Dimensions of arrays being concatenated are not consistent error .

Hello. I have to simulate a system of 2 differential equations using the State Space block. Problem is that one of the variables, a mass m, has to come after 0,2s from start of simulation. I've tried using a Step with "To Workspace" block but it outputs the variable as a timeseries and gives an error. So I switched it to an If case with a clock and the error is different now :D - namely:

Simulation (Elapsed: 0.506 sec) ===

Error:Invalid setting in 'LB3/State-Space' for parameter 'A'.

Caused by:

Error evaluating parameter 'A' in 'LB3/State-Space'

Dimensions of arrays being concatenated are not consistent..

Here's a photo to better understand what's going on.Also in the subsystem is just a PID controller with a saturation block - nothing special. And simulation is 1 second long.

Any help is much appreciated.

[Jon]

Sorry, I'm not understanding what you mean by: "Problem is that one of the variables, a mass m, has to come after 0,2s from start of simulation".

I'm assuming the system has some mass for the first 0.2s of simulation Are you saying that the mass suddenly changes after 0.2 s? Could you please attach you Simulink file rather than just a screen shot. Thanks

[Stilian Iliev]

For the first 0,2s the mass m is 0, after that it changes to 0,2kg for the rest of the simulation.

I attached the file.

[Jon]

I think the fundamental problem you have is that you would like the values of your state space matrix to change during the simulation (they change when m changes).

I don't think the state space block allows for this functionality. Note that even if you got the mass to write out to the workspace, I don't think Simulink will use these new values in computing the A,B,C,and D in the state space block. It only looks at the workspace when the simulation starts.

Since you system is not to complicated, just two states, I would suggest just going back to basics and modeling the state equations with integrators, summers, etc. To provide the variable mass in those equations use a product block to multiply the mass signal with whatever it needs to get multiplied with. Then generate the mass signal with your step.

When implementing the state equations using integrators, summers, gains etc, I suggest starting at a signal representing dx1/dt this will be the input to an integrator whose output is x1. Similarly dx2/dt will be the input to an integrator whose output is x2. Then work backward for how you compute the signals representing dx1/dt and dx2/dt using x1 and x2 (the outputs of the two integrators) along with an input signals, and of course the signal for your mass, m

To make your diagram a little cleaner you can put all of those interconnected integrators, summers etc that you use to implement your xdot = Ax + Bu y = Cx + Du all into a subsystem block.

There may be some other approaches using set_param, but I think even there you run into troubles with getting it to update on the fly.

Maybe someone else has a cleaner solution for this, but if you just need to get going, this approach should work and I don't think it is too hard.

[Stilian Iliev]

Yea, you are correct. I already have a very similar model done with basic blocks like you describe, which works fine, but my homework is to do it using State space block.

I decided to use 2 if statements for before and after 0,2s and then combine the output signals, althouh I don't know how correct this method is.

Here's the file if you want to check it out and thank you for all clarifications.

[Stilian Iliev]

A bit cleaner here, sorry for the spam.

[Jon]

There is a problem with your approach, which is setting the initial condition for the second block (the one that the switch is connected to after 0.2). Since physically the system states can not change instantaneously, the system state of the second block should match that of the first when the switch occurs. Unfortunately although the two systems will be driven by the same input, their states will not be the same because they have different parameters (the mass is different). So the states of the two blocks will not match at the time the switch occurs. To overcome this you would need a way to set the initial condition for the second block at the time of the switch. Unfortunately the Simulink state space block does not have any external input for setting the initial condition. The initial condition is a parameter, which stays constant throughout the simulation. So I don't see how you will do this.

Another approach, instead of using a switch would be to use two enabled subsystems, each with a state space block inside of them. The outputs of the two would be input to a merge block. Unfortunately I think you will have the same problem with initial conditions. There are some possibilities of resetting states, and hold outputs, that might hold some possibilities, but I don't immediately see a solution even using these.

There is one easy solution though if you have the Contol System Toolbox. The Varying State Space Model, which is in the Control System Toolbox, https://www.mathworks.com/help/control/ref/varyingstatespace.html would work perfectly for your application. You just feed it the time varying A,B,C,D and could provide any necessary switches (or maybe even just steps on those signals)

[Stilian Iliev]

I used your suggestion for the varying state space block and now the signal looks pretty correct!

Thank you alot for all the help!

Here's the file if you want to check it out.

[Jon]

Glad that seems to be working for you.

I assume that Matrix A1 and A2 are computed with the two different values of mass m, and similarly the two different matrices B1 and B2 are computed with the two different values of m.

It looks like the two different values of m are 0 and 0.2. Is it just coincidence that the value for the mass and the switch time are both 0.2?

I realized that I put down this answer as a comment to the original post. I'm going to copy it in as an answer, so in case anyone else has a similar issue they will see it as a possible answer.

Also, if this answered your question you can then accept it.

[Stilian Iliev]

Yea, it's just coincidence that both the mass and switch time are 0,2.

Answer 1

[Jon]

There is a problem with your approach, which is setting the initial condition for the second block (the one that the switch is connected to after 0.2). Since physically the system states can not change instantaneously, the system state of the second block should match that of the first when the switch occurs. Unfortunately although the two systems will be driven by the same input, their states will not be the same because they have different parameters (the mass is different). So the states of the two blocks will not match at the time the switch occurs. To overcome this you would need a way to set the initial condition for the second block at the time of the switch. Unfortunately the Simulink state space block does not have any external input for setting the initial condition. The initial condition is a parameter, which stays constant throughout the simulation. So I don't see how you will do this.

Another approach, instead of using a switch would be to use two enabled subsystems, each with a state space block inside of them. The outputs of the two would be input to a merge block. Unfortunately I think you will have the same problem with initial conditions. There are some possibilities of resetting states, and hold outputs, that might hold some possibilities, but I don't immediately see a solution even using these.

There is one easy solution though if you have the Contol System Toolbox. The Varying State Space Model, which is in the Control System Toolbox, https://www.mathworks.com/help/control/ref/varyingstatespace.html would work perfectly for your application. You just feed it the time varying A,B,C,D and could provide any necessary switches (or maybe even just steps on those signals)