In general, for a feedforward controller design of a motion system, it is essential to recognize the various components (acceleration feedforward, viscous friction and dry friction) present in the error signal. Consider the transfer function of the motion system given by
$G(s) = \dfrac{2.424 \cdot 10^{-07} z^3 + 1.303 \cdot 10{-06} z^2 + 3.295 \cdot 10^{-07} z - 8.486 \cdot 10^{-08}}{z^5 - 3.761 z^4 + 5.438 z^3 - 3.593 z^2 + 0.9157 z}$
The transfer function is discrete. I would like to point out certain observations that I made and doubts that I have:
- Looking at the powers of the numerator - does the extremely low values of the coefficients (compared to the coefficients in the denominator) be on account of discretization?
- How do you recognize the mass element for the feedforward design given the transfer function?
Any insight (especially mathematical) as to the understanding of the concept would be welcome. Please let me know in the comments sections if I am missing some information. Thanks as always!
To answer the first question, yes the really small coefficients of the numerator are on account of the process of discretization.
For the second question, motion systems are in general of second order at low frequencies and can be approximated by the transfer function $\dfrac{1}{ms^2}$. Using bode plots for the given transfer function and tuning $m$ to achieve overlap in low frequency region can be used to estimate the acceleration feedforward component of the feedforward controller design.