functiontestPoleAssignment3
Function to assess algorithms for pole assignment
Extends from Modelica.Icons.Function (Icon for functions).
Information
Computes the gain vector k for the state space system
ss = StateSpace(A=[-1,1;0,-2],B=[0, 1],C=[1,0; 0, 1],D=[0; 0])such that for the state feedback
u = -k*y = -k*xthe closed-loop poles are placed at
p = {-3,-4}.Inputs
| Type | Name | Default | Description |
|---|---|---|---|
| DesignData | data | Design.DesignData_Chow_Kokotovic() | |
| Types.AssignPolesMethod | method | Tests.Types.AssignPolesMethod.KNV | method for pole assignment |
| Boolean | isSI | true |
Outputs
| Type | Name | Default | Description |
|---|---|---|---|
| Real[size(data.B, 2),size(data.A, 1)] | K | Feedback gain matrix | |
| Complex[size(data.A, 1)] | calcPoles | ||
| Real | kappa2 | condition number kappa_2(X) = ||X||_2 * ||inv(X)||_2 | |
| Real | kappaF | condition number kappa_F(X) = ||X||_F * ||inv(X)||_F | |
| Real | zeta | condition number by Byers, zeta(X) = (||X||_F)^2 + (||inv(X)||_F)^2 | |
| Real | cInf | condition number vu1=||c||_inf = max(c_j) | |
| Real | nu2 | Euclidean norm of the feedback matrix | |
| Real | nuF | Frobenius norm of the feedback matrix | |
| Real | dlambda | Distance between the assigned and the calculated poles | |
| Real | gap | 0.0 | |
| Real[11] | Jalpha | Combined condition number, JKX=alpha/2*(kappa2X_B) + (1-alpha)/2*normFroK^2 | |
| Complex[:,:] | X | right eigenvectors of the closed loop system |