Block Diagram Algebra R1

Block diagram algebra solver for TI89 and TI92P, solve response in all nodal points of BDA circuit. Allow using blocks like source, transfer function, sum, gain, integrator etc.. For solving dynamic or discrete systems needs “Laplace and Z transform”. (http://www.ticalc.org/pub/89/basic/math/lzt.zip)

Installation

Send file named simR1.89g to your calc

on calc: Run sim\install() and choose Archive

Included function:

sim( [ blck1 ; blck2 ; … ; blckN ] )

Supported blocks:

Primary

uc( out , U(s|z) ) Complex source

ut( out , u(t) ) Transitional source

ud( out , u(k) ) Discrete source

tf( in , out , F(s|z) ) Transfer function

in( in , out , init. conditions ) Integrator

//each in and out is a NAME of NODAL POINT or list of NNPs

Secondary

tf( { in1 , in2 , -in3 } , out , 1 ) Sum

tf( in , out , GAIN ) Gain

tf( in , { out1 , out2 , -out3 } , F ) Branching

tf( { 1 , 2 , -3 } , { 4 , 5 , -6 } , F(s) )

//when two or more outputs are connected to the same NP, SUM is automatically added.

tf( in , out , z/(z-1)) ; ud( out , init. conditions )

or Accumulator (discrete integrator)

tf( in , out , 1/(z-1)) ; ud( out , init. conditions )

3 ways to realize SUM:

I.

uc( 1 , u1(s) );

uc( 2 , u2(s) );

tf( { 1 , -2 } , 3 , 1 );

tf( 3 , 4 , f(s) );

II.

uc( 1 , u1(s) );

uc( 2 , u2(s) );

tf( { 1 , -2 } , 4 , f(s) );

III.

uc( 3 , u1(s) );

uc( -3 , u2(s) );

tf( 3 , 4 , f(s) );

4 ways to realize feedback:

I.

uc( 1 , u1(s) );

tf( { 1 , -3 } , 2 , 1 );

tf( 2 , 4 , f(s) );

tf( 4 , 3 , G );

II.

uc( 1 , u1(s) );

tf( { 1 , -3 } , 4 , f(s) );

tf( 4 , 3 , G );

III.

uc( 2 , u1(s) );

tf( 2 , 4 , f(s) );

tf( 4 , -2 , G );

IV. for G = 1;

uc( 1 , u1(s) );

tf( { 1 , -4 } , 4 , f(s) );

Example:

Full description:

uc( 1 , u1(s) ); /a

ut( 6 , w ); /b

tf( { 2 , 3 } , 7 , 1 ); /c

tf( { -7 , 6 } , 5 , 1 ); /d

tf( 1 , 2 , f1(s) ); /e

tf( 4 , 3 , f2(s) ); /f

tf( 5 , 4 , r(s) ); /g

Reduced description:

uc( 7 , u1(s)*f1(s) ); /a/c/e

ut( 6 , w ); /b

tf( { 6 , -7 } , 7 , r(s)*f2(s) ); /d/f/g

Jiri Bazant

georger@razdva.cz