Advanced Servo TuningAdvanced Servo Tuning

Dr. Dr. RohanRohan MunasingheMunasingheDepartment of Electronic and Department of Electronic and

Telecommunication EngineeringTelecommunication EngineeringUniversity of University of MoratuwaMoratuwa

Motioncontroller(software)

Desired position generator is a piece of software that generates reference position command. Position decoder decodes the position feedback from the position encoder. Position error X is converted to control signal Y by the filter (say PID). DAC converts the control signal to analog.

position encoder

Servo System Servo System ElementsElements

Advanced Motion ControlAdvanced Motion Control

(Integrator Limit)

proportional

derivative

integral

acceleration feedforward

velocity feedforward

offset

±5V

software limit

Single pole software limit

Closes the loop, react quickly, according to the sign of the error

As long as there is any (even a slightest) error due to friction, the integrator keeps building up the control signal until it becomes large enough to overcome friction, and eventually makes the motor rotate to reduce the error.

Low KI ⇒ slow growing of signal (response delay)High KI ⇒ overshoot and instability

provides phase leadopens up BW

Structural resonances and distributed components (things are not perfect in nature) contribute to high frequency dynamics, which is amplified by too large D gain

PID againPID again

Integrator DesignIntegrator DesignLimit the integrator value (to say ±2V) to bout twice as big as friction. We just need to overcome any errors (due to friction and so on).

Freeze the Integrator while the motor is in motion. Of course, we will see large errors during motion particularly at the start of motion (p=0, ref=10), and that is noting abnormal, and there is no need to integrate it. If we do integrate error all the time, the integrator would cause unnecessary overshoots and undershoots about the reference value

Low Pass FilterLow Pass Filter

Limits the gain at high frequency so that the loop wont respond to structural resonances and noise.

LPF closes the BW, a counter action of derivative control.

Filter BW should be slightly bigger than system BW.

Design the D control first and then set the LPF

Notch FilterNotch Filter

Resonance frequency

There are imperfect couplings (not rigid) between motor and load that cause deflections and the plant behaves as a spring which has a certain resonance frequency. When there are resonances between motor andsensor, it affects close loop performance.

To avoid resonance, one way is to significantly reduce the system bandwidth ⇒ low gain, low responsiveness, undesirable

Resonances Are two complex conjugate pair of poles with high imaginary (oscillatory component) and small real (decay) component. These two poles, when we close the loop could easily cross over to the RHP⇒ System instability

If we place two zeros right (or close to) the resonance poles, the resonance effect can be cancelled outYet, its not practically possible to synthesis

only two zeros. The two zeros always come with two new poles.Then, we could place the new poles farther to

the –ve real axis so that their oscillatory response decays out quickly.Perfect pole-zero cancellation is not essential 20~30% offset would have enough cancellation of resonance poles.

Select three parameters NZ, NB, and NF of the notch

Simple Notch Filter DesignSimple Notch Filter Design

(simple observation)

simpleguess

FeedforwardFeedforward DesignDesign

FF signals are not part of CL system

No stability problems

They are smart bias signals

(mechanical systems don’t like step inputs)

Planned trajectory

OffsetOffsetFed directly to DAC

Torque LimitTorque LimitVoltage limiter just before it goes to the amplifier

(apply an offset and see how the motor responds)

uncertainity in motor polaity and +ve feedback

Fighting BacklashFighting Backlash

Backlash DilemmaBacklash Dilemma

delay ⇒ phase loss ⇒ instability

Stable less accurate system

orAccurate system with

risk of instability

Design ApproachesDesign Approaches

put encoder on the motor(80~90% of the cases)

[get rid of gears/belts ⇒ direct drive]happens to be expensive, not found in general applications, not always possible

practical methods

Open Loop Open Loop CompensationCompensation (stable)

Periodic calibrate is required

So that the load always lags behind the motorlow friction causes inertia to make overshootsIf it is the case, OLC does not work properly

If you know it how much- not overly acceptable

Motor immediately engages with the load

Motor engages with the load late

Final Point CorrectionFinal Point Correction

drive the motor to approximate position ⇒ check error ⇒ drive again ⇒ check error ⇒ drive again ….(multiple error correction)Need two encoders (expensive)

AdvantagesAdvantagesStable system (sensor is on the motor)Stable system (sensor is on the motor)Method works regardless of backlash sizeMethod works regardless of backlash size

DisadvantagesDisadvantagesCorrection is at the endCorrection is at the end--point onlypoint only

error remains along the path. OK for single axis motion, or multi-axis point to point motion. Not good for trajectory following applications (such as engraving)

Takes longer timeTakes longer time+ 20~100ms, may/not be acceptable+ 20~100ms, may/not be acceptable

Does not compensate for later disturbancesDoes not compensate for later disturbancesOnce the motion has been completed, controller stops watching on the load encoder (load encoder is not part of the closed loop), thus the loop doesn’t see disturbances

Conventional Dual Loop ControlConventional Dual Loop Control

supervisory outer loop⇒ eliminates position error

stableinner loop

backlash↑ ⇒ delay ↑ ⇒ stability ↑ ⇒ gain has to be reduced ⇒low stiffness (responsiveness) ⇒ position error ↑

Improved Dual Loop Improved Dual Loop ControlControl

Redistribution of PID in an optimal way ⇒ much better performance

strong good loop

weak bad loop

- Stable inner loop- Unstable outer loop- The more stronger

loop wins

Frequency ResponseFrequency Response

1ω 1ω

2ω

load loop

motor loop

load loop

motor loop

load loop reacts to a narrow band of low frequencies. It responds only for the steady state errors due to backlash and disturbances

load loop reacts to a wider range of frequencies, reacts more to backlash continuously

2ω

1ω

ComparisonComparison-- case studycase study

Single loop: No integrator (to make the system stable under hugebacklash), thus, motor never gets to desired position. Low gain ⇒ low bandwidth ⇒ long settling time

Dual loop: higher BW ⇒ responds quickly ⇒ short settling time, however, gain has to be controlled low enough to as integrator react to higher frequencies as well.

Improved dual loop: Integrator is restricted to low frequency ⇒ bandwidth of the inner loop can be further increased to react even faster.