If a system matrix in polynomial, or state-space, form has any decoupling zeros, then you will often want to remove them, since the input decoupling zeros cannot be influenced by the system inputs and the output decoupling zeros cannot contribute to the system output behavior. RemoveInputDecouplingZeros and RemoveOutputDecouplingZeros are functions that can be used to eliminate any input or output decoupling zeros, respectively, from a SystemMatrix object in polynomial, or state-space, form. These are analogous to Control System Professional functions ControllableSubsystem and ObservableSubsystem used with StateSpace objects. | RemoveInputDecouplingZeros[system] |
| | create a system matrix object with no input decoupling zeros |
| RemoveOutputDecouplingZeros[system] |
| | create a system matrix object with no output decoupling zeros |
The RemoveInputDecouplingZeros and RemoveOutputDecouplingZeros functions. Make sure the application is loaded. Consider the system matrix. | Out[3]= |  |
This removes its input decoupling zeros. | Out[5]= |  |
This also removes the output decoupling zeros and, thus, gives a least-order system matrix. | Out[7]= |  |
Although the resulting system matrix is dynamically much simpler, it still generates the same TransferFunction object. | Out[9]= |  |
Here is a system matrix in state-space form. | Out[12]= |  |
ControllableSubsystem finds (four) controllable modes of the StateSpace object. | Out[14]= |  |
Similarly, the function RemoveInputDecouplingZeros finds the controllable modes of the system matrix. | Out[16]= |  |
The system matrix object pr creates the same TransferFunction object as that obtained from the controllable subsystem cs of the original StateSpace object. | Out[18]= |  |
There are no input decoupling zeros in a system matrix that corresponds to the controllable subsystem. | Out[20]= |  |
Likewise, the state-space system that corresponds to the system matrix with any input decoupling zeros removed is controllable. | Out[22]= |  |
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