Diapositiva PPT

A gate has a moment of inertia I respect to its axis of rotation. It closes automatically, after being opened, by means of an elastic of constant K Kg.m2/s2. It has also a damper for the oscilations with a constant R Kg.m/s. The differential equation of the movement for the angle Z measured from its equilibrium position is:

I*Z''+ R*Z' + K*z = 0

If W is the angular velocity W=Z' the above equation is equivalent to the system of first order differential equations:

Z'=W W'=-R/I*W-K*Z/I

Z(T) and W(T) in function of the time T and in the phase space Z W.

NETWORK

C:: Z':=W; W':=-R*W/I-K*Z/I; (*equations of the system*)

GRAPH(0,80,BLACK,Oscilant Gate W Z T ;

TIME:6:2,WHITE;

W:6:1,Ang_Vel,-2,3,LIGHTBLUE;

Z:6:1,Angle,-2,3,GREEN);

GRAPH(0,80,BLACK,Oscilant Gate W Z ;

W:6:1,ANG_VEL,-2,2,LIGHTBLUE;

Z:6:1,ANGLE,-2,3,GREEN);

INIT ACT(C,0); Z:=1.4; W:=0.0;

R:=0.1; K:=0.9; I:=1.2;

TSIM:=80; DT_C:=0.0625;

INTI I:6:2:Moment of inertia; INTI R:6:2:Damping constant ;

INTI K:6:2:Elastic constant ;

DECL VAR W,Z:CONT; R,K,I:REAL;

END.

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