Example K G,(S) +1 Approximate Inverse without time-delay ≈ aS +1 1+st K K(a+2) Filter Approximate G(s= 1-Cs/2 2s+1 1+CS/2 PID G(S) (1+as/2)(1+sz)(1+as/2)(1+sr) K(a+n+ads/2)s K(a+n)
Example s p e s K G s 1 ( ) Inverse without time-delay K s G s m 1 ( ) Filter 1 1 ( ) s G s f Approximate e s s 1 K s s G s c ( ) 1 ( ) PI 1 / 2 1 / 2 s s e s Approximate K s s s K s s s s G s c ( ) (1 / 2)(1 ) ( / 2) (1 / 2)(1 ) ( ) PID f m m f m c G G G G G G 1
Reset windup and ant reset Windup scheme
Reset Windup All industrial processes are submitted to constraints ● Example A controller works in a limited range of 0-10V or 0-20 mA a valve cannot be opened more than 100% and less than 0% o a motor driven actuator has a limited speed etc
l All industrial processes are submitted to constraints. l Example: l A controller works in a limited range of 0‑ 10 V or 0‑ 20 mA l A valve cannot be opened more than 100% and less than 0%, l A motor driven actuator has a limited speed, etc