.TH PID "9" "2007-01-16" "LinuxCNC Documentation" "HAL Component"

.SH NAME
pid \- proportional/integral/derivative controller with automatic tuning support
.SH SYNOPSIS
\fBloadrt pid [num_chan=\fInum\fB | names=\fIname1\fB[,\fIname2...\fB]] [\fBdebug=\fIdbg\fR]

.SH DESCRIPTION
\fBpid\fR is a classic Proportional/Integral/Derivative controller,
used to control position or speed feedback loops for servo motors and other closed-loop applications.
.P
\fBpid\fR supports a maximum of sixteen controllers.
The number that are actually loaded is set by the \fBnum_chan\fR argument when the module is loaded.
Alternatively, specify names= and unique names separated by commas.
.P
The \fBnum_chan=\fR and \fBnames=\fR specifiers are mutually exclusive.
If neither \fBnum_chan=\fR nor \fBnames=\fR are specified, the default value is three.
If \fBdebug\fR 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.

.P
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.

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

.PP
\fBPgain\fR Proportional gain
.PD 0
.P
.PD
\fBIgain\fR Integral gain
.PD 0
.P
.PD
\fBDgain\fR Derivative gain
.PD 0
.P
.PD
\fBbias\fR Constant offset on output
.PD 0
.P
.PD
\fBFF0\fR \fR Zeroth order Feedforward gain
.PD 0
.P
.PD
\fBFF1\fR \fR First order Feedforward gain
.PD 0
.P
.PD
\fBFF2\fR \fR Second order Feedforward gain
.PD 0
.P
.PD
\fBFF3\fR \fR Third order Feedforward gain
.PD 0
.P
.PD
\fBdeadband\fR Amount of error that will be ignored
.PD 0
.P
.PD
\fBmaxerror\fR Limit on error
.PD 0
.P
.PD
\fBmaxerrorI\fR Limit on error integrator
.PD 0
.P
.PD
\fBmaxerrorD\fR Limit on error differentiator
.PD 0
.P
.PD
\fBmaxcmdD\fR Limit on command differentiator
.PD 0
.P
.PD
\fBmaxcmdDD\fR Limit on command 2nd derivative
.PD 0
.P
.PD
\fBmaxcmdDDD\fR Limit on command 3rd derivative
.PD 0
.P
.PD
\fBmaxoutput\fR Limit on output value
.P
All of the limits (max____) are implemented such that if the parameter value is zero, there is no limit.
.P
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.

.PP
\fBerrorI\fR Integral of error
.PD 0
.P
.PD
\fBerrorD\fR Derivative of error
.PD 0
.P
.PD
\fBcommandD\fR Derivative of the command
.PD 0
.P
.PD
\fBcommandDD\fR 2nd derivative of the command
.PD 0
.P
.PD
\fBcommandDDD\fR 3rd derivative of the command

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

.P
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
\fBAutomatic Tuning of Simple Regulators with Specifications on Phase and Amplitude Margins\fR 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, \fBPgain/Igain/Dgain\fR or \fBPgain/Igain/FF1\fR can be determined using the Ziegler-Nichols algorithm.
When using \fBFF1\fR tuning, scaling must be set so that \fBoutput\fR is in user units per second.

.P
During auto tuning, the \fBcommand\fR input should not change.
The limit cycle is setup around the commanded position.
No initial tuning values are required to start auto tuning.
Only \fBtune\-cycles\fR, \fBtune\-effort\fR and \fBtune\-mode\fR need be set before starting auto tuning.
Note that setting \fBtune\-mode\fR 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.
.P
To perform auto tuning, take the following steps.
Move the axis to be tuned somewhere near the center of it's travel.
Set \fBtune\-cycles\fR (the default value should be fine in most cases) and \fBtune\-mode\fR.
Set \fBtune\-effort\fR to a small value. Set \fBenable\fR to true. Set \fBtune\-mode\fR to true.
Set \fBtune\-start\fR to true. If no oscillation occurs, or the oscillation is too small, slowly increase \fBtune\-effort\fR.
Set \fBtune\-start\fR to true.
If no oscillation occurs, or the oscillation is too small, slowly increase \fBtune\-effort\fR
Auto tuning can be aborted at any time by setting \fBenable\fR or \fBtune\-mode\fR to false.

.SH NAMING
The names for pins, parameters, and functions are prefixed as:
  \fBpid.N.\fR for N=0,1,...,num\-1 when using \fBnum_chan=num\fR
  \fBnameN.\fR for nameN=name1,name2,... when using \fBnames=name1,name2,...\fR

The \fBpid.N.\fR format is shown in the following descriptions.

.SH FUNCTIONS

\fBpid.\fIN\fB.do\-pid\-calcs\fR (uses floating-point)
Does the PID calculations for control loop \fIN\fR.

.SH PINS

.TP
\fBpid.\fIN\fB.command\fR float in
The desired (commanded) value for the control loop.
.TP
\fBpid.\fIN\fB.Pgain\fR float in
Proportional gain.  Results in a contribution to the output that is the error multiplied by \fBPgain\fR.
.TP
\fBpid.\fIN\fB.Igain\fR float in
Integral gain.  Results in a contribution to the output that is the integral of the error multiplied by \fBIgain\fR.
For example an error of 0.02 that lasted 10 seconds would result in an integrated error (\fBerrorI\fR) of 0.2, and if \fBIgain\fR is 20, the integral term would add 4.0 to the output.
.TP
\fBpid.\fIN\fB.Dgain\fR float in
Derivative gain.  Results in a contribution to the output that is the rate of change (derivative) of the error multiplied by \fBDgain\fR.
For example an error that changed from 0.02 to 0.03 over 0.2 seconds would result in an error derivative (\fBerrorD\fR) of of 0.05, and if \fBDgain\fR is 5,
the derivative term would add 0.25 to the output.
.TP
\fBpid.\fIN\fB.feedback\fR float in
The actual (feedback) value, from some sensor such as an encoder.
.TP
\fBpid.\fIN\fB.output\fR float out
The output of the PID loop, which goes to some actuator such as a motor.
.TP
\fBpid.\fIN\fB.command\-deriv\fR 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.
.TP
\fBpid.\fIN\fB.feedback\-deriv\fR 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).
.TP
\fBpid.\fIN\fB.error\-previous\-target\fR 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.
.TP
\fBpid.\fIN\fB.error\fR float out
The difference between command and feedback.
.TP
\fBpid.\fIN\fB.enable\fR bit in
When true, enables the PID calculations.  When false, \fBoutput\fR is zero, and all internal integrators, etc, are reset.
.TP
\fBpid.\fIN\fB.index\-enable\fR bit in
On the falling edge of \fBindex\-enable\fR, 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 \fB\-deriv\fR inputs, this affects the D term as well.
.TP
\fBpid.\fIN\fB.bias\fR float in
\fBbias\fR 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.
\fBbias\fR 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.
.TP
\fBpid.\fIN\fB.FF0\fR float in
Zero order feed-forward term.
Produces a contribution to the output that is \fBFF0\fR multiplied by the commanded value.
For position loops, it should usually be left at zero.
For velocity loops, \fBFF0\fR can compensate for friction or motor counter-EMF and may permit better tuning if used properly.
.TP
\fBpid.\fIN\fB.FF1\fR float in
First order feed-forward term.
Produces a contribution to the output that is \fBFF1\fR 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.
.TP
\fBpid.\fIN\fB.FF2\fR float in
Second order feed-forward term.
Produces a contribution to the output that is \fBFF2\fR 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.
.TP
\fBpid.\fIN\fB.FF3\fR float in
Third order feed-forward term.
Produces a contribution to the output that is \fBFF3\fR 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.
.TP
\fBpid.\fIN\fB.deadband\fR float in
Defines a range of "acceptable" error.
If the absolute value of \fBerror\fR is less than \fBdeadband\fR, 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 \fBBUGS\fR).
.TP
\fBpid.\fIN\fB.maxoutput\fR float in
Output limit.  The absolute value of the output will not be permitted to exceed \fBmaxoutput\fR, unless \fBmaxoutput\fR is zero.
When the output is limited, the error integrator will hold instead of integrating, to prevent windup and overshoot.
.TP
\fBpid.\fIN\fB.maxerror\fR float in
Limit on the internal error variable used for P, I, and D.
Can be used to prevent high \fBPgain\fR 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.
.TP
\fBpid.\fIN\fB.maxerrorD\fR float in
Limit on the error derivative.  The rate of change of error used by the
\fBDgain\fR term will be limited to this value, unless the value is zero.
Can be used to limit the effect of \fBDgain\fR and prevent large output spikes due to steps on the command and/or feedback.
Not normally needed.
.TP
\fBpid.\fIN\fB.maxerrorI\fR float in
Limit on error integrator.  The error integrator used by the \fBIgain\fR 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.
.TP
\fBpid.\fIN\fB.maxcmdD\fR float in
Limit on command derivative.  The command derivative used by \fBFF1\fR will be limited to this value, unless the value is zero.
Can be used to prevent \fBFF1\fR from producing large output spikes if there is a step change on the command.  Not normally needed.
.TP
\fBpid.\fIN\fB.maxcmdDD\fR float in
Limit on command second derivative.  The command second derivative used by \fBFF2\fR will be limited to this value, unless the value is zero.
Can be used to prevent \fBFF2\fR from producing large output spikes if there is a step change on the command.  Not normally needed.
.TP
\fBpid.\fIN\fB.maxcmdDDD\fR float in
Limit on command third derivative.  The command third derivative used by \fBFF3\fR will be limited to this value, unless the value is zero.
Can be used to prevent \fBFF3\fR from producing large output spikes if there is a step change on the command.  Not normally needed.
.TP
\fBpid.\fIN\fB.saturated\fR bit out
When true, the current PID output is saturated.  That is,
.RS 12
\fBoutput\fR = \(+- \fBmaxoutput\fR.
.RE
.TP
\fBpid.\fIN\fB.saturated\-s\fR float out
.br
.ns
.TP
\fBpid.\fIN\fB.saturated\-count\fR s32 out
When true, the output of PID was continually saturated for this many seconds
(\fBsaturated\-s\fR) or periods (\fBsaturated\-count\fR).

.SS Additional auto tuning pins
.TP
\fBpid.\fIN\fB.tune\-mode\fR bit in
When true, enables auto tune mode.  When false, normal PID calculations are performed.
.TP
\fBpid.\fIN\fB.tune\-start\fR bit io
When set to true, starts auto tuning.  Cleared when the auto tuning completes.
.TP
\fBpid.\fIN\fB.tune\-type\fR u32 rw
When set to 0, \fBPgain/Igain/Dgain\fR are calculated. When set to 1, \fBPgain/Igain/FF1\fR are calculated.
.TP
\fBpid.\fIN\fB.tune\-cycles\fR u32 rw
Determines the number of cycles to run to characterize the process.
\fBtune\-cycles\fR actually sets the number of half cycles.
More cycles results in a more accurate characterization as the average of all cycles is used.
.TP
\fBpid.\fIN\fB.tune\-effort\fR float rw
Determines the effort used in setting up the limit cycle in the process.
\fBtune\-effort\fR should be set to a positive value less than \fBmaxoutput\fR.
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.
.TP
\fBpid.\fIN\fB.ultimate\-gain\fR float ro (only if debug=1)
Determined from process characterization. \fBultimate\-gain\fR is the ratio of \fBtune\-effort\fR to the limit cycle amplitude multiplied by 4.0 divided by Pi.
.TP
\fBpid.\fIN\fB.ultimate\-period\fR float ro (only if debug=1)
Determined from process characterization. \fBultimate\-period\fR is the period of the limit cycle.

.SH PARAMETERS
.TP
\fBpid.\fIN\fB.errorI\fR float ro (only if debug=1)
Integral of error.  This is the value that is multiplied by \fBIgain\fR to produce the Integral term of the output.
.TP
\fBpid.\fIN\fB.errorD\fR float ro (only if debug=1)
Derivative of error.  This is the value that is multiplied by \fBDgain\fR to produce the Derivative term of the output.
.TP
\fBpid.\fIN\fB.commandD\fR float ro (only if debug=1)
Derivative of command.  This is the value that is multiplied by \fBFF1\fR to produce the first order feed-forward term of the output.
.TP
\fBpid.\fIN\fB.commandDD\fR float ro (only if debug=1)
Second derivative of command.  This is the value that is multiplied by \fBFF2\fR to produce the second order feed-forward term of the output.
.TP
\fBpid.\fIN\fB.commandDDD\fR float ro (only if debug=1)
Third derivative of command.  This is the value that is multiplied by \fBFF3\fR to produce the third order feed-forward term of the output.

.SH 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 \fBpid\fR.
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.