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I am having a hard time linearizing the equation below of a non-linear time invariant MIMO system

$$m \cdot y_1''​+F_m = ​Fu11​−m \cdot g$$ (y1''=second derivative)

$$m \cdot y_2''​− F_m​​ = F_{u22} ​− m \cdot g$$ (y2''=second derivative)

where Fm= 65673.828125.(It is an equation. I have used the given values to solve it)

$$F_{u11} = \frac{u_1}{a(y_1+b)^4}$$ $$F_{u22}= \frac{u_2}{a(-y_2+b)^4}$$

The other model parameters are to be selected as: N=4, m=120 (g) , a=1.65, b=6.2, c=2.69, and d=4.2.

u1,u2 are the control inputs (related to coil currents),

a,b are constants,

𝑦1,𝑦2 are the positions of magnet 1 and magnet 2 respectively.

I have tried multiple times and got different answers each time.

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    $\begingroup$ Please use the edit button to add the methods that you tried and the answers that you got already. Linearisation is usually done by finding the derivatives of the expressions in the differential equation. Try to use LaTeX math to make reading the equations easier. $\endgroup$ Commented Oct 17 at 2:07
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    $\begingroup$ Generally speaking, to linearise about an operating point, you need the operating point $y_1_0$ and $y_2_0$ also. $\endgroup$ Commented Oct 17 at 2:12
  • $\begingroup$ Related $\endgroup$ Commented Oct 17 at 2:14
  • $\begingroup$ In the real world, you don't have to design your own MIMO controller. Dynamic Matrix Control has existed for a LONG time, and that is the standard solution for this type of problem. $\endgroup$ Commented Oct 24 at 23:49

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