Question

misici Duetmclent (h). .21. The following set of data were collected from a system. Would it be appropriate to assume that this system is first order? If so, find the time constant of the system. Also, what is an approximate value for the static sensitivity?

Answer 1

>> syms t
>> t=0:0.1:1;
>> x=[0.0 1.4 2.3 3.0 3.6 4.1 4.2 4.6 4.7 4.8 4.9]

x =

Columns 1 through 9

         0    1.4000    2.3000    3.0000    3.6000    4.1000    4.2000    4.6000    4.7000

Columns 10 through 11

    4.8000    4.9000

>> plot(t,x)
>> grid on

> > syms t > > t = 0: 0.1: 1 > > x = [0.0 1.4 2.3 3.0 3.6 4.1 4.2 4.6 4.7 4.8 4.9] x = Columns 1 through 9 0 1.4000 2.3000 3.0000 3.6000 4.1000 4.2000 4.6000 4.7000 Columns 10 through 11 4.8000 4.9000 > > plot(t, x) > > grid on plotting the data x_out (t) shows a steady state asymptotic of approx 5 k A = 5 plot shows a non linear indicating that the system can be modeled as first order x_out (t) = A(1 - e^- t/T) At, t = 0.2, x_out (2) = 2.3 At, t = 0.9 x_out (9) = 4.8 2.3 = A(1 = e^- 0.2 /t) 4.8 = A (1 - e^- 0.9 /T) dividing eqn 2 by eqn 3 2.3/4.8 = A(1 - e^- 0.2/T)/A(1 - e^- 0.9/T) implies 23/48 (1 - e^- 0.9/T) = (1 - e^- 0.2/T) implies 0.48 - 0.48 e^- 0.9/T = 1 implies e^- 0.2/T - (e^- 0.9/T - 0/48) = 0.52 implies T = 0.33 s calculate the value of A 4.8 = A(1 - e^- 0.9

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