Issues Replicating Simulink Model within MATLAB (2DOF)

[Sirsh]

Hey all,

I've been trying to debug a model I've created of a 4DOF geared system within Simulink by reproducing the results in MATLAB going from a 2DOF upwards to verify the dynamics are acting correctly.

At the moment I am purely trying to model the stiffness between two gears, my equations are simply:

From my reduced Simulink model, applying an initial displacement of the pinion of 1e-3m I get this response (sorry its hard to make out):

Obviously from the figure above, you can see the equal amplitude oscillations with opposite direction (as these gears are not on the same shaft). I zoomed into the plot and verified that the initial condition of the gear is what I set it to be.

However, I've written the following MATLAB code to try and recreate the above, but to no avail. I'm not sure where I am going wrong here..

Mainscript

clear all;
clc;
%% Defining global variables
global r_p r_g I_p I_g k_mb
% Assignment of ODE variable values:
r_p = 0.1297;   % Pinion radius (m)
r_g = 0.1297;   % Gear radius (m)
I_p = 0.0025;   % Pinion inertia (kg.m^2)
I_g = 0.0025;   % Gear inertia (kg.m^2)
k_mb = 100;
%==========================================================================
%% initial coditions for ode solver
%==========================================================================
z0 = [1e-3,0,0,0]; % Initial Conditions for ODE45.
t_span = [0 1];         % Timespan 0 - 1 second
opts = odeset('Reltol', 1e-3, 'AbsTol', 1e-3);
[t,z] = ode45(@ode2dof, t_span, z0, opts);
%==========================================================================
%% Post Processing
%==========================================================================
% Renaming the ode45 outputs for easier usage.
theta_2 = z(:,1);
theta_2d = z(:,2);
theta_3 = z(:,3);
theta_3d = z(:,4);

% Plotting
subplot(2,1,1)
plot(t,theta_2,t,theta_3), xlabel('Time (s)'), ...
    ylabel('Angular Displacement (rad)'),title('Angular Displacements'),...
    legend('theta 2','theta 3','Location', 'northwest'),grid;
subplot(2,1,2)
plot(t,theta_2d,t,theta_3d), xlabel('Time (s)'), ...
    ylabel('Angular Velocity (rad/s)'), title('Angular Velocities'),...
    legend('theta 2d', 'theta 3d','Location', 'northwest'),grid;

ODE Script

function zdot = ode2dof(t,z)
% defining global variables
global r_p r_g I_p I_g k_mb
%% S.S.E:
zdot(2) = ((k_mb*r_p)/I_p)*(z(3)*r_g-z(1)*r_p);     % theta_2dd
zdot(4) = ((k_mb*r_g)/I_g)*(z(1)*r_p-z(3)*r_g);     % theta_3dd

z(2) = zdot(1);
z(4) = zdot(3);
% Outputs
zdot = zdot';

The output plot looks like this instead:

Any help would be appreciated, as I'm lost at what's going on here even though its quite a simple system.

 

[mmwave]

Hello,

Thank you for sharing your question and code with us. After reviewing your code, I have identified a few potential issues that may be causing the discrepancy between your Simulink and MATLAB results.

1. In your ODE script, you are not initializing the remaining variables (theta_1 and theta_1d). This may be causing unexpected behavior in your simulation.

2. It appears that you are not taking into account the initial conditions of your system in your ODE script. In the ODE script, you are only using the values of theta_2 and theta_3 to calculate their derivatives, but not taking into account their initial values. This may be causing discrepancies in your results.

3. In your ODE script, you are assigning the values of z(2) and z(4) to be the derivatives of theta_2 and theta_3, respectively. However, in your main script, you are assigning the values of theta_2d and theta_3d to be the derivatives of theta_2 and theta_3. This inconsistency may be causing unexpected behavior in your results.

I would recommend reviewing your ODE script to ensure that all variables are properly initialized and that you are taking into account the initial conditions of your system. Additionally, I would suggest verifying that your main script and ODE script are consistent in the way they are handling the variables and their derivatives.

I hope this helps. Please let me know if you have any further questions or if the issue persists. Good luck with your simulation!