Extend pid(9) with explanation from pic.d source

Now explain the calculation done by the pid controller and how
each factor contribute to the total.

docs/man/man9/pid.9

@@ -21,6 +21,146 @@ 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
+
 .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