Continuous state-space system

Library

Linear

Description

This block realizes a continuous-time linear state-space system.

$$\dot x =Ax+Bu$$ (4.1)

$$y =C*x+D*u$$ (4.2)

The system is defined by the $(A,B,C,D)$ matrices and the initial state $x_0$. The dimensions must be compatible.

Dialog Box

Set continuous linear system parameters
A matrix	-1
B matrix	1
C matrix	1
D matrix	0
Initial state	0

• $A$ matrix: square matrix. The $A$ matrix
• B matrix: the $B$ matrix, [] if system has no input
• C matrix: the $C$ matrix , [] if system has no output
• D matrix: the $D$ matrix, [] if system has no D term.
• Initial state: A vector/scalar initial state of the system.

Default properties

• always active: yes
• direct-feedthrough: no
• zero-crossing: no
• mode: no
• number/sizes of inputs: 1 / 1
• number/sizes of outputs: 1 / 1
• number/sizes of activation inputs: 0 /
• number/sizes of activation outputs: 0 /
• continuous-time state: yes
• discrete-time state: no
• name of computational function: csslti4

Interfacing function

scilab/macros/scicos_blocks/linear/CLSS.sci

Computational function (type 4)

 
#include "scicos_block.h"
#include "../machine.h"

extern int C2F(dmmul)();
extern int C2F(dmmul1)();

void csslti4(scicos_block *block,int flag)
{
  /*  Copyright INRIA

      Scicos block simulator
      continuous state space linear system simulator
      rpar(1:nx*nx)=A
      rpar(nx*nx+1:nx*nx+nx*nu)=B
      rpar(nx*nx+nx*nu+1:nx*nx+nx*nu+nx*ny)=C
      rpar(nx*nx+nx*nu+nx*ny+1:nx*nx+nx*nu+nx*ny+ny*nu)=D */
  
  int un=1,lb,lc,ld;
  int nx=block->nx;
  double* x=block->x;
  double* xd=block->xd;
  double* rpar=block->rpar;
  double* y=block->outptr[0];
  double* u=block->inptr[0];
  int* outsz=block->outsz;
  int* insz=block->insz;
  
  lb=nx*nx;
  lc=lb+nx*insz[0];
  
  if (flag ==1 || flag ==6){
    /* y=c*x+d*u     */
    ld=lc+nx*outsz[0];
    if (nx==0) {
      C2F(dmmul)(&rpar[ld],outsz,u,insz,y,outsz,outsz,insz,&un);
    }else{
      C2F(dmmul)(&rpar[lc],outsz,x,&nx,y,outsz,outsz,&nx,&un);
      C2F(dmmul1)(&rpar[ld],outsz,u,insz,y,outsz,outsz,insz,&un);
    }
  }

  else if (flag ==0){
    /* xd=a*x+b*u */
    C2F(dmmul)(&rpar[0],&nx,x,&nx,xd,&nx,&nx,&nx,&un);
    C2F(dmmul1)(&rpar[lb],&nx,u,insz,xd,&nx,&nx,insz,&un);
  }
}