor.tex

@@ -1,12 +1,18 @@
-\section{DC brushed motor}
-\label{sec:dc_brushed_motor}
-
-We will be deriving a first-order \gls{model} for a DC brushed motor. A
-second-order \gls{model} would include the inductance of the motor windings as
-well, but we're assuming the time constant of the inductor is small enough that
-its affect on the \gls{model} behavior is negligible for FRC use cases (see
-subsection \ref{subsec:do_flywheels_need_pd_control} for a demonstration of this
-for a real DC brushed motor).
+\section{DC motor}
+\label{sec:dc_motor}
+
+We will be deriving a first-order \gls{model} for a DC motor. A second-order
+\gls{model} would include the inductance of the motor windings as well, but
+we're assuming the time constant of the inductor is small enough that its affect
+on the \gls{model} behavior is negligible for FRC use cases (see subsection
+\ref{subsec:do_flywheels_need_pd_control} for a demonstration of this for a real
+DC motor).
+\begin{remark}
+  For the brushless motor commutation methods currently available in FRC
+  (trapezoidal commutation, field-oriented control), brushed and brushless DC
+  motors have the same dynamics. However, more advanced commutation methods can
+  break the linear back-EMF assumption of the brushed motor model.
+\end{remark}
 
 The first-order \gls{model} will only require numbers from the motor's
 datasheet. The second-order \gls{model} would require measuring the motor
@@ -15,7 +21,7 @@ \section{DC brushed motor}
 
 \subsection{Equations of motion}
 
-The circuit for a DC brushed motor is shown in figure
+The circuit for a DC motor is shown in figure
 \ref{fig:dc_motor_circuit}.
 \begin{bookfigure}
   \begin{tikzpicture}[auto, >=latex', circuit ee IEC,
@@ -34,7 +40,7 @@ \subsection{Equations of motion}
                   to (end);
   \end{tikzpicture}
 
-  \caption{DC brushed motor circuit}
+  \caption{DC motor circuit}
   \label{fig:dc_motor_circuit}
 \end{bookfigure}
 
@@ -47,7 +53,7 @@ \subsection{Equations of motion}
   V = IR + \frac{\omega}{K_v} \label{eq:motor_V}
 \end{equation}
 
-The mechanical relation for a DC brushed motor is
+The mechanical relation for a DC motor is
 \begin{equation}
   \tau = K_t I
 \end{equation}
@@ -60,7 +66,7 @@ \subsection{Equations of motion}
 
 Substitute this into equation \eqref{eq:motor_V}.
 
-\index{FRC models!DC brushed motor equations}
+\index{FRC models!DC motor equations}
 \begin{equation}
   V = \frac{\tau}{K_t} R + \frac{\omega}{K_v} \label{eq:motor_tau_V}
 \end{equation}
@@ -124,11 +130,11 @@ \subsubsection{Angular velocity constant $K_v$}
 
 \subsection{Current limiting}
 
-Current limiting of a DC brushed motor reduces the maximum input voltage to
-avoid exceeding a current threshold. Predictive current limiting uses a
-projected estimate of the current, so the voltage is reduced before the current
-threshold is exceeded. Reactive current limiting uses an actual current
-measurement, so the voltage is reduced after the current threshold is exceeded.
+Current limiting of a DC motor reduces the maximum input voltage to avoid
+exceeding a current threshold. Predictive current limiting uses a projected
+estimate of the current, so the voltage is reduced before the current threshold
+is exceeded. Reactive current limiting uses an actual current measurement, so
+the voltage is reduced after the current threshold is exceeded.
 
 The following pseudocode demonstrates each type of current limiting.
 \begin{code}

system-modeling/newtonian-mechanics-examples/differential-drive.tex

@@ -1,9 +1,8 @@
 \section{Differential drive}
 \label{sec:differential_drive}
 
-This drivetrain consists of two DC brushed motors per side which are chained
-together on their respective sides and drive wheels which are assumed to be
-massless.
+This drivetrain consists of two DC motors per side which are chained together on
+their respective sides and drive wheels which are assumed to be massless.
 \begin{bookfigure}
   \input{figs/differential-drive-system-diagram}
   \caption{Differential drive system diagram}

system-modeling/newtonian-mechanics-examples/elevator.tex

@@ -1,7 +1,7 @@
 \section{Elevator}
 
-This elevator consists of a DC brushed motor attached to a pulley that drives a
-mass up or down.
+This elevator consists of a DC motor attached to a pulley that drives a mass up
+or down.
 \begin{bookfigure}
   \input{figs/elevator-system-diagram}
   \caption{Elevator system diagram}
@@ -17,8 +17,8 @@ \subsection{Equations of motion}
 $v$) given an input voltage $V$, which we can integrate to get carriage velocity
 and position.
 
-First, we'll find a torque to substitute into the equation for a DC brushed
-motor. Based on figure \ref{fig:elevator}
+First, we'll find a torque to substitute into the equation for a DC motor. Based
+on figure \ref{fig:elevator}
 \begin{equation}
   \tau_m G = \tau_p \label{eq:elevator_tau_m_ratio}
 \end{equation}
@@ -30,7 +30,7 @@ \subsection{Equations of motion}
 \end{equation}
 
 where $r$ is the radius of the pulley. Substitute equation
-\eqref{eq:elevator_tau_m_ratio} into $\tau_m$ in the DC brushed motor equation
+\eqref{eq:elevator_tau_m_ratio} into $\tau_m$ in the DC motor equation
 \eqref{eq:motor_tau_V}.
 \begin{align}
   V &= \frac{\frac{\tau_p}{G}}{K_t} R + \frac{\omega_m}{K_v} \nonumber \\

system-modeling/newtonian-mechanics-examples/flywheel.tex

@@ -1,6 +1,6 @@
 \section{Flywheel}
 
-This flywheel consists of a DC brushed motor attached to a spinning mass of
+This flywheel consists of a DC motor attached to a spinning mass of
 non-negligible moment of inertia.
 \begin{bookfigure}
   \input{figs/flywheel-system-diagram}
@@ -17,7 +17,7 @@ \subsection{Equations of motion}
 $\dot{\omega}_f$ given an input voltage $V$, which we can integrate to get
 flywheel angular velocity.
 
-We will start with the equation derived earlier for a DC brushed motor, equation
+We will start with the equation derived earlier for a DC motor, equation
 \eqref{eq:motor_tau_V}.
 \begin{align}
   V &= \frac{\tau_m}{K_t} R + \frac{\omega_m}{K_v} \nonumber

system-modeling/newtonian-mechanics-examples/single-jointed-arm.tex

@@ -1,7 +1,7 @@
 \section{Single-jointed arm}
 
-This single-jointed arm consists of a DC brushed motor attached to a pulley that
-spins a straight bar in pitch.
+This single-jointed arm consists of a DC motor attached to a pulley that spins a
+straight bar in pitch.
 \begin{bookfigure}
   \input{figs/single-jointed-arm-system-diagram}
   \caption{Single-jointed arm system diagram}
@@ -17,7 +17,7 @@ \subsection{Equations of motion}
 $\dot{\omega}_{arm}$ given an input voltage $V$, which we can integrate to get
 arm angular velocity and angle.
 
-We will start with the equation derived earlier for a DC brushed motor, equation
+We will start with the equation derived earlier for a DC motor, equation
 \eqref{eq:motor_tau_V}.
 \begin{align}
   V &= \frac{\tau_m}{K_t} R + \frac{\omega_m}{K_v} \nonumber