The transfer function of a small position Sensor

I have the below matlab code and I would like to find :

1. First Order Fit: try (polyfit), Find the Matlab function for fitting: P = WHAT_FUNCTION(WHAT TO FIT as what is x, WHAT TO FIT as what is y, ORDER); Force_Nm_Linear = P(1) * Displacement_d_mm + P(2);
2. Second Order Fit, same as above: what is x, y, ORDER P = WHAT_FUNCTION(WHAT TO FIT, WHAT TO FIT, ORDER); Force_Nm_2nd_Order = P(3) + P(2)*Displacement_d_mm + P(1)*Displacement_d_mm.*Displacement_d_mm;

Note: we have to set some of the coefficients to = 0 to check if it can be ignored:

P(3) = 0;

Force_Nm_2nd_two_Terms = P(3) + P(2)*Displacement_d_mm + P(1)*Displacement_d_mm.*Displacement_d_mm;

My Matlab code is::::::::::::::::

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all;

close all;

clc;

Displacement_d_mm = [0, 0.08, 0.16, 0.24, 0.32, 0.4, 0.48, 0.52];

Force_Nm = [0, 0.578, 1.147, 1.677, 2.187, 2.648, 3.089, 3.295];

% Part A: First Order Fit:

% In this case, x is the displacement and y is the force.

% where d is the displacement and F the force

P = polyfit(Displacement_d_mm, Force_Nm, 1);

Force_Nm_Linear = P(1) * Displacement_d_mm + P(2); % F = 6.3221d + 0.089

% Part B:

Displacement_d_mm_b = [0, 0.32, 0.52];

Force_Nm_b = [0, 2.187, 3.295];

% Second Order Fit:

P = polyfit(Displacement_d_mm, Force_Nm, 2);

Force_Nm_2nd_Order = P(3) + P(2)*Displacement_d_mm + P(1)*Displacement_d_mm.*Displacement_d_mm;

Answer 1

[Star Strider]

If you actually want the transfer function, use the System Identification Toolbox functions —

Displacement_d_mm = [0, 0.08, 0.16, 0.24, 0.32, 0.4, 0.48, 0.52]               % Output 'y(t)'

Displacement_d_mm = 1×8

0 0.0800 0.1600 0.2400 0.3200 0.4000 0.4800 0.5200

Force_Nm          = [0, 0.578, 1.147, 1.677, 2.187, 2.648, 3.089, 3.295]       % Input 'u(t)'

Force_Nm = 1×8

0 0.5780 1.1470 1.6770 2.1870 2.6480 3.0890 3.2950

Ts                = 1;                                                          % Sampling Interval (Replace With Actual Value)

idd = iddata(Displacement_d_mm(:), Force_Nm(:), Ts)

idd =

Time domain data set with 8 samples.
Sample time: 1 seconds               
                                     
Outputs      Unit (if specified)     
   y1                                
                                     
Inputs       Unit (if specified)     
   u1                                
                                     

ff_sys = tfest(idd,1)

ff_sys =
 
  From input "u1" to output "y1":
    5.26
  ---------
  s + 29.14
 
Continuous-time identified transfer function.

Parameterization:
   Number of poles: 1   Number of zeros: 0
   Number of free coefficients: 2
   Use "tfdata", "getpvec", "getcov" for parameters and their uncertainties.

Status:                                         
Estimated using TFEST on time domain data "idd".
Fit to estimation data: 77.7%                   
FPE: 0.00339, MSE: 0.001541                     

figure
compare(idd, ff_sys)

Experiment to get different results.

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[GHADAH AL-OBAIDI]

Thank you

[Star Strider]

As always, my pleasure!

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