Overall Course Objectives Develop the skills necessary to
function as an industrial process control engineer. Skills Tuning
loops Control loop design Control loop troubleshooting Command of
the terminology Fundamental understanding Process dynamics Feedback
control
Slide 3
Process Dynamics Chemical Engineering courses are generally
taught from a steady-state point-of-view. Dynamics is the time
varying behavior of processes. Chemical processes are dynamically
changing continuously. Steady-state change indicates where the
process is going and the dynamic characteristics of a system
indicates what dynamic path it will take.
Slide 4
Uses of Dynamic Process Models Evaluation of process control
configurations For analysis of difficult control systems for both
existing facilities and new projects Process design of batch
processes Operator Training Start-up/shut-down strategy
development
Slide 5
Classification of Models Lumped parameter models- assume that
the dependent variable does not change with spatial location within
the process, e.g., a perfectly well mixed vessel. Distributed
parameter models- consider that the dependent variable changes with
spatial location within the process.
Slide 6
Example of a Lumped Parameter Process
Slide 7
Example of a Distributed Parameter Process
Slide 8
Modeling Approaches Lumped parameter processes- Macroscopic
balances are typically applied for conservation of mass, moles, or
energy and result in ODEs. Distributed parameter processes-
Microscopic balances are typically applied yielding differential
equations for conservation of mass, moles, or energy for a single
point in the process which result in PDEs.
Slide 9
Conservation Equations: Mass, Moles, or Energy Balances
Slide 10
Mass Balance Equation
Slide 11
Accumulation Term
Slide 12
Other Terms in Mass Balance Eq.
Slide 13
Mole Balance Equation
Slide 14
Accumulation Term
Slide 15
Other Terms in Mass Balance Eq.
Slide 16
Thermal Energy Balance Equation
Slide 17
Accumulation Term
Slide 18
Other Terms in Energy Balance Eq.
Slide 19
Constitutive Relationships Usually in the form of algebraic
equations. Used with the balance equations to model chemical
engineering processes. Examples include: Reaction kinetic
expressions Equations of state Heat transfer correlation functions
Vapor/liquid equilibrium relationships
Slide 20
Degree of Freedom Analysis The number of degrees of freedom
(DOF) is equal to the number of unknowns minus the number of
equations. When DOF is zero, the equations are exactly specified.
When DOF is negative, the system is overspecified. When DOF is
positive, it is underspecified.
Slide 21
Different Types of Modeling Terms Dependent variables are
calculated from the solution of the model equations. Independent
variables require specification by the user or by an optimization
algorithm and represent extra degrees of freedom. Parameters, such
as densities or rate constants, are constants used in the model
equations.
Slide 22
Dynamic Models of Control Systems Control systems affect the
process through the actuator system which has its own dynamics. The
process responds dynamically to the change in the manipulated
variable. The response of the process is measured by sensor system
which has its own dynamics. There are many control systems for
which the dynamics of the actuator and sensor systems are
important.
Slide 23
Dynamic Modeling Approach for Process Control Systems
Slide 24
Dynamic Model for Actuators These equations assume that the
actuator behaves as a first order process. The dynamic behavior of
the actuator is described by the time constant since the gain is
unity
Slide 25
Heat addition as a Manipulated Variable Consider a steam heated
reboiler as an example. A flow control loop makes an increase in
the flow rate of steam to the reboiler. The temperature of the
metal tubes in the reboiler increases in a lagged manner. The flow
rate of vapor leaving the reboiler begins to increase. The entire
process is lumped together into one first order dynamic model.
Slide 26
Dynamic Response of an Actuator (First Order System)
Slide 27
Dynamic Model for Sensors These equations assume that the
sensors behave as a first order system. The dynamic behavior of the
sensor is described by the time constant since the gain is unity T
and L are the actual temperature and level.
Slide 28
Dynamic Model for an Analyzer This equation assumes that the
analyzer behaves as a pure deadtime element. The dynamic behavior
of the sensor is described by the analyzer deadtime since the gain
is unity
Slide 29
Dynamic Comparison of the Actual and Measured Composition
Slide 30
Model for Product Composition for CSTR with a Series
Reaction
Slide 31
Model for Cell Growth in a Fed- Batch Reactor
Slide 32
Class Exercise: Dynamic Model of a Level in a Tank Model
equation is based on dynamic conservation of mass, i.e.,
accumulation of mass in the tank is equal to the mass flow rate
into the tank minus the mass flow rate out.
Slide 33
Class Exercise Solution: Dynamic Model for Tank Level Actuator
on flow out of the tank. Process model Level sensor since the level
sensor is much faster than the process and the actuator
Slide 34
Sensor Noise Noise is the variation in a measurement of a
process variable that does not reflect real changes in the process
variable. Noise is caused by electrical interference, mechanical
vibrations, or fluctuations within the process. Noise affects the
measured value of the controlled variable; therefore, it should be
included when modeling process dynamics.
Slide 35
Modeling Sensor Noise Select standard deviation ( ) of noise.
is equal to 50% of repeatability. Generate random number. Use
random number in a correlation for the Gaussian distribution which
uses This result is the noise on the measurement. Add the noise to
the noise free measurement of the controlled variable.
Slide 36
Numerical Integration of ODEs Accuracy and stability are key
issues. Reducing integration step size improves accuracy and
stability of explicit integrators The ODEs that represent the
dynamic behavior of control systems in the CPI are not usually very
stiff. As a result, a Euler integrator is usually the easiest and
most effective integrator to use.
Slide 37
Development of Dynamic Process Models for Process Control
Analysis It is expensive, time consuming, and requires a specific
expertise. It is typically only used in special cases for
particularly difficult and important processes.
Slide 38
Overview Dynamic modeling for process control analysis should
consider the dynamics of the actuator, the process, and the sensor
as well as sensor noise.
