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* system.h
* This file provides the system definition.
* Specifically, this is watertank system in which a tank with a hole in the
* bottom receives an input water flow. Such input flow can
* be modulated between zero and its maximum by controlling a valve. The
* described controller aims at keeping the water level between an upper threshold
* and a lower threshold.
* Copyright 2017 Luca Geretti
* 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
* GNU Library 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 <ariadne.h>
namespace Ariadne {
* Construction of an automaton takes major six steps:
* 1. Creation of an automaton
* 2. Registration of variable on the automaton
* 3. Registration of events on the automaton
* 4. Registration of locations as modes of the automaton
* 5. Registration of dynamics for each mode
* 6. Registration of transitions from one mode to another mode
* As a 0-th step, we also need to create (valued) labels: system variables, parameters and events
* The creation of labels was numbered 0 since they may be shared between multiple automata, and we clearly
* need to define them only once in the given context, before any usage.
* While it may be convenient to define all the components of a system on the same context,
* for sufficiently complex automata it becomes preferable to separate automata within
* dedicated (header) files. In that case, shared labels must be redefined within each context.
* Finally, a system is obtained by automated composition of its components.
HybridIOAutomaton getSystem()
// 0: System variables
RealVariable a("a"); // Valve aperture
RealVariable x("x"); // Water level
/// Tank automaton
// 0: Parameters
RealParameter alpha("alpha",0.02); // The coefficient for output flow
RealParameter beta("bfp",Interval(0.3,0.32863)); // The coefficient for input flow, defined as an interval, meaning that all the values are considered
// 1. Automaton
HybridIOAutomaton tank("tank");
// 2. Registration of the input/output variables
// 4. Registration of the locations
DiscreteLocation flow("flow");
/// 5. Registration of the dynamics
tank.set_dynamics(flow, x, - alpha * x + beta * a);
/// Valve automaton
// 0. Parameters
RealParameter T("T",4.0); // Time constant for opening/closing the valve
// 1. Automaton
HybridIOAutomaton valve("valve");
// 2. Registration of the input/output variables
// 3 Registration of the input/internal events
DiscreteEvent e_open("open");
DiscreteEvent e_close("close");
DiscreteEvent e_idle("idle");
// 4. Registration of the locations
DiscreteLocation idle("idle");
DiscreteLocation opening("opening");
DiscreteLocation closing("closing");
// 5. Registration of the dynamics for each location
valve.set_dynamics(idle, a, 0.0);
valve.set_dynamics(opening, a, 1.0/T);
valve.set_dynamics(closing, a, -1.0/T);
/// 6. Transitions
// Guards
// The library assumes that given a guard g, the relation g >= 0 must hold in the current mode to have a transition
RealExpression a_geq_one = a - 1.0; // a >= 1
RealExpression a_leq_zero = - a; // a >= 0
// Resets
// We need to define a reset for each output variable of the automaton
std::map<RealVariable,RealExpression> rst_a_one;
rst_a_one[a] = 1.0; // a = 1
std::map<RealVariable,RealExpression> rst_a_zero;
rst_a_zero[a] = 0.0; // a = 0
// Forced transitions: transitions which implicitly have complementary guards and consequently
// force the transition to be taken immediately
// When the valve is fully opened, go from opening to idle
valve.new_forced_transition(e_idle, opening, idle, rst_a_one, a_geq_one);
// When the valve is fully closed go from closing to idle
valve.new_forced_transition(e_idle, closing, idle, rst_a_zero, a_leq_zero);
// Unforced transitions: transitions which do not have complementary guards hence do not
// necessarily force an immediate transition
// Transitions that depend on input events must be unforced and with no guard or reset
valve.new_unforced_transition(e_open, idle, opening);
valve.new_unforced_transition(e_close, idle, closing);
/// Controller automaton
// 0. Parameters
RealParameter hmin("hmin",5.75); // Lower threshold
RealParameter hmax("hmax",7.75); // Upper threshold
RealParameter delta("delta",0.1); // Indetermination constant
// 1. Automaton
HybridIOAutomaton controller("controller");
// 2. Registration of the input/output variables
// 3. Registration of the events
// 4. Registration of the locations
DiscreteLocation rising("rising");
DiscreteLocation falling("falling");
// 5. Transitions
// Invariants
// The library assumes that given an invariant i, the relation i <= 0 must hold in the current mode to allow evolution
RealExpression x_leq_hmax = x - hmax - delta; // x <= hmax + delta
RealExpression x_geq_hmin = hmin - delta - x; // x >= hmin - delta
// Registration of the invariants for each location
controller.new_invariant(rising, x_leq_hmax);
controller.new_invariant(falling, x_geq_hmin);
// Guards
RealExpression x_geq_hmax = x - hmax + delta; // x >= hmax - delta
RealExpression x_leq_hmin = hmin + delta - x; // x <= hmin + delta
// Unforced transitions: here they are used paired with invariants to limit the region of activation of the guard
controller.new_unforced_transition(e_close, rising, falling, x_geq_hmax);
controller.new_unforced_transition(e_open, falling, rising, x_leq_hmin);
/// Composition
/* Composition is obtained by progressively composing two automata. The first argument is the name of
* the resulting composition. Please note that the name is actually relevant only for the complete system
* The second and this arguments are the components.
* Then in the fourth and fifth argument we must define an initial location for each component,
* in order to have a compact composition which excludes states that would not be reachable from such initial location.
* Pay attention, during iterative composition, on ordering the initial state correctly in respect
* to the provided fourth and fifth arguments; discrete location names for composite locations are
* created by simply using the comma character between the location names of their components.
HybridIOAutomaton tank_valve = compose("tank,valve",tank,valve,flow,idle);
HybridIOAutomaton system = compose("tutorial",tank_valve,controller,DiscreteLocation("flow,idle"),rising);
return system;
#endif /* TUTORIAL_SYSTEM_H_ */