balance_grammian (MathScript RT Module Function)
- Updated2023-03-14
- 1 minute(s) read
balance_grammian (MathScript RT Module Function)
Owning Class: ssanals
Requires: Control Design and Simulation Module and MathScript RT Module
Syntax
SysBalSS = balance_grammian(SysIn)
[SysBalSS, d] = balance_grammian(SysIn)
[SysBalSS, d, T] = balance_grammian(SysIn)
[SysBalSS, d, T, Tinv] = balance_grammian(SysIn)
Legacy Name: balreal
Description
Balances a state-space model. A balanced state-space model has identical controllability and observability diagonal Grammians. This function also returns the transformation matrix this function uses to balance the model.
Inputs
| Name | Description |
|---|---|
| SysIn | Specifies a linear time-invariant (LTI) system in transfer function, zero-pole-gain, or state-space form. |
Outputs
| Name | Description |
|---|---|
| SysBalSS | Returns the balanced LTI state-space model that results when this function applies the transformation matrix T to the SysIn model. |
| d | Returns the diagonal vector of the observability and controllability Grammians of the SysBalSS model. d is a real vector. |
| T | Returns the transformation matrix this function uses to balance the SysIn model. This function calculates the T matrix using the Cholesky decomposition of the controllability and observability Grammians of the SysIn model. T is a real matrix. |
| Tinv | Returns the inverse of the transformation matrix T. Tinv is a real matrix. |
Details
The following table lists the support characteristics of this function.
| Supported in the LabVIEW Run-Time Engine | Yes |
| Supported on RT targets | Yes |
| Suitable for bounded execution times on RT | Not characterized |
Examples
SysIn = ss([-1, 0; 0.1, -3], [1, 0]', [0, 1], 0)
[SysBalSS, d, T, Tinv] = balance_grammian(SysIn)