How can I plot an internal value in a state space model?

I have a DC Motor model with a voltage and a torque disturbance as inputs, similar to this example (represented in code differently). I want to make sure that under no circumstances do I pass a voltage greater than 12 volts. So, I would like to plot, or saturate, the voltage value within my model so I get a more realistic representation. Given that the voltage is not a directly controlled input, I do no know how to get this value during a simulation.

In other words, if the image below represent my system, I would like to plot u during a simulation.

Currently my code looks like this:

%%Define Constants
j_motor = 0.01;   % kg.m^2
j_load = 10;      % kg.m^2

b_motor = 0.1;   % N.m.s
b_load = 0.001;  % N.m.s

k = 0.01;
r = 1;           % ohms
L = .005;        % henrys

G1 = 12;
G2 = 36;

j_t = j_motor + j_load*(G1/G2)^2;
b_t = b_motor + b_load*(G1/G2)^2;

%%Create State Space Representation
A = [-b_t/j_t k/j_t; -k/L -r/L];
B = [0 1/j_t; 1/L 0];
C = [1 0];
dcm = ss(A, B, C, 0);

%%Design with feed forward gains
Kff = 1./dcgain(dcm);
Kff = diag([Kff(1,1) 1]);
dcmff = dcm*Kff;
dcmff.InputName = {'voltage' 'disturbance torque'};
dcmff.OutputName = 'speed';

time = 0:.01:15;
Td = 50 * transpose((time>5 & time<7));
w_ref = 10* transpose(ones(size(time)));
u = [w_ref, Td];
figure
lsim(dcmff, u, time)
grid
title('Feed Forward Gain');
legend('Speed');

%%Design via pole placement

p1 = -10 + 10i;
p2 = -10 - 10i;

K = place(A,B,[p1 p2]);
dcm_cl = ss(A-(B*K), B, C, 0);
K_gain_cl = 1./dcgain(dcm_cl);
K_gain_cl = diag([K_gain_cl(1,1) 1]);
dcm_cl = dcm_cl * K_gain_cl;
dcm_cl.InputName = {'omega_ref' 'disturbance torque'};
dcm_cl.OutputName = 'speed';
figure
lsim(dcm_cl, u, time)
title('Pole Placement Compensator');
legend('Speed');

Answer 1

[M]

• Given that the voltage is not a directly controlled input, I do no know how to get this value during a simulation.

Is u the voltage ? In this case, yes it is a controlled input.