at_pid - proportional/integral/derivative controller with auto tuning
loadrt at_pid [num_chan=num | names=name1[,name2...]]
at_pid is a classic Proportional/Integral/Derivative controller, used to control position or speed feedback loops for servo motors and other closed-loop applications.
at_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.
at_pid has a built in auto tune mode. It works by setting up a limit cycle to characterize the process. From this, Pgain/Igain/Dgain or Pgain/Igain/FF1 can be determined using Ziegler-Nichols. When using FF1, 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. 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.
To perform auto tuning, take the following steps. Move the axis to be tuned, to 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. Auto tuning can be aborted at any time by setting enable or tune-mode to false.
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.
pid.N.do-pid-calcs (uses floating-point)
Does the PID calculations for control loop N.
pid.N.command float in
The desired (commanded) value for the control loop.
pid.N.feedback float in
The actual (feedback) value, from some sensor such as an encoder.
pid.N.error float out
The difference between command and feedback.
pid.N.output float out
The output of the PID loop, which goes to some actuator such as a motor.
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.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.Pgain float rw
Proportional gain. Results in a contribution to the output that is the error multiplied by Pgain.
pid.N.Igain float rw
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 rw
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.bias float rw
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 rw
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 rw
First order feed-forward term. Produces a contribution to the output that 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 rw
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, it should usually be left at zero.
pid.N.deadband float rw
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 rw
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 rw
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 rw
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 rw
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 rw
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 rw
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.tune-type u32 rw
When set to 0, Pgain/Igain/Dgain are caclulated. 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 effor 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.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.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.
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 at_pid. However, the default behavior should not be changed.