ZigangPan/LinearSystems | Paclet Repository

ZigangPan`LinearSystems`

EZDCF

{r,highfrequencygain,systemadd,transformation,zerodynamics}=EZDCF[system]

calculates the extended zero dynamics canonical form of LTI system with respect to the active inputs and active outputs whenever it exists. It requires that system admits at least one active input and at least one active output, and the number of active inputs equals to the number of active outputs.If the system with active inputs and active outputs can not be dynamically extended to admit vector relative degree, then the function returns 'error'.If the system may be dynamically extended to admit vector relative degree, then it is extended to an LTI system with uniform vector relative degree. From that extended system, one further calculates the extended zero-dynamics canonical form.

= the uniform relative degree (scalar);

highfrequencygain

= high frequency gain matrix of the extended system;

systemadd

= the LTI system when concatenate with the original system yields the extended system that admits the extended zero-dynamics canonical form, it is set to 'default' if the original system does not need to be dynamically extended to yield the zero-dynamics canonical form;

transformation

= the state transformation xold = transformation . xnew that brings the extended system into extended zero-dynamics canonical form;

zerodynamics

= the extended zero-dynamics canonical form of the extended system.

Examples

(1)

Basic Examples

(1)

In[1]:=

system={{x1,x2,x3},{u1,u2,w1,w2},{y1,y2,z1,z2},{{-1,2,0,0,0,0,1},{-2,-1,1,1,1,1,0},{-1,-2,-3,-1,1,1,1},{1,0,0,0,0,1,0},{0,0,1,0,0,0,1},{1,0,0,0,0,0,0},{0,0,1,0,0,0,0}},{1,2},{1,2},{1,2},{3,4},{1,2},{3,4}};

In[2]:=

EZDCF

[system]

System already has uniform vector relative degree!

State transformation is xold = transformation.xnew

Out[2]=

2,{{0,4},{-1,-4}},{{x4},{u3,u4},{y3,y4},{{0,1,0},{1,0,1},{0,0,1}},{1,2},{1,2},{1,2},{},{1,2},{}},{0,-1,0,-1},{1,0,0,0},-

,-1,0,{0,0,1,0},{{x11,x21,x31,x41},{u3,u4,u1,u2,w1,w2},{y3,y4,y1,y2,z1,z2},{{-4,1,-2,0,0,0,0,0,0,1},{-9,0,-4,0,0,4,0,4,4,5},{2,0,-1,1,0,0,-1,1,1,1},{9,0,4,0,-1,-4,0,-4,-4,-5},{0,-1,0,-1,0,1,0,0,0,0},{0,0,0,0,0,1,0,0,0,0},{1,0,0,0,0,0,0,0,1,0},{0,0,1,0,0,0,0,0,0,1},{1,0,0,0,0,0,0,0,0,0},{0,0,1,0,0,0,0,0,0,0}},{1,2},{3,4},{1,2,3,4},{5,6},{1,2,3,4},{5,6}}

SeeAlso

ZDCF

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EZDCFAD

RelatedGuides

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Guide for ZigangPan`LinearSystems`