Transcript 01_1 - Ferdowsi University of Mashhad

‫بسم هللا الرحمن الرحيم‬
Advanced Control
Lecture one
Mohammad Ali Fanaei
Dept. of Chemical Engineering
Ferdowsi University of Mashhad
Reference: Smith & Corripio, “Principles and practice of automatic process control, 3 rd ed., Wiley, 2006
Control objectives and structures
Safety
Environmental protection
Equipment protection
Smooth plant operation and production
Product quality
Profit optimization
Structures
Feedback
Feedforward
Feedback/Feedforward
Objectives
Feedback control
Final Control
Element
Controller
Sensor
Transmitter
Controller
Final
element
Sensor
Manipulated variable
Controlled
variable
Process
Disturbances
Other outputs
Advantages and disadvantages of feedback control
Disadvantages
• Very simple technique
• Effective for all disturbances
• Provides zero ss offset
• Works with minimum knowledge
of the process
• Does not take control action
until the process output has
deviated from set point
• Affects the closed-loop
stability
Advantages
Feedforward control
Advantages and disadvantages of feedforward control
Disadvantages
• Compensates for a disturbance
before the process output is
affected
• Does not affect the stability of
the control system
• Can not eliminate steady-state
offset
• Requires a sensor and model
for each disturbance
Advantages
Feedback / feedforward control
Modeling (relation between inputs and outputs of process)
We can tune the controller only after the process steady-state and
dynamic characteristics are known.
Types of model
• White box (first principles) n black box (empirical)
• Linear n non-linear
• Static n dynamic
• Distributed n lumped
• Time domain n frequency domain
• Continuous n discrete
For further reading refer to
: Roffel & Beltlem, “Process dynamics and control”, Wiley, 2006
A modeling procedure
1. Define goals
5. Analyze results
Specific design decisions
Check results for correctness
Numerical values
Limiting and approximate answers
Functional relationships
Accuracy of numerical method
Required accuracy
Interpret results
2. Prepare information
Plot solution
Sketch process and identify system
Characteristic behavior
Identify variables of interest
Relate results to data and assumptions
State assumptions and data
Evaluate sensitivity
3. Formulate model
Answer “what if” questions
Conservation balances
6. Validate model
Constitutive equations
Select key values for validation
Rationalize
Compare with experimental results
Check degrees of freedom
Compare with results from more
Dimensionless form
complex model
4. Determine Solution
Analytical
For further reading refer to: Marlin, “Process
Numerical
Control”, McGraw-Hill, 2nd Ed., 2000.
Example 1. Isothermal CSTR
F
Define Goals
F
V
CAo
1.
Dynamic response of a CSTR to
a step in the inlet concentration.
2.
The reactant concentration
should never go above 0.85
mole/m3
3.
When the concentration reaches
0.83 mole/m3, would a person
have enough time to respond?
What would a correct response
be?
CA
1.
The system is the liquid in
the tank (as shown in Fig.).
2.
The important variable is
the reactant concentration in
the reactor.
Prepare Information
Example 1. Isothermal CSTR
Prepare Information …
F
F
CAo
V
CA
3.
Assumptions
•
Well-mixed vessel
•
Constant density
•
Constant flow in
•
Constant temperature
4.
Data
•
F = 0.085 m3/min , V = 2.1 m3
•
(CAo)initial = 0.925 mole/m3 , DCAo = 0.925 mole/m3
•
The reaction rate is rA = -kCA , with k = 0.04 min-1
Example 1. Isothermal CSTR
Formulate Model
1.
Material balance:
F
F
CAo
V
CA
dC A
V
 FC Ao  FC A  kVC A
dt
2.
Rationalize :
dC A 1
F
 C A  C Ao
dt 
V
3.
where  
V
F  VK
Degrees-of-freedom: One equation, one variable(CA), two external
variables (F and CAo) and two parameters (V and k).
Since the DOF are zero, and the model is exactly specified.
Example 1. Isothermal CSTR
F
F
Analytical Solution
CAo
V
CA
C A  (C A )init  K p [C Ao  (C Ao )init ](1  e t / )
F
where K p 
 0.503,   12.4 min
F  Vk
Numerical Solution
Example 1. Isothermal CSTR