Electric Servo Systems

One of the things that I found out early in designing devices that incorporated electric servo motors is how important inertia matching was to a successful design aside from considering inertia to predict acceleration along with available torque. I'm sure this is oversimplifying, but with robots, the control system continuously monitors where you are and where you want to be and when. They then plan a paths for each axis. The servo motor is paired with a servo drive, or amplifier, that responds to a signal that traditionally been a speed command. You give it a voltage and it will produce a speed using whatever current, or torque necessary within it's capability. The servo drive and motor have their own closed loop to maintain a velocity based on a command voltage.

As a mechanical engineer, we were exposed to some closed loop controls systems in school. Electrical engineers got a lot more with their feedback and control systems studies. There are probably a lot of people that can explain this better than I can, but it involves mathematical relationships, or transfer functions. In servo systems there are limits to the ability for the closed loop system to operate within and remain stable. In the case of a robot using an electric servomotor, the variables that need to be considered along with available torque, acceleration and speed is the reflected inertia to the motor. In my experience, the reflected inertia needs to conform to a range expressed as a ratio of the system inertia divided by the inertia of the motor. This ratio typically needs to be between 1:1 and 4:1. Some manufacturers of motors and drives may have different requirements. I believe that the Yaskawa drives I was designing with could handle up to 5:1. I'm sure there are newer, and different ways of doing things that I've had experience with, but this range is what always worked well for me.

I have attached a scanned copy of the first round of inertia calculations I made for the EDY horizontal arm. There is way too much detail than is required, but I didn't know what I could reasonably neglect at the time until I went through the exercise. You will notice that there are two components to the inertia in many cases. Consider a large flat plate connected to end of a long slender rod. If you were rotate the rod about the other end the inertia of the plate comes in two forms. The first is that of the mass of the plate's center of gravity at the radius from the origin of rotation. The second is the rotation of the flat plate itself. I never considered the gyroscopic effects of rapidly rotating components in any of my torque calculations for this type of application. I suspect that I would have looked at them closely if I were designing something of a much more critical nature. (I plan on adding more detail later on the inertia ratio calculations and motor sizing)

If a system is designed properly and the inertia ratio is within specifications, the controls people will be very happy. What makes it difficult with robots, is that what a motor is driving changes shape and can have a payload, or not. This all leads to changes in the loads inertia and needs to be considered in the design. Too much reflected inertia and you will experience undershoot to start and overshoot at the end. Not enough reflected inertia and you will get too much overshoot at acceleration and possible instability. Some tuning can be done with the drive gains, but you really want to be in the specified range for optimal performance.

 

Some examples later. (Still under construction)

 

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