上海交通大学：《自动化仪表与过程控制》课程学习资料：高级过程控制 Advanced Topics Li Shaoyuan

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)