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@ -210,17 +210,17 @@ keyword is the name of an :doc:`equal-style variable <variable>` which
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should evaluate to a zero or non-zero value based on one or two or
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three variables which will store the x, y, or z coordinates of an atom
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(one variable per coordinate). If used, these other variables must be
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:doc:`equal-style variables <variable>` defined in the input script, but
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their formula can by anything. The *set* keyword is used to identify
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the names of these other variables, one variable for the x-coordinate
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of a created atom, one for y, and one for z.
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:doc:`internal-style variables <variable>` defined in the input script;
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their initial numeric value can be anything. The *set* keyword is
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used to identify the names of these other variables, one variable for
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the x-coordinate of a created atom, one for y, and one for z.
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When an atom is created, its x, y, or z coordinates override the
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formula for any *set* variable that is defined. The *var* variable is
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then evaluated. If the returned value is 0.0, the atom is not
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created. If it is non-zero, the atom is created. After all atoms are
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created, the formulas defined for all of the *set* variables are
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restored to their original strings.
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When an atom is created, its x,y,z coordinates become the values for
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any *set* variable that is defined. The *var* variable is then
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evaluated. If the returned value is 0.0, the atom is not created. If
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it is non-zero, the atom is created. After all atoms are created, the
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formulas defined for all of the *set* variables are restored to their
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original strings.
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As an example, these commands can be used in a 2d simulation, to
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create a sinusoidal surface. Note that the surface is "rough" due to
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@ -207,6 +207,10 @@ you should thus consider the *atom* and *atom/mpiio* styles (etc) to
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be inter-changeable. The one exception is how the filename is
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specified for the MPI-IO styles, as explained below.
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The precision of values output to text-based dump files can be
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controlled by the :doc:`dump_modify format <dump_modify>` command and
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its options.
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----------
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@ -0,0 +1,229 @@
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.. index:: fix controller
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fix controller command
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======================
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Syntax
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""""""
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.. parsed-literal::
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fix ID group-ID controller Nevery alpha Kp Ki Kd pvar setpoint cvar
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* ID, group-ID are documented in :doc:`fix <fix>` command
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* controller = style name of this fix command
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* Nevery = invoke controller every this many timesteps
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* alpha = coupling constant for PID equation (see units discussion below)
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* Kp = proportional gain in PID equation (unitless)
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* Ki = integral gain in PID equation (unitless)
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* Kd = derivative gain in PID equation (unitless)
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* pvar = process variable of form c_ID, c_ID[N], f_ID, f_ID[N], or v_name
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.. parsed-literal::
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c_ID = global scalar calculated by a compute with ID
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c_ID[I] = Ith component of global vector calculated by a compute with ID
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f_ID = global scalar calculated by a fix with ID
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f_ID[I] = Ith component of global vector calculated by a fix with ID
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v_name = value calculated by an equal-style variable with name
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* setpoint = desired value of process variable (same units as process variable)
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* cvar = name of control variable
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Examples
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""""""""
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.. parsed-literal::
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fix 1 all controller 100 1.0 0.5 0.0 0.0 c_thermo_temp 1.5 tcontrol
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fix 1 all controller 100 0.2 0.5 0 100.0 v_pxxwall 1.01325 xwall
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fix 1 all controller 10000 0.2 0.5 0 2000 v_avpe -3.785 tcontrol
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Description
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"""""""""""
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This fix enables control of a LAMMPS simulation using a control loop
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feedback mechanism known as a proportional-integral-derivative (PID)
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controller. The basic idea is to define a "process variable" which is
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a quantity that can be monitor during a running simulation. A desired
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target value is chosen for the process variable. A "control variable"
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is also defined which is an adjustable attribute of the simulation
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which the process variable will respond to. The PID controller
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continuously adjusts the control variable based on the difference
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between the process variable and the target.
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Here are examples of ways in which this fix can be used. The
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examples/pid directory contains a script that implements the simple
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thermostat.
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+-----------------------------------------+---------------------+---------------------+
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| Goal | process variable | control variable |
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+-----------------------------------------+---------------------+---------------------+
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| Simple thermostat | instantaneous T | thermostat target T |
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+-----------------------------------------+---------------------+---------------------+
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| Find melting temperature | average PE per atom | thermostat target T |
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+-----------------------------------------+---------------------+---------------------+
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| Control pressure in non-periodic system | force on wall | position of wall |
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+-----------------------------------------+---------------------+---------------------+
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| | | |
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+-----------------------------------------+---------------------+---------------------+
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.. note::
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For this fix to work, the control variable must actually induce
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a change in a running LAMMPS simulation. Typically this will only
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occur if there is some other command (e.g. a thermostat fix) which
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uses the control variable as an input parameter. This could be done
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directly or indirectly, e.g. the other command uses a variable as
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input whose formula uses the control variable. The other command
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should alter its behavior dynamically as the variable changes.
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.. note::
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If there is a command you think could be used in this fashion,
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but does not currently allow a variable as an input parameter, please
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notify the LAMMPS developers. It is often not difficult to enable a
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command to use a variable as an input parameter.
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The group specified with this command is ignored. However, note that
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the process variable may be defined by calculations performed by
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computes and fixes which store their own "group" definitions.
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The PID controller is invoked once each *Nevery* timesteps.
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The PID controller is implemented as a discretized version of
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the following dynamic equation:
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.. image:: Eqs/fix_controller1.jpg
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:align: center
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where *c* is the continuous time analog of the control variable,
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*e*\ =\ *pvar*\ -\ *setpoint* is the error in the process variable, and
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*alpha*\ , *Kp*\ , *Ki*\ , and *Kd* are constants set by the corresponding
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keywords described above. The discretized version of this equation is:
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.. image:: Eqs/fix_controller2.jpg
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:align: center
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where *tau* = *Nevery*\ *timestep is the time interval between updates,
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and the subsripted variables indicated the values of *c* and *e* at
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successive updates.
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From the first equation, it is clear that if the three gain values
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*Kp*\ , *Ki*\ , *Kd* are dimensionless constants, then *alpha* must have
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units of [unit *cvar*\ ]/[unit *pvar*\ ]/[unit time] e.g. [ eV/K/ps
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]. The advantage of this unit scheme is that the value of the
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constants should be invariant under a change of either the MD timestep
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size or the value of *Nevery*\ . Similarly, if the LAMMPS :doc:`unit style <units>` is changed, it should only be necessary to change
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the value of *alpha* to reflect this, while leaving *Kp*\ , *Ki*\ , and
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*Kd* unaltered.
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When choosing the values of the four constants, it is best to first
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pick a value and sign for *alpha* that is consistent with the
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magnitudes and signs of *pvar* and *cvar*\ . The magnitude of *Kp*
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should then be tested over a large positive range keeping *Ki*\ =\ *Kd*\ =0.
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A good value for *Kp* will produce a fast reponse in *pvar*\ , without
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overshooting the *setpoint*\ . For many applications, proportional
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feedback is sufficient, and so *Ki*\ =\ *Kd*\ =0 can be used. In cases where
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there is a substantial lag time in the response of *pvar* to a change
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in *cvar*\ , this can be counteracted by increasing *Kd*\ . In situations
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where *pvar* plateaus without reaching *setpoint*\ , this can be
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counteracted by increasing *Ki*\ . In the language of Charles Dickens
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(or Donald Trump), *Kp* represents the error of the present, *Ki* the
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error of the past, and *Kd* the error yet to come.
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Because this fix updates *cvar*\ , but does not initialize its value,
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the initial value is that assigned by the user in the internal-style
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variable command. This value is used (by the other LAMMPS command that
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used the variable) until this fix performs its first update of *cvar*
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after *Nevery* timesteps. On the first update, the value of the
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derivative term is set to zero, because the value of *e_n-1* is not
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yet defined.
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----------
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The process variable *pvar* can be specified as the output of a
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:doc:`compute <compute>` or :doc:`fix <fix>` or the evaluation of a
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:doc:`variable <variable>`. In each case, the compute, fix, or variable
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must produce a global quantity, not a per-atom or local quantity.
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If *pvar* begins with "c_", a compute ID must follow which has been
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previously defined in the input script and which generates a global
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scalar or vector. See the individual :doc:`compute <compute>` doc page
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for details. If no bracketed integer is appended, the scalar
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calculated by the compute is used. If a bracketed integer is
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appended, the Ith value of the vector calculated by the compute is
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used. Users can also write code for their own compute styles and :doc:`add them to LAMMPS <Section_modify>`.
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If *pvar* begins with "f_", a fix ID must follow which has been
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previously defined in the input script and which generates a global
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scalar or vector. See the individual :doc:`fix <fix>` doc page for
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details. Note that some fixes only produce their values on certain
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timesteps, which must be compatible with when fix controller
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references the values, or else an error results. If no bracketed integer
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is appended, the scalar calculated by the fix is used. If a bracketed
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integer is appended, the Ith value of the vector calculated by the fix
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is used. Users can also write code for their own fix style and :doc:`add them to LAMMPS <Section_modify>`.
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If *pvar* begins with "v_", a variable name must follow which has been
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previously defined in the input script. Only equal-style variables
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can be referenced. See the :doc:`variable <variable>` command for
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details. Note that variables of style *equal* define a formula which
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can reference individual atom properties or thermodynamic keywords, or
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they can invoke other computes, fixes, or variables when they are
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evaluated, so this is a very general means of specifying the process
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variable.
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The target value *setpoint* for the process variable must be a numeric
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value, in whatever units *pvar* is defined for.
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The control variable *cvar* must be the name of an :doc:`internal-style variable <variable>` previously defined in the input script. Note
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that it is not specified with a "v_" prefix, just the name of the
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variable. It must be an internal-style variable, because this fix
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updates its value directly. Note that other commands can use an
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equal-style versus internal-style variable interchangeably.
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----------
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Restart, fix_modify, output, run start/stop, minimize info
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""""""""""""""""""""""""""""""""""""""""""""""""""""""""""
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Currenlty, no information about this fix is written to :doc:`binary restart files <restart>`. None of the :doc:`fix_modify <fix_modify>` options
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are relevant to this fix.
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This fix produces a global vector with 3 values which can be accessed
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by various :ref:`output commands <howto_15>`. The values
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can be accessed on any timestep, though they are only updated on
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timesteps that are a multiple of *Nevery*\ .
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The three values are the most recent updates made to the control
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variable by each of the 3 terms in the PID equation above. The first
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value is the proportional term, the second is the integral term, the
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third is the derivative term.
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The units of the vector values will be whatever units the control
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variable is in. The vector values calculated by this fix are
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"extensive".
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No parameter of this fix can be used with the *start/stop* keywords of
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the :doc:`run <run>` command. This fix is not invoked during :doc:`energy minimization <minimize>`.
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Restrictions
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""""""""""""
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none
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Related commands
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""""""""""""""""
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:doc:`fix adapt <fix_adapt>`
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**Default:** none
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.. _lws: http://lammps.sandia.gov
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.. _ld: Manual.html
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.. _lc: Section_commands.html#comm
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@ -117,8 +117,8 @@ is more than one field. The *int* and *float* keywords take a single
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format argument and are applied to all integer or floating-point
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quantities output. The setting for *M string* also takes a single
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format argument which is used for the Mth value output in each line,
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e.g. the 5th column of output is output in high precision for "format
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5 %20.15g".
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e.g. the 5th column is output in high precision for "format 5
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%20.15g".
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The *format* keyword can be used multiple times. The precedence is
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that for each value in a line of output, the *M* format (if specified)
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@ -11,7 +11,7 @@ Syntax
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variable name style args ...
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* name = name of variable to define
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* style = *delete* or *index* or *loop* or *world* or *universe* or *uloop* or *string* or *format* or *getenv* or *file* or *atomfile* or *python* or *equal* or *vector* or *atom*
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* style = *delete* or *index* or *loop* or *world* or *universe* or *uloop* or *string* or *format* or *getenv* or *file* or *atomfile* or *python* or *equal* or *internal* or *vector* or *atom*
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.. parsed-literal::
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*delete* = no args
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