Problem 322 in Dynamic Systems Modeling Simulation and Contr

Problem 3.22 in Dynamic Systems: Modeling, Simulation, and Control

In Problem 3.11 The following empirical relationship relating inductor current I_L and magnetic flux linkage lambda was used I_L (lambda) = 97.3 lambda^3 + 4.2 lambda (amps, A) Use MATLAB to plot current I_L, as a function of flux linkage lambda for the range -0.4 lessthanorequalto lambda lessthanorequalto 0.4 Wb. Use the data from part (a) to plot flux linkage lambda as a function of current I_L. Write an M-file that uses the plot data from part (b) to estimate the inductance L and plot inductance as a function of flux linkage lambda

Solution

%% part a
lamda = -0.4:0.01:0.4;
IL = 97.3*lamda.^3+4.2.*lamda;
plot(lamda,IL,\'linewidth\',2)
grid on
figure(1)
title(\'Current as function of flux linkage\')
xlabel(\'flux linkage\')
ylabel(\'Current\')
grid on
%% part b
figure(2)
plot(IL,lamda,\'linewidth\',2)
title(\'flux linkage as function of current\')
xlabel(\'Current\')
ylabel(\'flux linkage\')
grid on
%% part c
% d(lamda)/dI = 1/(291.9 * lamda^2+4.2)
figure(3)
L = 1./(291.9 * lamda.^2 + 4.2);
plot(lamda,L,\'linewidth\',2)
title(\'Inductance as function of flux linkage\')
xlabel(\'flux linkage\')
ylabel(\'Inductance\')
grid on