Scilab 5.5.2
- Scilab Help
- CACSD (Computer Aided Control Systems Design)
- Formal representations and conversions
- Plot and display
- abinv
- arhnk
- arl2
- arma
- arma2p
- arma2ss
- armac
- armax
- armax1
- arsimul
- augment
- balreal
- bilin
- bstap
- cainv
- calfrq
- canon
- ccontrg
- cls2dls
- colinout
- colregul
- cont_mat
- contr
- contrss
- copfac
- csim
- ctr_gram
- damp
- dcf
- ddp
- dhinf
- dhnorm
- dscr
- dsimul
- dt_ility
- dtsi
- equil
- equil1
- feedback
- findABCD
- findAC
- findBD
- findBDK
- findR
- findx0BD
- flts
- fourplan
- freq
- freson
- fspec
- fspecg
- fstabst
- g_margin
- gamitg
- gcare
- gfare
- gfrancis
- gtild
- h2norm
- h_cl
- h_inf
- h_inf_st
- h_norm
- hankelsv
- hinf
- imrep2ss
- inistate
- invsyslin
- kpure
- krac2
- lcf
- leqr
- lft
- lin
- linf
- linfn
- linmeq
- lqe
- lqg
- lqg2stan
- lqg_ltr
- lqr
- ltitr
- macglov
- minreal
- minss
- mucomp
- narsimul
- nehari
- noisegen
- nyquistfrequencybounds
- obs_gram
- obscont
- observer
- obsv_mat
- obsvss
- p_margin
- parrot
- pfss
- phasemag
- plzr
- pol2des
- ppol
- prbs_a
- projsl
- repfreq
- ric_desc
- ricc
- riccati
- routh_t
- rowinout
- rowregul
- rtitr
- sensi
- sident
- sorder
- specfact
- ssprint
- st_ility
- stabil
- sysfact
- syslin
- syssize
- time_id
- trzeros
- ui_observer
- unobs
- zeropen
Please note that the recommended version of Scilab is 2025.0.0. This page might be outdated.
See the recommended documentation of this function
canon
canonical controllable form
Calling Sequence
[Ac,Bc,U,ind]=canon(A,B)
Arguments
- Ac,Bc
canonical form
- U
current basis (square nonsingular matrix)
- ind
vector of integers, controllability indices
Description
gives the canonical controllable form of the pair (A,B)
.
Ac=inv(U)*A*U, Bc=inv(U)*B
The vector ind
is made of the epsilon_i
's indices
of the pencil [sI - A , B]
(decreasing order).
For example with ind=[3,2]
, Ac
and Bc
are as follows:
[*,*,*,*,*] [*] [1,0,0,0,0] [0] Ac= [0,1,0,0,0] Bc=[0] [*,*,*,*,*] [*] [0,0,0,1,0] [0]
If (A,B)
is controllable, by an appropriate choice
of F
the *
entries of Ac+Bc*F
can be arbitrarily set to desired values (pole placement).
Examples
A=[1,2,3,4,5; 1,0,0,0,0; 0,1,0,0,0; 6,7,8,9,0; 0,0,0,1,0]; B=[1,2; 0,0; 0,0; 2,1; 0,0]; X=rand(5,5);A=X*A*inv(X);B=X*B; //Controllable pair [Ac,Bc,U,ind]=canon(A,B); //Two indices --> ind=[3.2]; index=1;for k=1:size(ind,'*')-1,index=[index,1+sum(ind(1:k))];end Acstar=Ac(index,:);Bcstar=Bc(index,:); s=poly(0,'s'); p1=s^3+2*s^2-5*s+3;p2=(s-5)*(s-3); //p1 and p2 are desired closed-loop polynomials with degrees 3,2 c1=coeff(p1);c1=c1($-1:-1:1);c2=coeff(p2);c2=c2($-1:-1:1); Acstardesired=[-c1,0,0;0,0,0,-c2]; //Acstardesired(index,:) is companion matrix with char. pol=p1*p2 F=Bcstar\(Acstardesired-Acstar); //Feedbak gain Ac+Bc*F // Companion form spec(A+B*F/U) // F/U is the gain matrix in original basis.
See Also
Report an issue | ||
<< calfrq | CACSD (Computer Aided Control Systems Design) | ccontrg >> |