I have a system with a motor, some masses, damping and springs. One of the masses is loaded with an unknown external force F. I want to estimate the force F using data of the motor (mainly current). There are some unknown disturbances, like temperature and friction in the system. Can this be done or are there better ways to estimate the unknown force? There will be no feedback loop. The available data will look be a time series of the current acting on the motor.

  • $\begingroup$ Do you know anything about the response or the state of the system as a result of the input current? Or is your data entirely one-sided? (Even knowing that the system always exists at a certain state because of a physical constraint would be helpful) $\endgroup$ Sep 8, 2015 at 16:19
  • $\begingroup$ I know that a constant external load is applied, and I have measurements of the state where no load is applied. Does that help? $\endgroup$ Sep 9, 2015 at 8:04
  • $\begingroup$ To a degree, but you need to know what's happening when the load is applied as well. Comparing the two is how you can find the load; if you can't look at the output of the system, knowing the input is pretty useless. It'd be like trying to figure out the performance difference in two cars by only looking at the tach. You can say the RPM in the engine is different, but if you don't know what the speed is at that RPM, you don't know which car is faster. $\endgroup$ Sep 9, 2015 at 18:45

1 Answer 1


First, start with a precise mathematical description of your system. Second, analyze it observability. If the system is observable, of course you can estimate the (augmented) state vector (along with the load as an unknown parameter). In practice, there are always some factors that are often a subject to experimental estimation rather than system identification. These are, for instance, the efficiency map of the motor, liquid friction coefficient (may be estimated from the step response), motor inertia etc. I do not know which exactly feedback loop you are taking about, but the mechanical torque in electrical machines can be estimated from the current, that is true.


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