PID(9)

NAME
pid - proportional/integral/derivative controller with automatic tuning support

SYNOPSIS
loadrt pid [num_chan=num | names=name1[,name2...]] [debug=dbg]

DESCRIPTION
pid is a classic Proportional/Integral/Derivative controller, used to control position or speed feedback loops for servo motors and other closed-loop applications.

pid supports a maximum of sixteen controllers. The number that are actually loaded is set by the num_chan argument when the module is loaded. Alternatively, specify names= and unique names separated by commas.

The num_chan= and names= specifiers are mutually exclusive. If neither num_chan= nor names= are specified, the default value is three. If debug is set to 1 (the default is 0), some additional HAL parameters will be exported, which might be useful for tuning, but are otherwise unnecessary.

In the following description, it is assumed that we are discussing position loops. However this component can be used to implement other loops such as speed loops, torch height control, and others.

Each loop has a number of pins and parameters, whose names begin with 'pid.N.', where 'N' is the channel number. Channel numbers start at zero.

The three most important pins are 'command', 'feedback', and 'output'. For a position loop, 'command' and 'feedback' are in position units. For a linear axis, this could be inches, mm, metres, or whatever is relevant. Likewise, for a angular axis, it could be degrees, radians, etc. The units of the 'output' pin represent the change needed to make the feedback match the command. As such, for a position loop 'output' is a velocity, in inches/sec, mm/sec, degrees/sec, etc.

Each loop has several other pins as well. 'error' is equal to 'command' minus 'feedback'. 'enable' is a bit that enables the loop. If 'enable' is false, all integrators are reset, and the output is forced to zero. If 'enable' is true, the loop operates normally.

The PID gains, limits, and other 'tunable' features of the loop are implemented as parameters. These are as follows:

Pgain Proportional gain
Igain Integral gain
Dgain Derivative gain
bias Constant offset on output
FF0 Zeroth order Feedforward gain
FF1 First order Feedforward gain
FF2 Second order Feedforward gain
FF3 Third order Feedforward gain
deadband Amount of error that will be ignored
maxerror Limit on error
maxerrorI Limit on error integrator
maxerrorD Limit on error differentiator
maxcmdD Limit on command differentiator
maxcmdDD Limit on command 2nd derivative
maxcmdDDD Limit on command 3rd derivative
maxoutput Limit on output value

All of the limits (max____) are implemented such that if the parameter value is zero, there is no limit.

A number of internal values which may be useful for testing and tuning are also available as parameters. To avoid cluttering the parameter list, these are only exported if "debug=1" is specified on the insmod command line.

errorI Integral of error
errorD Derivative of error
commandD Derivative of the command
commandDD 2nd derivative of the command
commandDDD 3rd derivative of the command

The PID loop calculations are as follows (see the code in pid.c for all the nitty gritty details):

    error = command - feedback
    if ( abs(error) < deadband ) then error = 0
    limit error to +/- maxerror
    errorI += error * period
    limit errorI to +/- maxerrorI
    errorD = (error - previouserror) / period
    limit errorD to +/- maxerrorD
    commandD = (command - previouscommand) / period
    limit commandD to +/- maxcmdD
    commandDD = (commandD - previouscommandD) / period
    limit commandDD to +/- maxcmdDD
    commandDDD = (commandDD - previouscommandDD) / period
    limit commandDDD to +/- maxcmdDDD
    output = bias + error * Pgain + errorI * Igain +
             errorD * Dgain + command * FF0 + commandD * FF1 +
             commandDD * FF2 + commandDDD * FF3
    limit output to +/- maxoutput

This component has a built in auto tune mode. It works by setting up a limit cycle to characterize the process. This is called the Relay method and described in the 1984 Automation paper Automatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins by Karl Johan Åström and Tore Hägglund (doi:10.1016/0005-1098(84)90014-1), https://lup.lub.lu.se/search/ws/files/6340936/8509157.pdf. Using this method, Pgain/Igain/Dgain or Pgain/Igain/FF1 can be determined using the Ziegler-Nichols algorithm. When using FF1 tuning, scaling must be set so that output is in user units per second.

During auto tuning, the command input should not change. The limit cycle is setup around the commanded position. No initial tuning values are required to start auto tuning. Only tune-cycles, tune-effort and tune-mode need be set before starting auto tuning. Note that setting tune-mode to true disable the control loop. When auto tuning completes, the tuning parameters will be set, the output set to bias and the controller still be disabled. If running from LinuxCNC, the FERROR setting for the axis being tuned may need to be loosened up, as it must be larger than the limit cycle amplitude in order to avoid a following error.

To perform auto tuning, take the following steps. Move the axis to be tuned somewhere near the center of it's travel. Set tune-cycles (the default value should be fine in most cases) and tune-mode. Set tune-effort to a small value. Set enable to true. Set tune-mode to true. Set tune-start to true. If no oscillation occurs, or the oscillation is too small, slowly increase tune-effort. Set tune-start to true. If no oscillation occurs, or the oscillation is too small, slowly increase tune-effort Auto tuning can be aborted at any time by setting enable or tune-mode to false.

NAMING
The names for pins, parameters, and functions are prefixed as:
  pid.N. for N=0,1,...,num-1 when using num_chan=num
  nameN. for nameN=name1,name2,... when using names=name1,name2,...

The pid.N. format is shown in the following descriptions.

FUNCTIONS

pid.N.do-pid-calcs (uses floating-point) Does the PID calculations for control loop N.

PINS

pid.N.command float in
    The desired (commanded) value for the control loop.

pid.N.Pgain float in
    Proportional gain. Results in a contribution to the output that is the error multiplied by Pgain.

pid.N.Igain float in
    Integral gain. Results in a contribution to the output that is the integral of the error multiplied by Igain. For example an error of 0.02 that lasted 10 seconds would result in an integrated error (errorI) of 0.2, and if Igain is 20, the integral term would add 4.0 to the output.

pid.N.Dgain float in
    Derivative gain. Results in a contribution to the output that is the rate of change (derivative) of the error multiplied by Dgain. For example an error that changed from 0.02 to 0.03 over 0.2 seconds would result in an error derivative (errorD) of of 0.05, and if Dgain is 5, the derivative term would add 0.25 to the output.

pid.N.feedback float in
    The actual (feedback) value, from some sensor such as an encoder.

pid.N.output float out
    The output of the PID loop, which goes to some actuator such as a motor.

pid.N.command-deriv float in
    The derivative of the desired (commanded) value for the control loop. If no signal is connected then the derivative will be estimated numerically.

pid.N.feedback-deriv float in
    The derivative of the actual (feedback) value for the control loop. If no signal is connected then the derivative will be estimated numerically. When the feedback is from a quantized position source (e.g., encoder feedback position), behavior of the D term can be improved by using a better velocity estimate here, such as the velocity output of encoder(9) or hostmot2(9).

pid.N.error-previous-target bit in
    Use previous invocation's target vs. current position for error calculation, like the motion controller expects. This may make torque-mode position loops and loops requiring a large I gain easier to tune, by eliminating velocity-dependent following error.

pid.N.error float out
    The difference between command and feedback.

pid.N.enable bit in
    When true, enables the PID calculations. When false, output is zero, and all internal integrators, etc, are reset.

pid.N.index-enable bit in
    On the falling edge of index-enable, pid does not update the internal command derivative estimate. On systems which use the encoder index pulse, this pin should be connected to the index-enable signal. When this is not done, and FF1 is nonzero, a step change in the input command causes a single-cycle spike in the PID output. On systems which use exactly one of the -deriv inputs, this affects the D term as well.

pid.N.bias float in
    bias is a constant amount that is added to the output. In most cases it should be left at zero. However, it can sometimes be useful to compensate for offsets in servo amplifiers, or to balance the weight of an object that moves vertically. bias is turned off when the PID loop is disabled, just like all other components of the output. If a non-zero output is needed even when the PID loop is disabled, it should be added with an external HAL sum2 block.

pid.N.FF0 float in
    Zero order feed-forward term. Produces a contribution to the output that is FF0 multiplied by the commanded value. For position loops, it should usually be left at zero. For velocity loops, FF0 can compensate for friction or motor counter-EMF and may permit better tuning if used properly.

pid.N.FF1 float in
    First order feed-forward term. Produces a contribution to the output that is FF1 multiplied by the derivative of the commanded value. For position loops, the contribution is proportional to speed, and can be used to compensate for friction or motor CEMF. For velocity loops, it is proportional to acceleration and can compensate for inertia. In both cases, it can result in better tuning if used properly.

pid.N.FF2 float in
    Second order feed-forward term. Produces a contribution to the output that is FF2 multiplied by the second derivative of the commanded value. For position loops, the contribution is proportional to acceleration, and can be used to compensate for inertia. For velocity loops, the contribution is proportional to jerk, and should usually be left at zero.

pid.N.FF3 float in
    Third order feed-forward term. Produces a contribution to the output that is FF3 multiplied by the third derivative of the commanded value. For position loops, the contribution is proportional to jerk, and can be used to compensate for residual errors during acceleration. For velocity loops, the contribution is proportional to snap(jounce), and should usually be left at zero.

pid.N.deadband float in
    Defines a range of "acceptable" error. If the absolute value of error is less than deadband, it will be treated as if the error is zero. When using feedback devices such as encoders that are inherently quantized, the deadband should be set slightly more than one-half count, to prevent the control loop from hunting back and forth if the command is between two adjacent encoder values. When the absolute value of the error is greater than the deadband, the deadband value is subtracted from the error before performing the loop calculations, to prevent a step in the transfer function at the edge of the deadband (see BUGS).

pid.N.maxoutput float in
    Output limit. The absolute value of the output will not be permitted to exceed maxoutput, unless maxoutput is zero. When the output is limited, the error integrator will hold instead of integrating, to prevent windup and overshoot.

pid.N.maxerror float in
    Limit on the internal error variable used for P, I, and D. Can be used to prevent high Pgain values from generating large outputs under conditions when the error is large (for example, when the command makes a step change). Not normally needed, but can be useful when tuning non-linear systems.

pid.N.maxerrorD float in
    Limit on the error derivative. The rate of change of error used by the Dgain term will be limited to this value, unless the value is zero. Can be used to limit the effect of Dgain and prevent large output spikes due to steps on the command and/or feedback. Not normally needed.

pid.N.maxerrorI float in
    Limit on error integrator. The error integrator used by the Igain term will be limited to this value, unless it is zero. Can be used to prevent integrator windup and the resulting overshoot during/after sustained errors. Not normally needed.

pid.N.maxcmdD float in
    Limit on command derivative. The command derivative used by FF1 will be limited to this value, unless the value is zero. Can be used to prevent FF1 from producing large output spikes if there is a step change on the command. Not normally needed.

pid.N.maxcmdDD float in
    Limit on command second derivative. The command second derivative used by FF2 will be limited to this value, unless the value is zero. Can be used to prevent FF2 from producing large output spikes if there is a step change on the command. Not normally needed.

pid.N.maxcmdDDD float in
    Limit on command third derivative. The command third derivative used by FF3 will be limited to this value, unless the value is zero. Can be used to prevent FF3 from producing large output spikes if there is a step change on the command. Not normally needed.

pid.N.saturated bit out
    When true, the current PID output is saturated. That is,
    output = ± maxoutput.

pid.N.saturated-s float out

pid.N.saturated-count s32 out
    When true, the output of PID was continually saturated for this many seconds (saturated-s) or periods (saturated-count).

  Additional auto tuning pins

pid.N.tune-mode bit in
    When true, enables auto tune mode. When false, normal PID calculations are performed.

pid.N.tune-start bit io
    When set to true, starts auto tuning. Cleared when the auto tuning completes.

pid.N.tune-type u32 rw
    When set to 0, Pgain/Igain/Dgain are calculated. When set to 1, Pgain/Igain/FF1 are calculated.

pid.N.tune-cycles u32 rw
    Determines the number of cycles to run to characterize the process. tune-cycles actually sets the number of half cycles. More cycles results in a more accurate characterization as the average of all cycles is used.

pid.N.tune-effort float rw
    Determines the effort used in setting up the limit cycle in the process. tune-effort should be set to a positive value less than maxoutput. Start with something small and work up to a value that results in a good portion of the maximum motor current being used. The smaller the value, the smaller the amplitude of the limit cycle.

pid.N.ultimate-gain float ro (only if debug=1)
    Determined from process characterization. ultimate-gain is the ratio of tune-effort to the limit cycle amplitude multiplied by 4.0 divided by Pi.

pid.N.ultimate-period float ro (only if debug=1)
    Determined from process characterization. ultimate-period is the period of the limit cycle.

PARAMETERS

pid.N.errorI float ro (only if debug=1)
    Integral of error. This is the value that is multiplied by Igain to produce the Integral term of the output.

pid.N.errorD float ro (only if debug=1)
    Derivative of error. This is the value that is multiplied by Dgain to produce the Derivative term of the output.

pid.N.commandD float ro (only if debug=1)
    Derivative of command. This is the value that is multiplied by FF1 to produce the first order feed-forward term of the output.

pid.N.commandDD float ro (only if debug=1)
    Second derivative of command. This is the value that is multiplied by FF2 to produce the second order feed-forward term of the output.

pid.N.commandDDD float ro (only if debug=1)
    Third derivative of command. This is the value that is multiplied by FF3 to produce the third order feed-forward term of the output.

BUGS
Some people would argue that deadband should be implemented such that error is treated as zero if it is within the deadband, and be unmodified if it is outside the deadband. This was not done because it would cause a step in the transfer function equal to the size of the deadband. People who prefer that behavior are welcome to add a parameter that will change the behavior, or to write their own version of pid. However, the default behavior should not be changed.

Negative gains may lead to unwanted behavior. It is possible in some situations that negative FF gains make sense, but in general all gains should be positive. If some output is in the wrong direction, negating gains to fix it is a mistake; set the scaling correctly elsewhere instead.