Process Control Engineering
Institute of Industrial Control,
Zhejiang University
2013/06/26
考核说明
考核：平时成绩 50%，包括课堂提问、

平时练习、综合练习；期末考试（闭
卷）50%
课堂提问


平时练习


满分20分。缺课1次扣5分。
满分10分。平时作业的平均分
综合练习 20分
概论





Origin of Process Control Systems（过程控制
系统的由来）
Important Terms and Objective of Process
Control Systems（过程控制的术语与目标）
Description of Process Control Systems（过程
控制系统的描述）
Types of Control Strategies （控制策略分类）
Course Tasks（课程任务）
Feedback Control Process
（反馈控制过程）
1. Measure the level by a sensor (传感器) and convert the output
from the sensor to an electric signal by a transmitter (变送器)
2. The controller（控制器/调节器） then receives the signal
and compares it with the value desired;
3. Depending on this comparison, the Qi
controller decides what to do to
correct for any deviation;
4. Based on this decision, it sends a
signal to the final control element（
执行单元）, e. g., a control valve
and change the controller process.
hsp
h
LT
21
Qo
LC
21
Important Terms （重要术语）
of Automatic Process Control

Controlled Variable (CV, 被控变量/受控变量)
The variable that must be maintained or controlled at
some desired value.

Setpoint (SP,设定值/给定值)
The desired value of the controlled variable.


Controller Output (OP, 控制器输出)
Manipulated Variable (MV,操纵变量/操作变量)
The variable used to maintain the controlled variable
at its setpoint.

Disturbance (DV,扰动/扰动变量)
Any variable that causes the controlled variable to
deviate away from its setpoint.
Control Diagram
Psp
Pm
PC
51
PT
51
u
F1
P2
f2
P
P1
f1
F2
Variable relations
are as follows:
dP
V
 K1 F1  K 2 F2
dt
F1  KV 1 f1 P1  P
f1 100 u
For the above pressure control
system, please describe its CV, SP, F2  KV 2 f 2 P  P2
OP, MV, DVs, control diagram as
well as control objective.
P2 Controlled by a single loop?
Psp
+
PC
51
_
u(t)
Control
Valve
P1
P2
f2
Disturbance
Path
(干扰通道)
f1
Control Path
(控制通道)
+
+
Controlled Process
Pm
PT
51
P(t)
Process Characteristics






Importance of Process Characteristics (过程
对象特性的重要性)
Introduction of Final Control Elements (执行
机构介绍)
Types of Processes (过程特性分类)
Obtaining Characteristics from Process
Dynamics (过程特性机理建模法)
Obtaining Characteristics from Process Data
(过程特性测试建模法)
Summary
Heat Exchanger
Temperature Control System
Tsp
Steam
u(t)
TC
22
Tm
The extended controlled
process (广义对象) is
anything except the
controller.
RV
TT
22
RF , Ti
Process
Fluid
T
Condensate
Tsp
u(t)
Controller
I/P
& valve
Heat
exchanger
Sensor
Transmitter
mA, CO
Tm(t)
mA, TO
Flow
T
mV
Types of Processes

Self-regulating processes (or stable
processes, 自衡过程/稳定对象)
(1) Single-Capacitance Processes
(2) Multi-Capacitance Processes

Non-self-regulating processes (or
unstable processes,非自衡过程)
Ex.: some level processes and some reactors
Terms that Describe
the Process Characteristics

Process Gain (K)
Ratio of the change in output (or responding variable)
to the change in input (or forcing function).
Output O final  Oinitial
K

Input
I final  Iinitial


Process Time Constant (T)
Process Dead Time (τ)
Notes to Process Gain



Process gain describes the sensitivity
of the output variable to a change in
input variable.
Process gain includes three parts: Sign,
Numerical value and Units.
Process gain relates only steady-state
values, so the gain is a steady-state
characteristic of the process.
Obtain the Dynamic Terms from
the Step Response Curve
Controller Output
65
%
60
T  1.5  t0.632 O  t0.283 O 
55
?
50
45
0
10
20
30
40
50
Heat Exchanger Outlet Temp.
160
  t0.632 O  T0  T
158
63.2%
Cent
156
154
?
28.3%
152
150
148
T2
T0
0
10
T1
20
30
time, min
40
50
PID Controller





Selection of Valve Action (调节阀作用选择)
Action of Feedback Controllers (反馈控制器
的正反作用)
Performance Criterion of Process Control
Systems (过程控制系统的性能指标)
Understand P, PI and PID Controllers
Problem Discussion
Types of Control Valves
pc
.......
.......
.......
.......
Fail-opened
Valve
(气关阀)
pc
Fail-closed
Valve
(气开阀)
Action of Controllers

Direct Action (正作用)
when the signal from the transmitter
increases, the controller output also increases.

Reverse Action (反作用)

when the signal from the transmitter
increases, the controller output decreases on
the contrary.
Note: The set point is not part of decision.
Selection of Controller Action
Controlled Plant
D (t)
ysp
u(t) Final Control
e(t)
+
ym(t)
Controller
Element
_
MV
Disturbance
Path
Control
Path
+
Sensor &
Transmitter
Principle: to construct a negative feedback loop ?
+
y(t)
Controller action selection
based on loop analysis Ex. 1
Tsp
TC
22
u(t)
Steam
Step 1: plot block diagram
RV
Step 2: indicate the action direction for each
block except the controller.
Tm
TT
22
Heat Exchanger
RF , Ti
Process
Fluid
T
Step 3: determine the action of the controller
to construct a negative feedback loop
Condensate
TC 22
must be
reverse
D (t)
(+)
Tsp
e(t)
+
u(t)
TC 22
_
(+)
Steam
Valve
(+)
Tm
TT 22
RV
Heat
Exchanger
(+)
T
PID Controller: Effect of P on
Control Performances



P controllers have only one tuning parameter,
Kc. However, they suffer a major disadvantage
– there exists an Offset of the controlled
variable from the set point. (Why ?)
For a given step disturbance, the magnitude of
the offset depends on the value of the gain.
The larger the gain, the smaller the offset.
Above a certain Kc, most processes go unstable.
Effect of Integral Action on
Control Performances


PI controllers have two tuning parameter: the
gain or proportional band, and the integral time
or the integral rate (1/Ti ). The advantage is
that the integration removes the offset. (Why ?)
The disadvantage of PI controllers is that the
addition of integration adds some amount of
instability to the system. The smaller the
integral time, the stronger the integral action,
the faster the system removes the offset, but
the weaker the stability of the system.
Effect of Derivative Action on
Control Performances


PID controllers have three tuning parameter:
the gain, the integral time and the derivative
time. The derivative action gives the controller
the capability to anticipate.
PID controllers are recommended for use in
slow processes with long time constants, such
as temperature loops, which are usually free of
noises. For fast processes with noises, such as
flow loops and pressure loops, the use of
derivative action will amplify the noise and
therefore should not be used.
PID Tuning






Selection of PID Controller Types （PID控制
器类型选择）
Tuning of PID Controller Parameters （控制
器参数整定）
Flow Control （流量控制）
Level Control （液位控制）
Reset Windup and Its Prevention （积分饱和
与防止）
Summary
Obtain Initial PID Para.
(Ziegler-Nichols Method)
Controller
Kc
P
 1  T 
  
 K   
PI
PID
 0.9   T 

 
 K   
 1.2   T 

 
 K   
Ti
Td
3.33 
2.0 
0.5 
Note: the above method was developed for 0    T
Obtain Initial PID Para.
(Lambda Tuning Method)
Controller
Kc
P
1  T 
 

 K     
1  T 
 

K



  

PI
PID
1  T 
 

K



  

Ti
Td
Initial Value
 0
 
T
T
τ/2
  0.2 
Note: the above method is not limited by the value of  / T
Digital PID





Concept of Digital Control Systems
Selection of Digital Filters
Digital PID Controllers and Its Improved
Version
Concept of Distributed Control Systems
Summary
Digital PID Positional Algorithm

Ideal analog PID algorithm

1
u (t )  Kc e(t ) 
Ti


t
0

de(t ) 
0 e( )d  Td dt   u0 , e(t )  ysp (t )  y(t )
t
k
e( )d  Ts  e( j )
j 0
d e(t ) e(k )  e(k  1)

dt
Ts
Digital PID positional algorithm （位置算法）

Ts
u (k )  Kc e(k ) 
Ti


Td
e( j )   e(k )  e(k  1)   u0

Ts
j 0

k
Digital PID Incremental Algorithm

Digital PID positional algorithm

Ts
u (k )  Kc e(k ) 
Ti



Td
e( j )   e(k )  e(k  1)   u0

Ts
j 0

k
Digital PID incremental algorithm（增量算法）
u (k )  u (k )  u (k  1)


Ts
Td
 K c  e(k )  e(k  1)   e(k )   e(k )  2e(k  1)  e(k  2)   ,
Ti
Ts


u (k )  u (k  1)  u (k )
PID incremental algorithm
with derivative action first

Digital PID incremental algorithm


Ts
Td
u (k )  K c  e(k )  e(k  1)   e(k )   e(k )  2e(k  1)  e(k  2) 
Ti
Ts



Digital PID incremental algorithm with derivative
action first （微分先行PID增量算法）


T
T
u (k )  K c  e(k )  e(k  1)   s e(k )  d   y f (k )  2 y f (k  1)  y f (k  2)   ,
Ti
Ts


u (k )  u (k  1)  u (k )
Cascade Control





Concept of Cascade Control（串级控制概念）
Characteristics of Cascade Control（串级控制
系统的特性分析）
Design Principle of Cascade Control （串级控
制的设计原理）
Implementation and Tuning of Controllers
（串级控制器的实现与参数整定）
Simulation Examples（仿真举例）
Process Example:
A Cascade Control Scheme
TC
23
Tsp
Tm
(1) This scheme consists of
two sensors, two transmitters,
two controllers, and one valve.
Fsp
Fm
FC
13
u(t)
FT
13
TT
23
Ti (t)
T
Process
Fluid
Fgas
Fuel Gas
Please plot block
diagram of the system ?
(2) This scheme results in two
control loops, one loop
controlling T and the other loop
controlling Fgas.
Note: The flow of fuel gas is
used only as an intermediate
variable to improve control
performance.
Cascade Control Diagram for
Outlet Temp. of Process Fluid
D2
Tsp
＋
－
Tm
TC
23
Fsp
＋
－
Fm
FC
13
Control
Valve
Fuel Supply
Subsystem
D1
T
Furnace
Fgas
FT 13
TT 23
where TC 23 is called “primary/master controller (主控制
器)”, and FC 13 is called “secondary/slave controller (副控
制器)”; D1 denotes disturbances entering the outer loop, D2
denotes disturbances entering the inner loop.
General Cascade Control Diagram
D2
D1
Secondary / Slave /
Inner Loop
y1,sp
＋
－
y2,sp
Gc1
＋
－
Gc2
ym2
Gv
Gm2
ym1
Gp2
＋
＋
y2
Gp1
＋
＋
y1
Primary /
Master /
Outer Loop
Gm1
Note: D1 denotes the effect of primary disturbances on primary
CV, D2 denotes the effect of secondary disturbances. “Primary
Loop” presents the outer loop where the inner loop is closed
and set in remote set point or cascade mode.
Design Principles of Cascade
Control Systems


The secondary variable must respond faster to
changes in some disturbances than the primary
variable does — the faster, the better
Secondary loop or inner loop must include some
obvious disturbances to primary variable— the more
the better

If possible, secondary loop should include some
nonlinear plant
Typical cascaded loops:
temp. to flow, concentration to flow, pressure to
flow, level to flow, temp. to pressure, temp. to
temp.
Cascade Control Examples
of Heat Exchanger
Fsp
PV
FC
17
Fm
FT
17
Psp
Steam
RV
Tsp
TC
27
PV
PC
37
Tm
Pm
TT
27
Ti
TC
27
PT
37
RV
Condensate
Condensate
Psp
PV
PC
37
Pm
PT
37
Steam
RV
TC
27
Tsp
TT
27
Ti
Scheme #2
T
Process
Fluid
Condensate
T
Process
Fluid
Tm
TT
27
Tsp
Tm
Ti
T
Process
Fluid
Scheme #1
Steam
Scheme #3
Feedforward Control






Feedforward Concept
Design of Linear Feedforward Controllers
Design Examples of Feedforward Control
Feedforward-Feedback Control
Simulation Results
Summary
Design of Linear Feedforward
Controllers (cont.)
D (t)
Disturbance Path
GYD (s)
Disturbance
Measurement
GDM (s)
Dm (t)
Feedforward
Controller
GFF (s)
u(t)
＋
Control Path
GYC (s)
＋
ym (t)
Extended Controlled Process
Design Objective:
Ym ( s)
 GYD ( s)  GYC ( s)GFF ( s)GDM ( s)
D( s )
0
Design formula for the feedforward
controller:
GYD ( s)
GFF ( s)  
GYC ( s)GDM ( s)
Design of Linear Feedforward
Controllers (cont.)
Design formula for the feedforward controller:
GYD ( s)
GFF ( s)  
GYC ( s)GDM ( s)
GDM (s)  K DM
KYD
GYD ( s) 
exp  D s 
TYD s  1
GFF ( s)  K FF
K FF
KYD

KYC K DM
KYC
GYC ( s) 
exp  C s 
TYC s  1
TYC s  1
exp  FF s 
TYD s  1
 FF  max0, D  C  ( Why ? )
Feedforward / Feedback Control
ysp
Feedforward
control system
+
+
∑
Feedforward
control system
u(t)
Process
y(t)
D(t)
ysp
Comparison of Feedforward
and Feedback Control
Feedforward Control
Feedback Control
Disturbances are measurable
CV is measurable
Control MV based on
disturbances
Control MV based on control
ERROR
Open-loop, No Stability Problem
Closed-loop, Stability is the
most important
Only some disturbances are
detected
All disturbances are detected
Accurate model needed for both
of Control and Disturbance Paths
No accurate model needed
Not adaptable to nonlinear or
time-varied systems
Adaptable to nonlinear or timevaried systems
Ratio Control




Concept of Ratio Control
Design of Ratio Control Schemes
Cross-limiting Control of Air/Fuel
Ratio in a Boiler or Furnace
Summary
Ratio Control
QB
IB
K1
IA
Suppose both of the flow
transmitters are linear.
Sometimes, they are nonlinear
Steady-state condition:
I A I 0  K1 ( I B  4)  4 mA
FC
Q
QA
QB
 K1
, K AB  A
QA max
QB max
QB
QA
QB max
K1  K AB
QA max
Air/Fuel Ratio in a Boiler
Control Scheme
Steam
ASP
PT
22
AT
25
P
PC
22
%O2
AC
25
PSP
Stack
PC22.OP
LS
HS
FC23.SP
FC23.PV
RF
FC
23
FC24.SP
FC
24
×
FC24.PV
Cross-limiting
control with O2 trim
RA
FT
23
Fuel
KFA
FT
24
FC
FO
Air
（带有O2调节的双
交叉控制）
Override and Selective




Override/Constraint Control Problem
Design of Constrain Control Systems
Reset Windup and Its Prevention in
Constrain Control
Selective Control Schemes
Override Control Scheme
Feed liquid
LS: Low Selector（低选器）
u(t) = min(u1, u2)
hmin
LT
23
h1
LC
23
u2(t)
SW
Fsp
u1(t) FC
LS
(＋)
u(t)
12
Fm
(－
)
FT
12
F(t)
hmin
FC
Valve
To process
Smooth Switch problem between two loops ?
Override Control Scheme
Feed liquid
LS: Low Selector（低选器）
u(t) = min(u1, u2)
LT
23
h1
hmin
LC u2(t)
23
RFB
Fsp
LS
u1(t) FC
12
Fm
RFB
FT
12
u(t)
hmin
F(t)
To process
RFB: (external) reset feedback（外部积分反馈）
Reset Windup Prevention in
Constraint Control
hm
1
Ti 2 s  1
LC 23
－
＋
KC2
u 2
v2
＋
u2
RFB
＋
hmin
LS
u
Fsp
＋
－
Fm
KC1
u1
u1
RFB
＋
＋
FC 12
1
Ti1 s  1
v1
Discuss: ONLY the controller in closed-loop condition has integral action, and
the output of inactive controller will follow the output of active controller.
Selective Control Example
Feed
Coolant
TSP
Tm1
Tm2
Tm
TC
HS
Tm3
Tm4
Coolant
Reactor
Product
Parallel Positioning Control



Concept of Parallel Positioning Control
(分程控制)
Application of Parallel Valve-Positioning
Control --- Batch Reactor Control
Concept & Application of Valve Position
Control
Combination of Parallel Valves
FC
“
FC
f (%)
B”
“
“
A”
FC
f (%)
”
A
“ O
F
B”
100
100
0
0
0.02
0.06
0.02
0.10
0.06
MPa
MPa
100
“
f (%)
FO
B”
A”
“
B”
“ O
F
”
A
“ O
F
FC
100
f (%)
0.10
0
0
0.02
0.06
MPa
0.10
0.02
0.06
MPa
0.10
Parallel Valve Positioning
Control Scheme #1
Tsp
100
Heated
Water
FC
B”
“
f (%)
FO
电/气
转换器
TT
34
T
I/P
”
Tm
A
“
TC
34
u
0
Coolant
Water
Y
“A”
“B”
Steam
Analyze the whole control process
0.02
0.06
0.10
MPa
Problem:
(1) Choose the FO or FC
type of control valves;
(2) Plot the diagram;
(3) Determine the controller
action
Methods for Compensating
Process Nonlinearity






Nonlinear Valves
Cascade Control
Variable Ratio Control
Nonlinear Gain Compensation
Nonlinear Transformation
Identification + Adaptive Control
Dead Time - Smith Predictor
D (s)
R (s)
U (s)
Gc(s)
+ _
+
+
+
K p g p ( s )e
K m g m ( s )e  m s
K m g m (s )
Y (s)
 p s
_
+
+
Gf(s)
1
Prediction Error Filter：G f (s) 
Tf s 1
Coupling Analysis of
Multivariable Systems
(多变量系统的关联分析)
Computation of Relative Gain
for n×n Systems
y  u
yi
K ij 
u j
ij 
yi u j
yi u j
u  y,    1
H ji 
ue  0
ue  0
ye  0
 K ij  H ji ,
u j
yi
ye  0
yi
1
u j
     
ye  0
T
ij
Note: “●” means the multiplication of matrix
elements
K non-invertible?
Decoupling Control Schemes
of Multivariable Systems
(多变量系统的解耦控制)
Block Diagram for a General 2*2
System with Decoupler #1
y1, sp
y2, sp



v1
Gc1(s)
Gc2(s)

u1
D11(s)
v2

G11(s)

D21(s)
G21(s)
D12(s)
G12(s)
D22(s)


u2
G22(s)
Decoupling Conditions ?


y1m


y2m
Decoupler #1
for a General 2*2 System
 y1m ( s)   G11 G12  D11

  

 y2 m ( s)   G21 G22  D21
y2 m
 0,
v1
D12  v1 ( s) 


D22  v2 ( s) 
y1m
0
v2
G11D12  G12 D22  0, G21D11  G22 D21  0
If D11  1,
D22  1
G12
G21
D12  
, D21  
G11
G22
About Decoupler #1
y1, sp
y2, sp



u1
v1
Gc1(s)
Gc2(s)




G21 ( s )
G22 ( s )
G21(s)

G12 ( s )
G11 ( s )
G12(s)

v2
G11(s)

G22(s)


y1m


y2m
u2
Problem: (1) initial MVs’ value; (2) “Man/Auto” mode switch;
(3) limit of MVs.
Block Diagram for a 2*2 System
with Feedforward Decoupler
Man1
y1,sp
y2,sp



GC1(s)
GC2(s)

M
v1
G11(s)


A
D21(s)
G21(s)
D12(s)
G12(s)


A
G22(s)
v2
M
Decoupler
u1
Man2
u2


 y1m
 y2m
Boiler



Process Diagram and Control Problems of
Boiler (锅炉设备的生产流程与控制问题)
Characteristic Analysis & Three-element
Control for Drum Level (汽包水位特性分析与
三冲量控制)
Cross-limiting Air/Fuel Ratio Combustion
Control (双交叉空燃比燃烧控制)
Two-element (双冲量) Control
D(t)
Steam
FT
02
Drum
Hsp
H(t)
LT
11
Hm
IV
LC
11
IL
∑
u = C0+C1IL+C2IV
F(t)
Feedwater
Problem discussion:
(1) Point out the kind of
control methods ?
(2) Obtain control diagram
of the scheme.
(3) Select the controller
action, the symbol and the
value of C2, if the valve is a
fail-open valve and C1=1.
Distillation





Distillation Principle & Control Problems
Column Pressure Control
Material Balance (物料平衡) Control
Product Purity Control
(1) Distillate Purity Control
(2) Bottom Purity Control
(3) Both Distillate & Bottom Purity Control
Other Control Schemes