Simulink's integrator gives weird output

Hello, I am trying to simulate when a robot grasps an object's end point, and calculate the object's center of mass' (COM) acceleration via the robot's end-effector's motion data. Then, I integrate the acceleration to obtain the velocity of the object's COM. The robot standing still untill 4 seconds, then starts to generate the motion.

However, the output of the integrator (velocity) does not match with the input ( calculated COM acceleration). First of all, the sign of the input and the output is different. The input goes to minus but the output goes to the plus.

When I used actual value of the COM acceleration as the input of the integrator, the sign of the output was same as the input. When I used lsim to integrate the calculated COM acceleration by using simulink's integrator model (https://kr.mathworks.com/help/simulink/slref/integrator.html), the sign of the input and the output were same. What made this difference and how can I solve it?

I'll attach the actual and calculated acceleration of COM and it's integration (velocity) of my simulation. Each data's 1st column is time, 2nd to 4th columns are x, y, z directional data, respectively. I used ode4 (Runge-Kutta) of Fixed-step.

[Paul]

What is the distinction between "calculated" and "actual" acceleration? Same question for velocity.

If you can, attach a screen shot of the relevant portion of the block diagram from the simulink model and indicate which signals are in this discussion.

[Jaeyoung Jang]

As I wrote, 'calculated' means calculated acceleration of COM of the object grasped by robot, that is calculated with the robot's motion data.

'actual' means actual acceleration of COM data directly obtained from the simulation.

'velocity' means output of the integrator, whose input is the acceleration.

What I really can't understand is, as you can see, 'calculated' and 'actual' acceleration is very similar.

However, When I put them into the integrator, the results are greatly different.

Moreover, 'calculated' acceleration goes to negative values after 4 seconds, then the integration output (velocity) should goes to negative.

But, as you can see, the result goes to positive values.

[Paul]

As I understand it, in the Simulink simulation there is a signal that is input to an integrator. That signal is the 'actual' acceeleration. The output of the integrator in the simulation is the 'actual' velocity. And the 'actual' velocity and the 'actual' acceleration are consistent with each other. Is my understanding correct?

If my understanding is correct, who or what is computing the 'calculated' acceleration and 'calculated velocity' and how is that calculation being done? Not the details of the calculation, just the general idea. For example, is the 'calculated' velocity computed by integrating the 'calculated' acceleration?

As best I can tell with my current understanding, everything in Simuink is working as expected and the only issue is with the computation of the 'calculated' velocity.

Also, perhaps not relevant to the Question at hand, but 'actual' acceleration shows the robot is not standing still until t = 4, it looks like there is some motion around t = 0.

[Jaeyoung Jang]

1. Yes. For 'actual' case, the input of the integrator is 'actual' acceleration and the output of the integrator is 'actual' velocity and they are consistent with each other.
2. Imagine that a robot grasps an end point of a bar and generates swinging motion. 'calculated' acceleration means the acceleration of the COM of the bar is calculated with the data of the robot's swinging motion.
3. Yes. For 'actual' case, the input of the integrator is 'actual' acceleration and the output of the integrator is 'actual' velocity and they are consistent with each other. In contrast, in 'calculated' case, the input of the integrator is 'calculated' acceleration and the output of the integrator is 'calculated' velocity and they are not consistent with each other. When I used lsim with 'calculated' case data, the input and the output are consistent with each other.
4. Yes, there is some perturbation in 'actual' acceleration in t = 0, so the robot standing still until t = 4 to wait there is no pertubation.

[Paul]

How is Simulink involved, if at all, for the "calculated" case? If Simulink is not doing the computations for the 'calculated' case, who or what is?

I'm still confused by this question because when the robot moves the COM of the object accelerates, and that acceleration is specifically determined by the robot motion. So, in response to robot motion there is only one acceleration vs. time history. Same for velocity. Yet here we have 'actual' and 'calculated' and I still don't know the difference between how the 'actual' and 'calculated' are determined.

[Jaeyoung Jang]

I used an external dynamic simulator (it's name is 'RecurDyn'). Simulink gives input to the simulator, then the simulator simulates with given input, then exports the output, and then Simulink makes another input for the simulator with the output from the simulator. That process keeps on till the end of the simulation.

So, 'actual' means the acceleration of COM is directly obtained from the simulator, and 'calculated' means the acceleration of the COM is indirectly obtained by the motion of the robot like acceleration of the end-effector of the robot. For both case, velocity is obtained by integrating the acceleration with the integrator.

[Paul]

Does RecurDyn compute the 'actual' and 'calculated' acceleration of the COM?

Why are the 'actual' and 'calculated' acceleration of the COM different, even though they should both represent the exact same physical quantiity?

Does the Simulink model have two integrator blocks? One with input 'actual' acceleration and the other with input 'calculated' acceleration?

[Jaeyoung Jang]

1. No, RecurDyn gives 'actual' acceleration of the COM. For 'calculated', I made MATLAB function to calculate the accleration of the COM with the linear and angular acceleration, angular velocity of the end-effector, and distance between the robot's grasping point and COM.
2. Both acceleration are exactly same (of course there is some numerical error, but that is very small). The problem is velocity. If you are asking about the pertubation from t = 0 in 'actual' case and no pertubation in 'calculated' case, I just set the 'calculated' acceleration to 0 because the motion starts at t = 4, and you can see the 'actual' acceleration becomes 0 before t = 4.
3. Yes. and I didn't change any setting of both of them.

[Paul]

In short, the Simulink model has two integrators. Each integrator has identical settings. Each has a separate input, but the inputs are essentially identical functions of time. However, the outputs of each integrator are very different.

If that's the observation, I'm afraid I can't be of any more help. If you attach a .slx file that illustrates the observed behavior (not necessarily the entire model, just the two integrators and a means to generate the integrator inputs), someone might be willing to download that .slx file and try to replicate what you're seeing and offer a path forward.