PID
filter control
The
SmartMotor™ includes a very high quality, high performance brushless
D.C. servomotor. It has a rotor with extremely powerful rare earth
magnets and a stator (the outside, stationary part) that is a
densely wound multi-slotted electro-magnet.
Controlling
the position of a brushless D.C. servo's rotor with only electro-magnetism
working as a lever is like pulling a sled with a rubber band.
Accurate control would seem impossible.
The
parameter that makes it happen is found in the PID (Proportional,
Integral, Derivative) filter section. These are the three fundamental
coefficients to a mathematical algorithm that intelligently recalculates
and delivers the power needed by the motor about 4,000 times per
second. The input to the PID filter is the instantaneous actual
position minus the desired position, be it at rest, or part of
an ongoing trajectory. This difference is called the error.
The
Proportional parameter of the filter creates a simple spring constant.
The further the shaft is rotated away from its target position,
the more power is delivered to return it. With this as the only
parameter the motor shaft would respond just as the end of a spring
would if you grabbed and twisted it.
If
you twist the spring and let go it will vibrate wildly. This sort
of vibration is hazardous to most mechanisms. In this scenario
a shock absorber is added to cancel the vibrations which is the
equivalent of what the Derivitive parameter does. If you sat on
the fender of a car it would dip down because of your weight based
on the constant of the car's spring. You would'nt know if the
shocks were good or bad. If you jumped up and and down on the
bumper, however, you could quickly tell whether the shock absorbers
were working. That's because they are not activated by position
but by speed. The Derivative parameter steals power away as a
function of the rate of change of the overall filter output. The
parameter gets its name from the fact that the derivative of position
is speed. Electronically stealing power based on the magnitude
of the motor shafts vibration has the same effect as putting a
shock absorber in the system, and the algorithm never goes bad.
Even
with the two parameters a situation can arise that will cause
the servo to leave its target created by dead weight". If a constant
torque is applied to the end of the shaft, the shaft will comply
until the deflection causes the Proportional parameter to rise
to the equivalent torque. There is no speed so the Derivative
parameter has no effect. As long as the torque is there, the motor's
shaft will be off of its target.
That's
where the Integral parameter comes in. The integral of position
is time, and the Integral parameter mounts an opposing force that
is a function of time. As time passes and there is a deflection
present, the Integral parameter will add a little force to bring
it back on target each cycle. There is also a separate parameter
(KL) used to limit the Integral parameter's scope of what it can
do.
Each
of these parameters have their own scaling factor to tailor the
overall performance of the filter to the specific load conditions
of any one particular application. The scaling factors are as
follows:
KP
Proportional
KI
Integral
KD
Derivative
KL
Integral Limit
Tuning
the filter
The
task of tuning the filter is complicated by the fact that the
parameters are so interdependent. A change in one can shift the
optimal settings of the others. The automatic utility relieves
you of this aggravation, but you still may want to know how to
tune a servo.
When
tuning the motor it is useful to have the status monitor running.
This will allow you to monitor various bits of information that
will reflect the motors performance.
KP=exp
Set KP, proportional coeff.
KI=exp
Set KI, time-error coefficient
KD=exp
Set KD, damping coefficient
KL=exp
Set KL, time-error term limit
F Update
PID filter
The
main objective in tuning a servo is to get KP as high as possible,
while maintaining stability. The higher the KP the stiffer the
system and the more under control it is. A good start is to simply
query what to begin with (RKP) and then start increasing it 10%
to 20% at a time. It is a good idea to start with KI equal to
zero. Keep in mind that the new settings do not take effect until
the F command is issued. Each time you raise KP, try physically
to destabilize the system, by bumping or twisting it. Alternatively,
you could have a program loop cycling that invokes abrupt motions.
As long as the motor always settles to a quiet rest, you can keep
raising KP.
As
soon as you reach the limit, you need to rediscover the appropriate
derivative compensation. Move KD up and down until you locate
the position that gives you the quickest stability. If KD is way
too high, you will hear a grinding sound. It is not really grinding,
but it is a sign that you will want to go the other way. A good
tune is not only stable, but reasonably quiet. After optimizing
KD, you may find that you can raise KP a little more. Keep going
back and forth until you have exhausted all you can do to improve
the stiffness of the system. Then it is time to take a look at
KI.
KI
in most cases is used to compensate for friction. Without it you
will never get exactly on target. Begin with KI equal to zero
and KL equal to 1000. Move the motor off target and start increasing
KI and KL. Keep KL at least ten times KI during this phase.
Continue
to increase KI until the motor always reaches its target, and
once that happens add about 30% to KI and start bringing down
KL until you notice it hampering the ability for the KI term to
close the position precisely to target. Once you reach that point,
increase KL by about 30% as well. You want the Integral term to
be strong enough to overcome friction, but you also want the limit
to be set so that an unruly amount of power will not be delivered
if the mechanism were to jam or simply find itself against one
of its ends of travel.
E=expression Set maximum position error
The
difference between where the motor shaft is and where it is supposed
to be is appropriately called the error". The magnitude and sign
of the error is delivered to the motor in the form of torque,
after it is put through the PID filter. The higher the error,
the more out of control the motor is. Therefore, it is often useful
to put a limit on the allowable error, after which time the motor
will be turned off. That is what the E command is for. It defaults
to 1000 encoder counts, but can be set from 1 to 32,000.
There
are still more parameters that can be utilized to reduce the position
error of a dynamic application. Most of the forces that aggravate
a PID loop through the execution of a motion trajectory are unpredictable,
but there are some that can be predicted and further eliminated
preemptively.
KG=expression Set KG, Gravity offset term
KGOFF Kill KG term during error
KGON Maintain KG during error
The
simplest of these is gravity. Why burden the PID loop with the
effects of gravity in a vertical load application, if it can simply
be weeded out. If in a particular application, motion would occur
with the power off due to gravity, a constant offset can be incorporated
into the filter to balance the system. KG is the term. KG can
range from -8388608 to 8388607. To tune KG simply issue the KGON
command, while the motor is not servoing, and make changes to
KG until the load equally favors upward and downward motion. If
when there is a position error you want the motor to drop the
load, then issue KGOFF.
KV=expression Set KVff, velocity feed forward
Another
predictable cause of position error is the natural latency of
the PID loop itself. At higher speeds, because the calculation
takes a finite amount of time, the result is somewhat old news".
The higher the speed, the more the actual motor position will
slightly lag the trajectory calculated position. This can be programmed
out with the KV term. KV can range from zero to 65,535. Typical
values range in the low hundreds. To tune KV simply run the motor
at a constant speed, if the application will allow, and increase
KV until the error gets reduced to near zero and stays there.
KA=expression Set KAff, acceleration feed forward
Force
equals mass times acceleration. If the SmartMotor™ is accelerating
a mass, it will be exerting a force during that acceleration.
This force will disappear immediately upon reaching the cruising
speed. This momentary torque during acceleration is also predictable
and need not aggravate the PID filter. It's effects can be programmed
out with the KA term. It is a little more difficult to tune KA,
especially with hardware attached. The objective is to arrive
at a value that will close the position error during the acceleration
and deceleration phases. It is better to tune KA with KI set to
zero because KI will address this constant force in another way.
It is best to have KA address 100% of the forces due to acceleration,
and leave the KI term to adjust for friction.
KS=expression Set KS, dampening sample rate
You
can reduce the sampling rate of the derivative term, KD, with
the KS term. This can sometimes add stability to very high inertial
loads. Useful values of KS range from 1 (the default) to 20. Results
will vary from application to application.
PID1
Set normal PID update rate
PID2
Divide normal PID update rate by 2
PID4
Divide normal PID update rate by 4
PID8
Divide normal PID update rate by 8
The
trajectory and PID filter calculations occur within the SmartMotor™
4069 times per second. That is faster than is necessary for very
good control, especially with the larger motors. A reduction in
the PID rate can result in an increase in the SmartMotor™ application
program execution rate. The ‘PID2 command will divide the PID
rate by two, and the others even more. The most dramatic effect
on program execution rate occurs with PID4. PID8 does little more
and is encroaching on poor control. If you do lower the PID rate,
keep in mind that this is the sample" rate that is the basis
for Velocity values, Acceleration values, PID coefficients and
wait times. If you cut the rate in half, expect to do the following
to keep all else the same:
Halve wait times
Double Velocity
Increase Acceleration by a factor of 104
Current
limit control
AMPS=expression Set current limit, 0 to 1000
In
some applications, if the motor misapplied full power the mechanism
could be damaged. It can be useful to reduce the maximum amount
of current available thus limitimg the torque the motor can put
out. Use the AMPS command with a number, variable or expression
within the range of 0 to 1000. The units are tenths of percent
of full scale peak current, and varies with the size of your SmartMotor™.
