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Merge pull request #1801 from petterreinholdtsen/man-pid-calc
Extend pid(9) with explanation from pic.d source
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‎docs/man/man9/pid.9‎

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@@ -21,6 +21,146 @@ value is three. If \fBdebug\fR is set to 1 (the default is 0), some
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additional HAL parameters will be exported, which might be useful
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for tuning, but are otherwise unnecessary.
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.P
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In the following description, it is assumed that we are discussing
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position loops. However this component can be used to implement other
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loops such as speed loops, torch height control, and others.
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.P
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Each loop has a number of pins and parameters, whose names begin
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with 'pid.N.', where 'N' is the channel number. Channel numbers start
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at zero.
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.P
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The three most important pins are 'command', 'feedback', and 'output'.
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For a position loop, 'command' and 'feedback' are in position units.
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For a linear axis, this could be inches, mm, metres, or whatever is
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relevant. Likewise, for a angular axis, it could be degrees, radians,
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etc. The units of the 'output' pin represent the change needed to
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make the feedback match the command. As such, for a position
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loop 'Output' is a velocity, in inches/sec, mm/sec, degrees/sec, etc.
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.P
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Each loop has several other pins as well. 'error' is equal
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to 'command' minus 'feedback'. 'enable' is a bit that enables the
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loop. If 'enable' is false, all integrators are reset, and the output
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is forced to zero. If 'enable' is true, the loop operates normally.
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.P
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The PID gains, limits, and other 'tunable' features of the loop are
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implemented as parameters. These are as follows:
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.PP
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\fBPgain\fR Proportional gain
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.PD 0
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.P
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.PD
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\fBIgain\fR Integral gain
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.PD 0
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.P
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.PD
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\fBDgain\fR Derivative gain
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.PD 0
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.P
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.PD
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\fBbias\fR Constant offset on output
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.PD 0
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.P
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.PD
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\fBFF0\fR \fR Zeroth order Feedforward gain
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.PD 0
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.P
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.PD
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\fBFF1\fR \fR First order Feedforward gain
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.PD 0
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.P
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.PD
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\fBFF2\fR \fR Second order Feedforward gain
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.PD 0
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.P
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.PD
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\fBFF3\fR \fR Third order Feedforward gain
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.PD 0
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.P
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.PD
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\fBdeadband\fR Amount of error that will be ignored
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.PD 0
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.P
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.PD
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\fBmaxerror\fR Limit on error
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.PD 0
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.P
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.PD
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\fBmaxerrorI\fR Limit on error integrator
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.PD 0
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.P
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.PD
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\fBmaxerrorD\fR Limit on error differentiator
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.PD 0
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.P
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.PD
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\fBmaxcmdD\fR Limit on command differentiator
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.PD 0
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.P
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.PD
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\fBmaxcmdDD\fR Limit on command 2nd derivative
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.PD 0
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.P
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.PD
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\fBmaxcmdDDD\fR Limit on command 3rd derivative
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.PD 0
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.P
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.PD
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\fBmaxoutput\fR Limit on output value
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.P
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All of the limits (max____) are implemented such that if the parameter
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value is zero, there is no limit.
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.P
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A number of internal values which may be useful for testing and tuning
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are also available as parameters. To avoid cluttering the parameter
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list, these are only exported if "debug=1" is specified on the insmod
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command line.
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.PP
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\fBerrorI\fR Integral of error
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.PD 0
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.P
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.PD
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\fBerrorD\fR Derivative of error
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.PD 0
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.P
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.PD
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\fBcommandD\fR Derivative of the command
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.PD 0
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.P
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.PD
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\fBcommandDD\fR 2nd derivative of the command
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.PD 0
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.P
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.PD
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\fBcommandDDD\fR 3rd derivative of the command
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.P
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The PID loop calculations are as follows (see the code in pid.c for
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all the nitty gritty details):
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.IP
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.nf
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error = command - feedback
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if ( abs(error) < deadband ) then error = 0
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limit error to +/- maxerror
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errorI += error * period
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limit errorI to +/- maxerrorI
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errorD = (error - previouserror) / period
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limit errorD to +/- maxerrorD
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commandD = (command - previouscommand) / period
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limit commandD to +/- maxcmdD
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commandDD = (commandD - previouscommandD) / period
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limit commandDD to +/- maxcmdDD
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commandDDD = (commandDD - previouscommandDD) / period
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limit commandDDD to +/- maxcmdDDD
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output = bias + error * Pgain + errorI * Igain +
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errorD * Dgain + command * FF0 + commandD * FF1 +
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commandDD * FF2 + commandDDD * FF3
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limit output to +/- maxoutput
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.fi
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.SH NAMING
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The names for pins, parameters, and functions are prefixed as:
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\fBpid.N.\fR for N=0,1,...,num\-1 when using \fBnum_chan=num\fR

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