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Control Terminology
controlled variables - these are the variables which quantify
the performance or quality of the final product, which are
also called output variables.
manipulated variables - these input variables are adjusted
dynamically to keep the controlled variables at their set-
points.
disturbance variables - these are also called "load"
variables and represent input variables that can cause the
controlled variables to deviate from their respective set
points.
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Control Terminology (2)
set-point change - implementing a change in the operating
conditions. The set-point signal is changed and the
manipulated variable is adjusted appropriately to achieve
the new operating conditions. Also called servomechanism
(or "servo") control.
disturbance change - the process transient behavior when a
disturbance enters, also called regulatory control or load
change. A control system should be able to return each
controlled variable back to its set-point.
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Assumptions:
1. w1 is constant
2. x2 = constant = 1 (stream 2 is pure A)
3. Perfect mixing in the tank
Control Objective:
Keep x at a desired value (or “set point”) xsp, despite variations in
x1(t). Flow rate w2 can be adjusted for this purpose.
Terminology:
• Controlled variable (or “output variable”): x
• Manipulated variable (or “input variable”): w2
• Disturbance variable (or “load variable”): x1
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Design Question. What value of is required to have
2
w
?
SP
x x
Overall balance:
Component A balance:
1 2
0 (1-1)
w w w
1 1 2 2 0 (1-2)
w x w x wx
(The overbars denote nominal steady-state design values.)
• At the design conditions, . Substitute Eq. 1-2,
and , then solve Eq. 1-2 for :
SP
x x
SP
x x
2 1
x 2
w
1
2 1 (1-3)
1
SP
SP
x x
w w
x
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• Equation 1-3 is the design equation for the blending
system.
• If our assumptions are correct, then this value of will keep
at . But what if conditions change?
x
SP
x
Control Question. Suppose that the inlet concentration x1
changes with time. How can we ensure that x remains at or near
the set point ?
As a specific example, if and , then x > xSP.
SP
x
1 1
x x
2 2
w w
Some Possible Control Strategies:
Method 1. Measure x and adjust w2.
• Intuitively, if x is too high, we should reduce w2;
2
w
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• Manual control vs. automatic control
• Proportional feedback control law,
2 2 (1-4)
c SP
w t w K x x t
1. where Kc is called the controller gain.
2. w2(t) and x(t) denote variables that change with time t.
3. The change in the flow rate, is proportional to
the deviation from the set point, xSP – x(t).
2 2,
w t w
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• Because Eq. (1-3) applies only at steady state, it is not clear
how effective the control law in (1-5) will be for transient
conditions.
Method 3. Measure x1 and x, adjust w2.
• This approach is a combination of Methods 1 and 2.
Method 4. Use a larger tank.
• If a larger tank is used, fluctuations in x1 will tend to be damped
out due to the larger capacitance of the tank contents.
• However, a larger tank means an increased capital cost.
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• It is important to make a distinction between negative feedback
and positive feedback.
Engineering Usage vs. Social Sciences
• Advantages:
Corrective action is taken regardless of the source of
the disturbance.
Reduces sensitivity of the controlled variable to
disturbances and changes in the process (shown later).
• Disadvantages:
No corrective action occurs until after the disturbance
has upset the process, that is, until after x differs from
xsp.
Very oscillatory responses, or even instability…
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Incentives for Chemical Process Control
• Reasons to do Process
Control
– Safety
– Production Specifications
– Environmental Regulations
– Operational Constraints
– Economics
• Tasks the Control System
Should Perform
– Suppress the effects of
external disturbances
– Ensure the stability of the
process
– Optimize the performance of
the process
Control
System
Process
Monitoring
Intervention
This is a
“control loop”
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Safety (Process Safety)
• Avoid situations that lead to
– Massive loss of containment (chemical release)
– Explosion
– Fire
• Control layers (order of increasing severity)
– Basic regulatory control
– Alarm with operator intervention
– Automatic preprogrammed abnormal situation management
– Safety Instrumented System (SIS)
Process
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Process Safety – Incidents to Learn from and Not Repeat
• ICMESA, Sevesa, Italy, July 10, 1976
– Reactor overheated, resulting in an explosion and release of mixture
containing 2,4,5-Trichlorophenol.
• Union Carbide, Bhopal, India, December 3, 1984
– Methyl Isocyanate release due to water entering vessel and reacting with
contents. 2000 immediate fatalities with another 8000 delayed. Many
thousands of injuries.
• BP, Texas City, Texas, March 23, 2005
– Distillation tower overfilled and caused release of hydrocarbons which
subsequently vaporized. Vapor cloud ignited/exploded killing 15 and injuring
180.
• Arkema, Crosby, Texas, August 31, 2017
– Flooding as a result of Hurricane Harvey caused loss of power and backup
power and consequently loss of refrigeration. Organic peroxides
decomposed and exploded and burned releasing toxic vapors.
• Many others
• United States Chemical Safety Board www.csb.gov
Paul Gruhn
lecture
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Environmental Regulations
• Legal obligation to satisfy regulations
– Air permits
– Water permits
– Ground contamination
– Remediation (of past mistakes)
• Good Corporate Citizenship to be responsible stewards
of the environment (beyond regulations)
If Not
• Fines
• Lawsuits
• Damaged Reputation
• Criminal Charges
• Loss of License to Operate
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Economics
• Operate profitably
• Operate the most profitably possible subject to constraints
(optimization)
– Drive process to the most profitable operating point and keep it there
(continuous)
• The location of the most profitable point depends on the current conditions,
which are constantly changing.
• Requires constant adjustment
– Drive process along the most profitable profile in time (batch)
• Example: Maximizing yield from a batch reactor may require following a certain
temperature profile in time,
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Suppress the effect of external disturbances
• “Process” is whatever is inside the system boundary
– What you are modeling, controlling, analyzing, or studying
• “Environment” is everything else
• “Disturbances” are variables that cross the boundary
Environment
Process
Weather
• Temperature
• Sunlight
• Rain
• Wind
• Pressure
Utilities
• Air pressure
• N2 pressure
• Fuel gas HV
• CW temperature
• Steam pressure and quality
Raw Materials
• Composition
• Temperature
• Pressure
Other
Process
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Ensure the Stability of the Process
• Process can be:
– Physical process (open loop – without control)
– Combination of physical process and control system (closed loop)
• Physical process can be stable or unstable
– Unstable process can be stabilized by properly designed feedback control
– Stable process can be destabilized by poor control design (avoid this)
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Optimize the Performance of the Process
• Operate the process at the “best” point or along the “best”
trajectory
• What is “best” requires the objective to be defined
– Profit
– Throughput
– Environmental Considerations
• Best point
– can vary over time based on external disturbances
– Must respect constraints (physical, operational, quality)
• Control system should adjust accordingly
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Example: Stripping Column Economic objective
• Bottom product is valuable
• Top product is incinerated
• Manipulated variables:
– Steam flow
– Top product flow
– Feed rate
• Controlled variable: Bottom product purity
• Easiest way to run
– Moderate feed rate
– High steam flow
– High top product flow
• Best way to run
– High feed rate
– Just enough steam flow
– Just enough top product flow
Easy to avoid flooding
High separation
High impurity removal
Limits
Production
rate
Wastes
steam
Wastes
product
Maximize production
Just enough separation
Just meet specification
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Other Examples
• Batch reactor example 1.3 from book
– Economic objective: maximize profit
• No steam gives little product
• Too much steam produces too much byproduct (and wastes steam)
• Want it just right – and just the right time profile
• Fired heater
– Environmental objective: minimize emissions
– Economic objective: efficient use of fuel
• Air/fuel ratio too low produces too much CO and wastes fuel due to
incomplete combustion
• Air/fuel ratio too high produces too much NOX and wastes fuel due to heating
excess air
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Summary: Incentives for Chemical Process Control
• Reasons to do Process
Control
– Safety
– Production Specifications
– Environmental Regulations
– Operational Constraints
– Economics
• Tasks the Control System
Should Perform
– Suppress the effects of
external disturbances
– Ensure the stability of the
process
– Optimize the performance of
the process
Control
System
Process
Monitoring
Intervention
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Hierarchy of Process Control activities
1. Measurement
and Actuation
2. Safety, Environment
and Equipment
Protection
3a. Regulatory
Control
4. Real-Time
Optimization
5. Planning and
Scheduling
Process
3b. Multivariable
and Constraint
Control
(days-months )
(< 1 second)
(< 1 second)
(seconds-minutes)
(minutes-hours )
(hours-days )
Figure 1.8 Hierarchy of
process control activities.