PTFE4761_equatins used

PTFE4761_equatins used - cos bt [ z 2-(cos b)z ] / [ z 2-...

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f(t) L[f(t)] c o c o /s bt sin ) /( 2 2 b s b + bt cos ) /( 2 2 b s s + at e ) /( 1 a s - bt e at sin ] ) /[( 2 2 b a s b + - bt e at cos ] ) /[( ) ( 2 2 b a s a s + - - LT of derivatives: ) 0 ( ) ( )] ( ' [ f s sF t f L - = ) 0 ( ... ) 0 ( ' ) 0 ( ) ( )] ( [ ) 1 ( 2 1 ) ( - - - - - - - = n n n n n f f s f s s F s t f L LT of integrals: ) ( 1 ) ( 0 s F s dt t f L t = Time delay: ) ( )] ( [ a s F t f e L at - = Initial and final value: ) ( lim ) ( lim 0 s sF t f s t = ) ( lim ) ( lim 0 s sF t f s t = First order model: G(s) = ) / 1 ( / τ + s c y o ss 1-exp(-1) 63.2% Second order model: G(s) = 2 2 2 n n n ss s s y ϖ ζϖ + + ϖ n = 2 2 2 9 s p t t + π ζ = 3/(t s ϖ n ) For quadratic equation α s 2 + β s + γ = 0, the roots are s = α αγ β 2 4 2 - ± - PID controller: G c = K P + K I /s + K D s C(s) = G c E(s) Modified PI: C(s) = (K P + K I /s) E(s) + K F R(s) C= controlled variable, R = reference, E = error = R-Y f(nT) F(z) c o c o z/(z-1)
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Unformatted text preview: cos bt [ z 2-(cos b)z ] / [ z 2- (2 cos b)z + 1] sin bt (sin b) z / [ z 2- (2 cos b)z + 1] c(a n ) cz/(z-a) Initial and value theorem: ) ( / ) 1 ( lim ) ( lim 1 z F z z nT f z n-= ) ( lim ) ( lim z F nT f s n = Time shift: Z[ f(nT+T) ] = zF(z) zf(0) A+0 = A A+1=1 A+A=A A+ =1 A(B+A) = A A 0 = 0 A 1=A A A=A A =0 A+B = A B AB = A + B X i + = Reset Xi X i + Set Xi X i X i + = Reset Xi (X i + Set Xi )...
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