.TH AT_PID "9" "2007-05-12" "LinuxCNC Documentation" "HAL Component" .de TQ .br .ns .TP \\$1 .. .SH NAME at_pid \- proportional/integral/derivative controller with auto tuning .SH SYNOPSIS \fBloadrt at_pid [num_chan=\fInum\fB | names=\fIname1\fB[,\fIname2...\fB]] .SH DESCRIPTION \fBat_pid\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 \fBat_pid\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 \fBnames=\fR 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. .P 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 \fBat_pid\fR has a built in auto tune mode. It works by setting up a limit cycle to characterize the process. From this, \fBPgain/Igain/Dgain\fR or \fBPgain/Igain/FF1\fR can be determined using Ziegler-Nichols. When using \fBFF1\fR, 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. When auto tuning completes, the tuning parameters will be set. 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, to 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. 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 .TP \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.feedback\fR float in The actual (feedback) value, from some sensor such as an encoder. .TP \fBpid.\fIN\fB.error\fR float out The difference between command and feedback. .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.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.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. .SH PARAMETERS .TP \fBpid.\fIN\fB.Pgain\fR float rw Proportional gain. Results in a contribution to the output that is the error multiplied by \fBPgain\fR. .TP \fBpid.\fIN\fB.Igain\fR float rw 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 rw 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.bias\fR float rw \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 rw 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 rw First order feed-forward term. Produces a contribution to the output that \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 rw 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, it should usually be left at zero. .TP \fBpid.\fIN\fB.deadband\fR float rw 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 rw 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 rw 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 rw 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 rw 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 rw 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 rw 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.tune-type\fR u32 rw When set to 0, \fBPgain/Igain/Dgain\fR are caclulated. 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 effor 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.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.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 multipled by 4.0 divided by Pi. \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 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 \fBat_pid\fR. However, the default behavior should not be changed.