From 2b0b7e965df9604dd1f6a915ce6c8a8f5a64dbcf Mon Sep 17 00:00:00 2001 From: Jason Daming Date: Mon, 9 Sep 2024 23:32:02 -0500 Subject: [PATCH] Make math proper with subscripts (#2734) --- .../system-identification/introduction.rst | 10 +++++----- 1 file changed, 5 insertions(+), 5 deletions(-) diff --git a/source/docs/software/advanced-controls/system-identification/introduction.rst b/source/docs/software/advanced-controls/system-identification/introduction.rst index 882d76d314..6802687211 100644 --- a/source/docs/software/advanced-controls/system-identification/introduction.rst +++ b/source/docs/software/advanced-controls/system-identification/introduction.rst @@ -40,7 +40,7 @@ Several of these options use nearly identical robot-side code, and differ only i The simple motor identification tool determines the best-fit parameters for the equation: -.. math:: V = kS \cdot sgn(\dot{d}) + kV \cdot \dot{d} + kA \cdot \ddot{d} +.. math:: V = K_s \cdot sgn(\dot{d}) + K_v \cdot \dot{d} + K_a \cdot \ddot{d} where :math:`V` is the applied voltage, :math:`d` is the displacement (position) of the drive, :math:`\dot{d}` is its velocity, and :math:`\ddot{d}` is its acceleration. This is the model for a permanent-magnet dc motor with no loading other than friction and inertia, as mentioned above, and is an accurate model for flywheels, turrets, and horizontal linear sliders. @@ -48,17 +48,17 @@ where :math:`V` is the applied voltage, :math:`d` is the displacement (position) The elevator identification tool determines the best-fit parameters for the equation: -.. math:: V = kG + kS \cdot sgn(\dot{d}) + kV \cdot \dot{d} + kA \cdot \ddot{d} +.. math:: V = K_g + K_s \cdot sgn(\dot{d}) + K_v \cdot \dot{d} + K_a \cdot \ddot{d} -where :math:`V` is the applied voltage, :math:`d` is the displacement (position) of the elevator, :math:`\dot{d}` is its velocity, and :math:`\ddot{d}` is its acceleration. The constant term (:math:`kG`) is added to correctly account for the effect of gravity. +where :math:`V` is the applied voltage, :math:`d` is the displacement (position) of the elevator, :math:`\dot{d}` is its velocity, and :math:`\ddot{d}` is its acceleration. The constant term (:math:`K_g`) is added to correctly account for the effect of gravity. #### Arm Identification The arm identification tool determines the best-fit parameters for the equation: -.. math:: V = kG \cdot cos(\theta) + kS \cdot sgn(\dot{\theta}) + kV \cdot \dot{\theta} + kA \cdot \ddot{\theta} +.. math:: V = K_g \cdot cos(\theta) + K_s \cdot sgn(\dot{\theta}) + K_v \cdot \dot{\theta} + K_a \cdot \ddot{\theta} -where :math:`V` is the applied voltage, :math:`\theta` is the angular displacement (position) of the arm, :math:`\dot{\theta}` is its angular velocity, and :math:`\ddot{\theta}` is its angular acceleration. The cosine term (:math:`kG`) is added to correctly account for the effect of gravity. +where :math:`V` is the applied voltage, :math:`\theta` is the angular displacement (position) of the arm, :math:`\dot{\theta}` is its angular velocity, and :math:`\ddot{\theta}` is its angular acceleration. The cosine term (:math:`K_g`) is added to correctly account for the effect of gravity. ## Installing SysId