Process Control

1
Chapter 1 Process Control
Li Shaoyuan E-mail syli_at_sjtu.edu.cn
2
Basic Concepts
3
Control of Industrial Process
4
Temperature control of Steam Heating
5
Temperature control of Electric Heating
6
Level Control
7
Closed-Loop Transfer Functions
Set point change, load is constant
Load change, constant set point
8
PID Control
9
Why PID Control

• Simple, easy to use
• Wide Application Petrochemical, Pharmaceuticals,
  Food, Chemical, Aerospace and Semiconductor, etc.
• Robust Insensitive to changes to plant parameter
  and disturbance.

• Over 90 control loops are PID with two
  exceptions
• On/off control for those with low control
  requirement loops
• Advanced control for those difficult systems and
  with high control quality.

10
Proportional Function
The controller output u is proportional to error
signal e
is proportional band
where
P control has steady state error.
11
Example
Temperature control of heating system ?T obtains
temperature of hot water ? and sends ?c ?c
regulate steam valve to keep constant outlet
temperature. load hot water flow rate Q and
outlet temperature ? P control, opening of
regulating valve ? controller output
12
Integral Function
Controller output is proportional to error e.

• Output of I control is constant only e0, no
  steady state error.
• Reduce system stability. I control is always
  slower than that of P control,
• Open loop gain is proportional to S0, increase S0
  reduce system stability.

In
13
PI Control
P to improve response time and reject
disturbance, I to eliminate steady state error.
14
Derivative Function
Output of controller is proportional to the
differential of error
or
Prediction Adjusting the output according to
speed of error. D function must be formed to PD
or PID controllers. Controller takes no action if
rate of change very small, accumulate error.
15
PD and PID Control

• Properties
• Steady state, de/dt0, PD control has steady
  state error.
• D function reduces oscillation, increases system
  stability.
• Adding D increase open loop gain, increase
  response speed.
• Sensitive to disturbance.

16
General rules of Design PID Controller

• Use D function, if system has large time constant
  and time delay.
• Using PD if the system allows steady state error,
  otherwise, using PID
• Use PI, if system has small time constant, small
  disturbance and requires no steady state error.
• Use P, if system has small time constant, small
  disturbance and allow steady state error.
• Use more advanced control scheme, if system has
  large time constant, large time delay and
  disturbance.

17
Stability of Closed-Loop Systems
18
Stability Criterion
Denominator of the closed loop transfer function
The roots of the characteristic equation (s pi )
determine responses
19
Routh Stability Criterion
Characteristic equation
 Any coefficients negative or zero, system
unstable. All coefficients positive, Routh
Array
20
Example
Characteristic equation
unstable
21
Bode stability criterion
Closed-loop system unstable if the FR of the
open-loop T.F. has amplitude ratio greater than
one at the critical frequency
22
Example
Determine closed-loop stability for proportional
control with values of KC 1, KC 4 and KC 20
23
Controller Design Based on Transient Response
Criteria
24
Desirable Controller Features

• Quick responding
• Adequate disturbance rejection
• Insensitive to model, measurement errors
• Avoids excessive controller action
• Suitable over a wide range of operating
  conditions
• Impossible to satisfy all Alternatives for
  Controller Design
• Tuning correlations - limited to lst order and
  dead time
• Closed loop transfer function - analysis of
  stability
• Repetitive simulation (computer and interactive
  graphics)
• Frequency response-stability and performance
  (computer and graphics)
• On-line controller cycling (field tuning)

 
25
Controller design based on response points
Settling time, overshoot, rise time, decay
ratio
1st order process model
Ziegler-Nichols, Cohen-Coon based on ¼ decay
ratio
26
Optimization Methods (minimize integral)
Integral of absolute value of error (IAE)
Integral error (IE)
Integral squared error (ISE)
Integral Time Weighted Absolute Error (ITAE)
27
Example (IAE)
28
Controller Design Based on Frequency Response
Criteria
29
Advantages and Disadvantage

• Applicable to dynamic model of any order
• Desired closed-loop response characteristics can
  be specified
• Information on stability and sensitivity provided.

Tends to be iterative and time consuming -
interactive computer graphics desirable
30
FR Characteristics of Controllers
a) Proportional Controller
b) PI Controller
c) PD Controller
d) Ideal PID Controller
31
Example
32
Ultimate Gain and Ultimate Period
Ultimate Gain Max Gain value results in a
stable closed-loop system for proportional-only
control
Ultimate Period
33
Gain and Phase Margins
How close a system is to a stability limit.
Gain Margin
Then
stability
Phase Margin
Phase angle
Rules of Thumb
34
Tuning Relationships
KC decreases as
increases
increase as
increases
and
Reduce
when adding integral action
, when adding derivative action
Increase
To reduce oscillation, decrease
and increase