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Question: 22 transfer function of a position sensor the transfer function...

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2.2 Transfer function of a position sensor. The transfer function of a small position sensor is evaluated experimentally. The sensor is made of a very small magnet and the position with respect to the centerline (see Figure 2.24) is sensed by the horizontal, restoring force on the magnet. The magnet is held at a fixed distance, h, from the iron plate. The measurements are given in the table below a. Find the linear transfer function that best fits these data. b. Find a transfer function in the form of a second-order polynomial (v= a + bf+cfa), where y is the displacement and,f is the restoring force by evaluating the constants a, b, and c. c. Plot the original data together with the transfer functions in (a) and (b) and discuss the errors in the choice of approximation FIGURE 2.24 A simple position senso Magnet SI Displacement, d [mm0.08 0.16 0.24 0.32 04 0.48 0.52 Force [mN] 0 0.578 1.147 1.677 2.187 2.648 3.089 3.295

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