Chapter 2 Advanced Topics Li Shaoyuan E-mail:syli@sjtu.edu.cn
Chapter 2 Advanced Topics Li Shaoyuan E-mail: syli@sjtu.edu.cn
Structure ofaC
Structure of APC
Direct synthesis Closed loop transfer function C GG r 1+g Desired closed loop response R)d 1|(R R
Direct Synthesis Closed loop transfer function 1 C P C P C G G R G G Desired closed loop response C R d 1 1 C P d d C R G G C R
Example G(s)= K (S+1)(z2S+1 PI control G(S) K(,S+D) k(1+) TS TIS et v=171>7 C KK R;S(z2S+1)+1 r=√2 K Select kc to gives
Example 1 2 ( ) ( 1)( 1) P K G s s s PI control 1 (1 ) ( 1) ( ) I I C C C Is K s G s K s let I 1 1 2 1 2 ( 1) 1 C s s C KK R 1 2 KC 1 2 1 2 KC Select KC to give
IMC Tuning rules Controller P rocess y G -1° Ifg=g.e= d for all u If G=l and gmt is an inverse of gn, d canceled perfectly The controller GGG
IMC Tuning Rules If Gm = Gp , e = d for all u. If Gf = 1 and Gm + is an inverse of Gp , d canceled perfectly. f m m f m c G G G G G G 1 The controller
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
Input Limitations ● magnitude limitation ● rate limitation u>u max max max max u <u<i <1 min max at min at au u< min min mIn at where u and ur are also referred to as the controller output and the real process input, respectively
l magnitude limitation min min min max max max ; ; ; u u u u u u u u u u u r l rate limitation min min min max max max ; ; ; v t u v v t u u v v t u v t u r where u and ur are also referred to as the controller output and the real process input, respectively
Phenomenon Derivative Mod K tirne(secs)