From 091e6558810ec62289f9128a722adf75c13bdac9 Mon Sep 17 00:00:00 2001 From: Jan Marco Ruiz de Vargas Staudacher Date: Mon, 13 May 2024 16:47:34 +0200 Subject: [PATCH] adding english and math description for actuator travel --- docs/design/source/core_kpi.rst | 18 ++++++++++++++++++ 1 file changed, 18 insertions(+) diff --git a/docs/design/source/core_kpi.rst b/docs/design/source/core_kpi.rst index b51dacdb2..61e0840c6 100644 --- a/docs/design/source/core_kpi.rst +++ b/docs/design/source/core_kpi.rst @@ -227,6 +227,24 @@ Maximum allowed capital cost relies on the BOPTEST user, who can use the objective quantification of this KPI to take the decision. +Actuator travel +~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + + The actuator travel measures how frequent and how strong an actuator + is turned on and off. This measure is important to assess the wear and + tear of the equipment, because frequent and erratic switching of control + signals can lead to equipment damages and shorter equipment lifespan. + Actuator travel also gives a measure of phenomena such as cycling and hunting. + + The actuator travel :math:`AT(u)` of a trajectory :math:`u(t)` is calculated as + the ratio of the arc of :math:`u(t)` from :math:`t_0` to :math:`t_f` + to the time passed :math:`t_f-t_0`: + + .. math:: AT(u) = \frac{\int_{t_0}^{t_f} \left \sqrt{(1+(u'(t))^2)} \right dt}{t_f-t_0}, + + where :math:`\int_{t_0}^{t_f} \left \sqrt{(1+(u'(t))^2)` is the formula for + calculating the arc of function :math:`u(t)` by integration. + Calculation Module ---------------------