Adaptive speed controller gain
Adaptive gain in the speed controller offers the ability to automatically lower the controller's gain at low speed and increase the gain as the motor RPMs increase.
The gain value for a speed controller is often referred to as Kp. When adaptive Kp is enabled, the Kp has the ability to change with motor speed. As an example, in the figure below, Gain 1 = 30, Gain 2 = 100, Speed 1 = 100rpm, and Speed 2 = 500rpm. With these settings, the Kp that the speed controller will utilize will be 30 for speeds below 100rpm. The Kp will be 100 for speeds above 500rpm. The Kp will linearly ramp between 30 and 100 as the motor RPMs increase between 100 and 500. This would result in a Kp = 65 at 300rpm.
What a typical speed controller with adaptive gain might look like.
Adaptive Kp is a good feature to use in order to avoid the problem of instability at near-zero speeds after the machine’s mechanics have loosened up. Since most machines do not produce material at very low motor speeds, why keep the gain at high levels when it is not necessary? If the servomotor always accelerates to a high rpm immediately after it is enabled, then adaptive gain may not be as critical. However, for motors that might be enabled at very low speeds and run at crawl speeds or homing speed, adaptive Kp can help avoid instability issues.
Resolution of encoder feedback
Another factor that can cause instability at low speeds is insufficient resolution on the motor's feedback device. Since servomotors do not usually use pulse encoders, the low-resolution feedback device of choice is the resolver, while the high-resolution feedback device is the optical encoder, also called sin/cos or incremental. Resolution is defined as the ability of a feedback device to detect small changes in angular position of the motor shaft.
Some people may disagree with the classification of a resolver as a low-resolution device, since it has an analog output, which in theory should have infinite incremental values for one revolution. While this may be true, the reality is that, in today's servo drives, analog signals have to be processed by analog-to-digital devices (A/D converters) in order for the positional information to be utilized. As a result of this limitation, most resolvers have fewer than 10,000 increments/revolution.
In contrast, sin/cos optical encoders transmit 2,048 sine waves and 2,048 cosine waves for every revolution. The drive's electronics take multiple samples of each wave, which can result in the processing of more than 1 million increments/revolution. This factor of 100 in difference of resolution can have a large impact on your ability to properly tune your motor for an application.
Marcus, thank you for an informative article. I was just at a seminar given by a semiconductor vendor on a new microcontroller targeted at the motor control market. These incorporate motor control timers as well as fast A/D converters. All of these are built in to the SoC, so that the measurement and correction strategies you discuss can be implemented.
As long as a servo drive permits access to and real time changes in its gains, then it's not strictly necessary to have a modern servo drive in order to take advantage of the concept. The system controller could change the gains and feed them to the drive. It's not as elegant as a self-contained drive, but it does permit use of this neat concept.
Wish I could afford a driver like this one. I accidentally hit the end of travel on one of my servos on my CNC mill. The momentary stall ended up letting all the "magic smoke" out of one of my servo drivers. A driver that would properly compensate for drive error like the above one would be most handy.
Don't forget friction! Friction is a nasty thing that makes accurate position control difficult. Slip stick itself is one of the reasons for growling at low speeds. However, sometimes a dither (vibration) signal is added to the torque reference in order to keep the mechanical system in a small movement all the time. This avoids the slip stick phenomena but unfortunately has audible noise as byproduct.
By the way, there is a slight error in the explanation of the Bode plot (apparently this is a transfer function from motor air-gap torque to motor speed). The plot line below about 20 Hz describes the motor and load moving together as one piece. Around 29 Hz only the motor moves but not the load (this frequency is also known as anti-resonance frequency). Between 29 Hz and 53 Hz the load is more and more accelerating when the motor is decelerating and vice versa thus finally reaching the resonance at 53 Hz. Above 53 Hz the plot shows more and more only the inertia of the motor.
You can check this with the rubber band and ball. If you move your hand very slowly up and down, the ball will follow. When you increse the frequency you will find there is a frequency where your hand moves but the ball does not move. This is the anti-resonance frequency. Increasing the frequency still you will finally get into resonance frequency where the ball is moving very much even when your hand movement is small. Increasing the frequency yet higher (if you can) you will find that the ball is again more or less standing still although your hand moves a lot.
I have been thinking more about this rubber string analogy and there was an error in my earlier post too.
The system consists of two masses, the ball and your hand, and a spring between them, the rubber band. Your muscles provide the force to your hand that is moving it. In a servo drive the force is the air-pap torque, the hand corresponds to the inertia of the servomotor's rotor and the ball corresponds to the driven load. The rubber band corresponds to the shafts and the coupling between the motor and the load.
Now when you slowly use your muscles to move your hand up and down the ball will follow. When you increase the frequency of the movement you will find that it becomes more and more "stiff", that is, more difficult to move your hand although the ball is moving up and down. This is the anti-frequency resonance where it is difficult to get the hand tomove. By increasing the frequency further it becomes again easier to move your hand and the amplitudes of the hand and the ball oscillations increases a lot when the frequency is approaching the resonance frequency. Above the resonance frequency the ball movement decreases and your muscles are moving mainly your hand.
The anti-resonance frequency makes it difficult to control the motor movement near and above it and thus limits the dynamics that is possible to be achieved. Note that the anti-resonance frequency is defined only by the torsional stiffnesses of the coupling and the shaft and the inertia of the load. Thus the servo control system cannot improve the control response beyond that. As a rule of thumb the shortest possible response time of the speed control is the inverse of the anti-resonance frequency.
Reduction gear is often used with servo drives. The reduction gear decreases the ioad inertia seen on the motor shaft. Thus in practice the anti-resonance frequency is important only for servo drives that do not have reduction gear.
Good points about adaptive gains, tuning and resonances. I've often seen that the effect of mechanical resonances and changes over time are not taken into consideration when tuning a servo. The problem is that nine times out of ten you can get away with it, so the tenth time seems like a "mystery" when it occurs.
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