Sine input for a state space model

% set up model,in 2nd order form
J = 2; % kg-m^2
k = 2; % N-m/rad, coil spring
J_left = J; J_mid = J; J_right = J;
k_wall = k; k_left = k; k_right = k;
%% set up inertia and elastic matrices
mass = diag([J_left J_mid J_right]);
stif = [(k_wall+k_left) -k_left 0;
 -k_left (k_left+k_right) -k_right;
 0 -k_right (k_right+k_wall)];
diss = zeros(3,3);
t7=0:1:30;
inp_2nd = [0;5*sin.(sqrt(2*k/J).*t7);0]; %excitation influence matrix
%%convert to state space
%%states: [positions and velocities of (disc_left, disc_mid, disc_rght)]
AA = [zeros(3,3) eye(3); -inv(mass)*stif -inv(mass)*diss];
BB = [zeros(3,1);(mass)\inp_2nd];
p_left = [1 0 0 0 0 0]; %displ of left disc
p_mid = [0 1 0 0 0 0]; %displ of mid disc
p_right= [0 0 1 0 0 0]; %displ of right disc
CC = [p_left;p_mid;p_right];
DD = zeros(3,1);

ini_c = [1 0 -1 0 0 0]
tFinal = 30;
hw3 = ss(AA,BB,CC,DD);
% Plots of each disk
[y,t] = initial(twoa,conditionc,tfinal);
subplot(3,1,1)
plot(t,y(:,1))

title('response to initial conditions c')
ylabel('Left (radians)')

subplot(3,1,2)
plot(t,y(:,2))
xlim([0 10])
ylabel('Mid (radians)')

subplot(3,1,3)
plot(t,y(:,3))
xlim([0 10])
ylabel('Right (radians)')

xlabel('time (seconds)')

So I'm not sure how to use a sinusoidal input for my B matrix to plot a response is there anyway I can get some help in general on how to put a sine input into a state space model represantation for plotting purposes.

Answer 1

[Sulaymon Eshkabilov]

Hi,

There are several errors in your script:

(1) inp_2nd = [0;5*sin.(sqrt(2*k/J).*t7);0]; has to be inp_2nd = [0, 5*sin(sqrt(2*k/J)*t7), 0];

(2) BB = [zeros(3,1);(mass)\inp_2nd]; does not work because the size of the mass matrix is 3-by-3 and the size of inp_2nd is 33.

[Anthony Siddique]

Yeah that's my problem I'm trying to put the sine input in the b matrix but it won't work and I'm not sure how. I can use 0 instead to indicate a 0 force on the disk and it works.