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+/* motor_model.c - DC motor model. */
+/* motor - Motor control module. {{{
+ *
+ * Copyright (C) 2006 Nicolas Schodet
+ *
+ * APBTeam:
+ * Web: http://apbteam.org/
+ * Email: team AT apbteam DOT org
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or
+ * (at your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful,
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+ * GNU General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
+ *
+ * }}} */
+#include "common.h"
+#include "motor_model.host.h"
+
+/**
+ * This file models a DC motor. There is two parts, electric model and
+ * mechanic model.
+ *
+ * You can find documentation about this subject on:
+ * - maxon motor web site: http://www.maxonmotor.com/
+ *
+ * From there, you can find the following differential equations:
+ * u(t) = R i(t) + L di(t)/dt + 1/Ke o(t)
+ * J do(t)/dt = Kt i(t) - Rf o(t)
+ * dth(t)/dt = o(t)
+ *
+ * (see motor_t for variables description)
+ *
+ * The gearbox reduction and efficiency have to be added in the equations,
+ * this is left as an exercice for the reader.
+ *
+ * Those equations can be solved numerically thanks to Euler method:
+ *
+ * i(t+h) = i(t) + h (1/L u(t) - R/L i(t) - 1/(Ke L) o(t))
+ * o(t+h) = o(t) + h (i_G^2 ro_G)/J (Kt i(t) - Rf o(t))
+ * th(t+h) = th(t) + h o(t)
+ */
+
+/** Make a simulation step. */
+void motor_model_step (motor_model_t *m)
+{
+ double i_, o_, th_; /* New computed values. */
+ double h; /* Infinitesimal step... Well, not so infinite. */
+ int d;
+ d = m->d;
+ h = m->h / d;
+ /* Make several small steps to increase precision. */
+ for (; d; d--)
+ {
+ /* Make one little step. */
+ i_ = m->i
+ + h * (1.0 / m->m.L * m->u
+ - m->m.R / m->m.L * m->i
+ - 1.0 / m->m.Ke / m->m.L * m->o);
+ o_ = m->o
+ + h * m->m.i_G * m->m.i_G * m->m.ro_G / m->m.J
+ * (m->m.Kt * m->i - m->m.Rf * m->o);
+ th_ = m->th + h * m->o;
+ /* Test for limits overflow, I have no proof it works right for the
+ * moment, only suspicions. */
+ if (th_ < m->m.th_min)
+ {
+ th_ = m->m.th_min;
+ o_ = 0.0;
+ }
+ else if (th_ > m->m.th_max)
+ {
+ th_ = m->m.th_max;
+ o_ = 0.0;
+ }
+ /* OK, now store this step. */
+ m->i = i_;
+ m->o = o_;
+ m->th = th_;
+ }
+ /* Finished! */
+ m->t += m->h;
+}
+