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### fix mesh/surface/stress/servo command

Syntax:

    fix ID group-ID mesh/surface/stress/servo file filename premesh_keywords premesh_values mesh_keywords mesh_values surface_keyword surface_values stress_keywords stress_values servo_keywords servo_values

- ID, is documented in fix command, the group-ID is ignored for this command.
- mesh/surface/stress/servo = style name of this fix command
- file filename premesh_keywords premesh_values mesh_keywords mesh_values surface_keyword surface_values stress_keywords stress_values are documented in fix mesh/surface/stress.
- zero or more servo_keyword/value pairs may be appended servo keywords = com (obligatory) or dim (obligatory) or ctrlPV (obligatory) or vel_max (obligatory) or kp or ki or kd

      com values = x, y, z
          x, y, z = coordinates of the center of mass of the body (distance units)
      ctrlPV values = force or torque
          force = use force as controll process value, i.e. control force
          torque = use torque as controll process value, i.e. control torque
      axis args = x y z
          x y z = vector direction to apply the controlled mesh motion
          x or y or z can be a variable (see below)
      target_val values = val
          val = target value for the controller (force units or torque units, depending on ctrlPV)
      vel_max values = v
          v = maximum velocity magnitude for servo wall (velocity units)
      kp values = k
          k = proportional constant for PID controller
      ki values = k
          k = integral constant for PID controller
      kd values = k
          k = differential constant for PID controller
      mode values = auto
          auto = use alternative controller algorithm
      ratio values = dr
          dr = constant for the alternative controller approach (mode = auto)

Examples:

    fix servo all mesh/surface/stress/servo file plate.stl type 1 com 0. 0. 0. ctrlPV force axis 0. 0. 1. target_val 10 vel_max 1. kp 5.
    fix servo all mesh/surface/stress/servo file stirrer.stl type 1 com 0. 0. 0. ctrlPV torque axis 0. 0. 1. target_val 10 vel_max 1. ratio 0.01 mode auto

Description:

This fix implements the functionality of fix mesh/surface/stress but it additionally assumes the mesh being a servo wall that compacts a particle packing until either a total force (for ctrlPV = force) or a total torque (for ctrlPV = torque) is acting on the mesh. The target value is defined via keyword target_val. The servo can act in any dimension (as specified by the axis keyword). Only the direction of the axis is important; it's length is ignored. A negative value for target_val leads to a wall motion towards negative axis-direction and vice versa. The user has to specify the center of mass (keyword com) and the maximum velocity allowed for the servo wall by keyword vel_max. Note that vel_max < skin /(2* timestep ) is required.

The controller itself is a proportional-integral-derivative (PID) controller which is controlled by 3 constants kp, ki, kd:

output = kp * error + ki * errorsum + kd * errorchange

where 'error' is the current deviation of the controll process value to the target value, 'errorsum' is the time integration (sum) of the error values and 'errorchange' its derivative. The controller also includes an "anti-wind-up scheme" which prohibits accumulation of erroneous controller output caused by the integral part due to unavoidable long-lasting deviations.

By using the keyword mode = auto an alternative controller approach is applied. It is a pure proportional controller with gain scheduling. In the absence of neighbour particles the servo wall may move with maximum velocity (defined by vel_max). Otherwise, the maximum wall velocity is defined by ratio * min(radius) / dt. Approaching target_val the maximum velocity decreases to 0.1 * ratio * min(radius) / dt.

Restart, fix_modify, output, run start/stop, minimize info:

This fix stores a global vector with 9 components for access by various output commands. The first 3 components are equal to the total force on the mesh, the next 3 components store the total torque on the mesh. The last 3 components output the wall position. Furthermore, this fix writes the state of the servo wall to binary restart files so that a simulation can continue correctly. This fix supports fix_modify with option integrate = 'start' or 'stop' to start or stop the servo wall integration inbetween two runs. This fix also supports fix_modify with option target_val = val to change the target value inbetween two runs. This fix also supports fix_modify with option ctrlParam = kp ki kd to change the controller params inbetween two runs.

Restrictions:

When using this fix, along with scaling or rotate the body, all the servo_keyword/value pairs have to represent the state after scaling/rotation. Mesh elements may not be deleted in case due to leaving the simulation box for a fixed boundary. In this case, an error is generated. See boundary command for details. This fix can not be used in conjunction with another fix that manipulates mesh geometry, such as a fix move/mesh

Related commands:

fix mesh/surface/stress, fix wall/gran

Default:

kp = 1e-2, ki = 0, kd = 0