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Easy links between Mathematica Automatic Control Package and NC Algebra.

• Current status of bakshee port
• The mathematica input file, NCControl.m
• Sample notebook using NCControl.m

 
 
 

The  parts of Mma Control package which we are linking to NCAlgebra.

NO     Ch 3.1 fails,

YES   Ch  3.2, 3.3 F.R.F. and state space.

Review Form

TransferFunction[vars, m] WE NEED TO SEE WHAT IT DOES.-

MAYBE gives transfer function??

StateSpace

Sampled Option, makes Discrete time.

ContinuousTimeQ, DiscrerteTimeQ

NOT     Ch 3.4 continuous vs. discrete?? looks uncharted (needs E(A, t)).

NOT     Ch 4 Time-domain response

(does  noncom(t) dt just return itself? if yes - good)

NOT       Ch 5 Plots lots

YES       Ch 6 Systems Interconnections

NOT      Ch 7 Controllability Observability

Gramians -makes eqs for them, discrete and continuousis automatic -use MatMult

NCGramians[statespace, GC, GO]

NCControlabilityGramians[statespace, GC]

NCObservabilityGramians[statespace, GO]

Dual - transpose sys construction in ZDG book.

-we call it NCCongugateSystem now - can change also to make Disc and contin time automatic

we also do InverseSys -

? Ch 9 Realization

SimilarityTransform[sys,T]

NOT   Ch 9 Pole assignment

NOT  Ch 10 LQG numerical -

 

Ch  10  we could produce Riccati equations.

This is like our NCSystems pack- Need -- NCRiccati[ sys, V] gives Riccs, as in SYSDef1x1 . Use blocks to make 2x2 automatically.

Are there Contrl Riccs and estimation Riccs,? see HJ appendix.

SOON   --JUAN  make a Hamiltonian for an  A,B,C,D   system. Use MatMult.so that B,C can have lotsa channels.

 

NOT   Ch 11

Yesish Ch 12.1 Show decomposition

SETTING SYSTEMS

Sys1 and sys2 have same FRF

NCSysEqual[s1,s2 ,T]

Energy conserving[sys,V] eqs on V.

DELL's controllability maybe??

 
 
 
 

We did the Ch 7 conversions in Mma Control Package. That is, we did the Connections.m, conversion to NCAlgebra and we found what changes are needed. They were as follows:

In the file Connections.m Line 329 is changed from

e = Inverse[IdentityMatrix[Length[i]] - columns[cl,sts+i]];

to

e = NCMatMult`invMat2[IdentityMatrix[Length[i]] - columns[cl,sts+i]];

and Line 334 is changed from

sys = sys + columns[sys,sts+i].e.cl;

to

sys = sys + NCMatMult`MatMult[ NCMatMult`MatMult[ 
columns[sys,sts+i], e], cl ];

Our plan would be to use your heads such as Head StateSpace[ ]. If we simply use it in an NC envioronment with entries declared noncommuting, then it appears that your Connection commands will work. At this point the block structure of NC feedback connections would be limited, but if we decide to go ahead with this then we shall improve that (namely, generalize invMat2x2 to invMatkxk or at least invmat 4x4)
 

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Mon Jun 21 11:55:39 PDT 1999