SYNOPSIS

DESCRIPTION

NAMING

FUNCTIONS

PINS

PARAMETERS

BUGS

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

nameN.

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
multipled 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.