Product of two state space models

Hi,

In the example of Control of Two-Tank System under Robust Control Toolbox, there is a MATLAB command that connects two state space models together using the following script.

tank1and2u = [0 1; tank2u]*tank1u;

Both tank2u and tank1u are uncertain continuous state space model. I can sort of figure out that the second row of tank2u*tank1u is equivalent to series connection, but not the first row. Can some explain the role of [0 1] in that script? Why is [0 1] used?

Thanks

Answer 1

[Anshuman]

Hi Mathias,

The above script is used to connect two state space models in series. The [0 1] matrix in the script is called a feedthrough matrix, which connects the input to the output of the state space model.

In this specific example, the first tank (tank 1) is connected to the second tank (tank 2) through a valve. The feedthrough matrix [0 1] indicates that the input to the system is the control signal applied to the valve, and the output of the system is the level of the second tank.

In other words, the [0 1] matrix specifies how the input signal affects the output of the system. The value '0' in the first column of the matrix indicates that the control signal does not directly affect the level of the first tank, while the value '1' in the second column indicates that the control signal directly affects the level of the second tank.

By concatenating the [0 1] matrix and the uncertain state space model for tank 2 (tank2u), the resulting matrix tank2u*tank1u represents the state space model for the system consisting of tanks 1 and 2 connected in series. Finally, the entire system is connected to the control signal through the matrix tank1and2u, which is the result of multiplying [0 1; tank2u] by tank1u.

Hope it helps!!

Answer 2

[Mathias Foo]

Thanks for the explanation. It is really helpful.