Control Basics - MAELabs UCSD

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Digital control - derivative Derivative calculation (first order) f ( ti!1) = f ( ti) ! f " ( ti)#t +O ( #t) Derivative calculation (second order for reference) 2 $ f " ( ti) = f t ( i) ! f ( ti!1) +O ( #t) #t f ! ( t) = 3 f t ( i) " 4 f ti"1 2#t KD f ! ( ti) = f t ( i) " f ti"1 #t ( ) ( ) ( ) + f t i"2 ( ) = K $ ' D & ) ( f ( ti) " f ( ti"1) ) = CD f ( ti) " f ti"1 % #t ( MAE 156A + ( #t) 2 Derivative gain in control loop (without division) ( ) ( )
z = KI s y ! z s = KI y zi " zi"1 #t Digital control - integral y KI s z = KI yi ! zi = zi"1 + ( KI#t ) yi = zi"1 + ( KI#t ) yi = zi"1 + CI yi MAE 156A
Page 1 and 2: MAE 156A - Winter 2011 Control Basi
Page 3 and 4: Math review e i!t = cos ( !t) + isi
Page 5 and 6: m!!x + c!x + kx = F ms 2 ( + cs + k
Page 7 and 8: xc + - e Or equivalently: xc + - K
Page 9 and 10: xc + - e K K = K Pe + K I System tr
Page 11 and 12: Assume the following properties:
Page 13 and 14: K P = 2000 V/m K I = 0 K D = 0 sta
Page 15 and 16: K P = 25000 V/m K I = 0 K D = 0 Exa
Page 17 and 18: 0.012 0.01 0.008 0.006 0.004 0.002
Page 19 and 20: K = K P + K I s + K D s 1+! 1 s ( )
Page 21: G = KP + KI s + KDs ! ! $ # & # " %
Page 25 and 26: xc + - m!!x + c + K ! mK $ e # " R

Control Basics - MAELabs UCSD

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