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I am wondering why the servo position loops are mostly dual-loop consisting of position and velocity loops while the position can be controller by using only the position PID controller. I am aware that a dual loop allows the system to use two encoders, one is on the shaft (velocity loop) one is on the load (position loop). In this case, using a dual-loop makes sense.

But, what if we have only one encoder (either on the shaft or on the load)? What would be different using a dual loop controller with derived velocity feedback compared to a single loop position controller?

If you support your answer with an academic reference or any mathematical proof, I would be grateful.

Thanks in advance,

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  • \$\begingroup\$ Dual loops work best when the time constant of the two responses differ by at least an order of magnitude \$\endgroup\$
    – crasic
    Commented Dec 19, 2021 at 0:39
  • \$\begingroup\$ @crasic Could you please elaborate it a bit? \$\endgroup\$ Commented Dec 19, 2021 at 5:53
  • \$\begingroup\$ Dual loop allows more natural handling of saturation and rate limits in intermediate values like limits to velocity in a force->velocity->position control system, which is a pretty important benefit \$\endgroup\$
    – Pete W
    Commented Dec 25, 2021 at 2:35

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I am sure this is a much broader topic then what I know and could summarize. I worked for a company that sells VFD's that employed a dual loop position controller, a P-I velocity controller, and outer P position controller. Legacy VFD's came with an option where the dual loop controller can be turned off and a single PID controller turned on in its place. The option for the PID controller was ditched as it was found none of our customers used it. From the customer's perspective tuning the velocity P-I loop was straight forward, and once that was dialed in having a single P term to tune how aggressive a machine moved between positions was far simpler than tuning the three PID gains.

From my perspective developing the product, implementing a dual loop controller is simpler than a redundant PID position controller. For most applications our customers are concerned with Velocity control. This led to the development of a robust and efficient velocity control scheme. Adding another P-Loop is relatively simple to do from a development stand point, many of the kinks were worked out making a solid velocity controller.

If you think about it, if a system is following the velocity commands correctly the final position would be the desired position. From a dynamics perspective the dual loop controller offers similar performance to a PID loop. The open loop gain of the PID loop can be approximated as the product of the P gain of the position controller and the velocity controller's gain. The integrator action of the velocity PI loop will eliminate steady state velocity error which will eliminate steady state position error. This is because whenever a position error exists, the velocity controller will have a non-zero input that it will eventually meet thanks to its integrator component.

In the end the benefits of a dual loop controller coupled with the existing need for a velocity controller made dual loop control preferable to an additional PID position controller.

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