1. CHE517 Advanced Process Control
Prof. Shi-Shang Jang
Chemical Engineering Department
National Tsing-Hua University
Hsin Chu, Taiwan

2. Course Description Course: CHE517 Advanced Process Control
Instructor: Professor Shi-Shang Jang
Text: Seborg, D.E., Process Dynamics and Control, 2nd Ed., Wiley, USA, 2003.
Course Objective: To study the application of advanced control methods to chemical and electronic manufacturing processes
Course Policies: One Exam(40%), a final project (30%) and biweekly homework(30%)

3. Course Outline Review of Feedback Control System
Dynamic Simulation Using MATLAB and Simu-link
Feedforward Control and Cascade Control
Selective Control System
Time Delay Compensation
Multivariable Control

4. Course Outline - Continued
7. Computer Process Control
8. Model Predictive Control
9. R2R Process Control

5. Chapter 1 Review of Feedback Control Systems
Terminology
Modeling
Transfer Functions
P, PI, PID Controllers
Block Diagram Analysis
Stability
Frequency Response
Stability in Frequency Domain

6. Feedback Control Examples: Room temperature control
Controller
Transmitter
Set point
stream
Temp
sensor
Heat loss
condensate
Examples:
Room temperature control
Automatic cruise control
Steering an automobile
Supply and demand of chemical engineers

7. Feedback Control-block diagram
Manipulated
variable
disturbance
error +
Controller
process
Controlled variable Σ
Set point -
Measured value
Sensor +
transmitter
Terminology:
Set point
Manipulated variable (MV)
Controlled variable (CV)
Disturbance or load (DV)
Process
controller

8. Instrumentation Transmitter Controller Set point Temp Heat loss sensor
Signal Transmission: Pneumatic 3-15psig, safe longer time lags, reliable
Electronic 4-20mA, current, fast, easy to interface with computers, may be sensitive to magnetic and/or electric fields
Transducers: to transform the signals between two types of signals, I/P: current to pneumatic, P/I, pneumatic to current
Controller
Transmitter
Set point
stream
Temp
sensor
Heat loss
condensate

9. Modeling
Mass M Cp T Q
Q=UA(T-T0)
Rate of accumulation = Input – output + generation – consumption
At steady state : let T = TS and Q = QS  0 = QS – UA(TS - T0S)
Deviation variables : let T = TS+Td , Q = QS+Qd , T0 = T0s+T0d
Then :
If system is at steady state initially Td(0) = 0

10. Laplace Transforming:
Transfer Functions
Laplace Transforming:
M Cp S Td(S) = qd(S) - U A (Td(S) – Tod(S)) Or ∑
Td(S) +
qd(S)
Tod(S)

11. Non-isothermal CSTR Total mass balance: Mass balance :
condensate
T V ρ CA CB F0 ρ0
CA0 T0 F ρ CA T
steam
A  B
rA = - KCA mol/ft3
K = αe-E/RT
Total mass balance:
Mass balance :
Energy balance :
Initial conditions : V(t=0) = Vi , T(t=0) = Ti , CA(t=0) = CAi
Input variables : F0 , CA0 , T0 ,F

12. Linearization of a FunctionX0
X0 -△
X0+△
-△ △
F(X) X
aX+b

13. Linearization

14. Linearization of Non-isothermal CSTR

15. Common Transfer Functions K=Gain; τ=time constant; ζ=damping factor; D=delay
First Order System
Second Order System
First Order Plus Time Delay
Second Order Plus Time Delay

16. Transfer Functions of Controllers
Proportional Control (P)
m(s) = Kc[ e(s) ]
e = Tspt - T Kc
e(s)
m(s)
Proportional Integral Control (PI)
e(s)
m(s)
Proportional-Integral-Derivative Control (PID)
e(s)
m(s)

17. The Stability of a Linear System
Given a linear system y(s)/u(s)=
G(s)=N(s)/D(s) where N, D are polynomials
A linear system is stable if and only if all the roots of D(s) is at LHS, i.e., the real parts of the roots of D(s) are negative.

18. Stability in a Complex PlaneRe Im
Purdy oscillatory
Fast Decay
Slow Decay
Exponential Decay
with oscillatory
Slow growth
Fast Exponential
growth
Exponential growth
Stable (LHP)
Unstable (RHP)

19. Partial Proof of the Theory
For example: y(s)/u(s)=K/(τs+1)
The root of D(s)=-1/τ
In time domain: τy’+y=ku(t)
The solution of this ODE can be derived by y(t)=e-t/τ [∫e1/τku(t)dt+c]
It is clear that if τ<0, limt→∞y →∞.

20. Transfer functions in parallel
X(S)= G1(S)*U1(S) + G2(S)*U2(S)
X1(S) X2(S) Σ
U1(S)
U2(S)
G1(S)
G2(S)
X1(S)
X2(S) +
X (S)

21. Transfer function Block diagramΣ Kc + -
Tset
control QS
process 1
Measuring device Td
Proportional control No measurement lags

22. Block Diagram Analysis∑
X(S) +
GL(S)
GP(S)
Gm(S)
L(S) m
Gc(S) - Xs Xm X1 e
e = Xs – Xm
m = Gc (S) e(s) = Gc e
X1 = Gp m = Gp Gc e
X = GL L + X1 = GL L + Gp Gc e
Xm = Gm X = Gm GL L + Gp Gc e
X = GL L + Gp Gc[Xs – Xm]
= GL L + Gp Gc [Xs] – Gp Gc [Xm]
=GL L + Gp Gc Xs – Gp Gc Gm X

23. Stability of a Closed Loop System
A closed loop system is stable if and only of the roots of its characteristic equation :
1+Gc(s)Gp(s)Gm(s)=0
are all in LHP

24. Level System

25. The jacketed CSTR W
Set Point
TRC FC
2A  B Tc Wc
T, Ca

26. A Nonisothermal Jacketed CSTR
(i) Material balance of species A
(ii) Energy balance of the jacket
(iii) Energy balance for the reactor
(iv) Dependence of the rate constant on temperature

27. Linearization of Nonisothermal CSTR
CV=T(t)
MV=Wc(t)
It can be shown that

28. A Practical Example –Temperature Control of a CSTR Method of Reaction Curveτ D
Dead time
Maximum slope △C
Process
output
Time constant
time

29. Ziegler-Nichols Reaction Curve Tuning Rule
P only PI
PID Kc
/DKp
0.9/DKp
1.2/DKp I
n.a.
D/0.3
D/0.5 D
0.5D

30. △C τ D △m
Kc=
τi =3.33
D= 1
τ =13
k =

32. setpoint

34. Ziegler-Nichols Ultimate Gain Tuning Find the ultimate gain of the process Ku. The period of the oscillation is called ultimate period Pu
P only PI
PID Kc
Ku/2
Ku/2.2
Ku/1.7 I
n.a.
Pu/1.2
Pu/2 D
Pu/8

35. Measuring Controller Performance

36. Upper Limit of Designed Controller Parameters of PID Controllers
Q: Given a plant with a transfer function G(s), one implements a PID controller for closed loop control, what is the upper limit of its parameters?
A: The upper limit of a controller should be bounded at its closed loop stability.

37. Approaches Direct Substitution for Kc Root Locus method for Kc
Frequency Analysis for all parameters

38. An Example Kc ○ － ＋

39. 1. Stability Limit by Direct Substitution
At the stability limit (maximum value of Kc permissible), roots cross over to the RHP. Hence when Kc=Ku, there are two roots on the imaginary axis s=±iω
(s+1)(s+2)(s+3)+Ku=0, and set s= ±iω, we have (iω+1)(iω+2)(iω+3)+Ku= 0, i.e. (6+Ku-6ω2)+i(11ω-ω3)=0. This can be true only if both real and imaginary parts vanishes: 11ω-ω3=0→ ω= ±√11 ; 6+Ku-6×11=0 →Ku=60

40. 2. Method of Root Locus
Rlocus (sys,k)
k(12) ans =

41. 3. Frequency Domain Analysis
Definitions: Given a transfer function G(s)=y(s)/x(s); Given x(t)=Asinωt; we have y(t) →Bsin(ωt+ψ)
We denote Amplitude Ratio=AR(ω) =B/A; Phase Angle=ψ(ω)
Both AR and ψ are function of frequency ω; we hence define AR and ψ is the frequency response of system G(s)

42. An Example
A sin(wt)
B = sin(wt+f)

43. Frequency Response of a first order system

44. Basic Theorem Given a process with transfer function G(s);
AR(ω)=︳G(iω)︳
φ(ω)=∠ G(iω)
Basically, G(iω)=a+ib

45. Example: First Order System

46. Corollary If G(s)=G1(s)G2(s)G3(s) Then AR(G)=AR(G1) AR(G2) AR(G3)
φ(G)=φ (G1) +φ (G2)+φ (G3)
Proof: Omitted

47. Example

48. Bode Plot: An example G(s)=1/(s+1)(s+2)(s+3) where db=20log10(AR)

49. Nyquist Plot sys=tf(num,den) NYQUIST(sys,{wmin,wmax}))

50. Nyquist Stability Criteria
Given G(iω), assume that at a frequency ωu, such that φ=-180° and one has AR(ωu), the sufficient and necessary condition of the stability of the closed loop of G(s) is such that: AR(ωu) ≦1

51. The Extension of Nyquist Stability Criteria
Given plant open loop transfer function G(s), such that at a frequency ωu, the phase angle φ(ωu)=-180°. At that point, the amplitude ratio AR=｜G (ωu) ｜, then the ultimate gain of the closed loop system is Ku=1/AR, ultimate period Pu=2π/ ωu.

52. Simulink Example
time
Response
D1.4
 =2.3

53. Simulink Example - Continued
>> sys=tf(1,[ ])
Transfer function: 1
s^3 + 6 s^ s + 6
>> bode(sys)
u=3.5
ARu=-38db
=10-38/20
=0.0162
Ku=1/ARu=80

54. Simulink Example - Continued
1. Reaction Curve Approach: KC=1.2/DKp=1.2*2.5/(0.5*0.165)=36; I=D/0.5=1;D=D*0.5=0.25

55. Simulink Example - Continued
Ultimate properties Approach:
Ku/1.7=80/1.7=47;I=Pu/2= 2* / 2U =0.9;D=Pu/8=0.22