Mass Balance on a Draining Tank:
Drain Flow Sq. root of Hydrostatic Head
Linearization Taylor Series:
First Order ODE:
Second Order ODE:
Second Order Underdamped Form:
Case 1: > 1 (overdamped): [Stable] real negative distinct roots, -p1, -p2
ChE 3015 Study Guide for Test # 1 - revised 2/15/07 Test #1 will be held on Thursday, 2/22/2007 from 7:00-8:30 PM in 120 Randolph Hall. A test review session will be held on Wednesday, 2/21/07 at the regularly scheduled class time. Attendance is volu
Workshop 2 ANSWER KEY P-Only Control of Tank Level
Objective: To design and test a P-Only controller for tracking changes in set point and rejecting disturbances. Also, to explore how controller gain impacts P-Only performance. 1) Click "Gravity Drai
Control Loop Block Diagram:
Following the diagram of Fig. 1.4, a sensor measures the measured process variable and transmits, or feeds back, the signal to the controller. This measurement feedback signal is subtracted from the set point to obtain th
What is Input Aliasing (or how to digitize analog data
accurately)
Reading: pp.53-59 in Fundamentals of Instrumentation & Process Control
Input aliasing is a phenomenon that occurs from
digital processing of a signal.
When a signal is processed digitally
Examples:
1. Distillation column - one plate =
one FO system
2. Tubular Flow reactor - one
cylindrical reactor broken up into
"n" # of CSTRs in series
y(t) = KpU(t-ThetaP)[1 - exp(t-ThetaP/TauP)]
PPC, Chapter 13, pp.126-130
Example - an insulated CSTR wit
Linearization of Nonisothermal Reactor - This problem begins with the nonlinear model developed in
Section 11.6 of "Practical Process Control" (PPC) and applies the linearization techniques described
in Chapter 12 of PPC so that the final result is a line
Derivation of Unsteady-State Mass & Energy Open Loop Balances
Step-by-Step Modeling Procedure (Chapters 11 & 12 in Practical Process Control)
1.Write USS mass or energy balance equations that describe the dynamic model of a
system.
Identify constant param
-_' Discuss This Articiel n
15 mg
with ind m. Wynn!
Pmmnyhculnn Room mam
*M' '_
Cut the Cost and Raise
the Reliability of Your
Instrumentation
Review your maintenance, engineering,
purchasing, and construction practices.
Often, big improvements are p
What is a Centrifugal Pump?
Reading: pp.118-130 in Fundamentals of Instrumentation & Process Control
The centrifugal pump is so named because it
relies on centrifugal forces to create the kinetic
energy in the fluid to impart flow.
A centrifugal pump has
What Temperature Instruments Do We Use
Temperature is one of the most common process
variables.
Temperature is most commonly measured by
Thermocouples
Resistance Temperature Devices (RTD)
Thermistors (may also be found embedded in some
control equipment)
OUTLINE OF MODELING PART OF COURSE
Chapter 11 PPC - Open Loop (OL) Systems
First-order systems
Derivation of mass/energy balance models Kp, p, p
Open loop transfer function - open loop time constant and gain
Effect of dead time
Chapter 12 - Nonlinear
Good Practice and Troubleshooting
The Method
Reading: pp.156-159 in Fundamentals of Instrumentation & Process
Control
Check each subsystem separately
Final Control Elements
Sensors
The Controller
The Process
Copyright 2007 Control Station, Inc. All Rights
Examples:
1. Distillation column - one plate =
one FO system
2. Tubular Flow reactor - one
cylindrical reactor broken up into
"n" # of CSTRs in series
y(t) = KpU(t-ThetaP)[1 - exp(t-ThetaP/TauP)]
PPC, Chapter 13, pp.126-130
What is value of the damping ra
1 L 1 i?
> r h
n munfmau-nu 4m Minam- r - LA w
I:
W
'2; u :aQ;:L:V-m
:21 ~ a. 1*-
V 1 3 r
V i
x
.6. ~._. - :nluJQum22Jmmugx-mkusu. ~ I
we "umJl
m at; - A man a
f r
la:m=" - a
E 1 1 l i
I .2 2 1 :
uyamlunxA:.-gu:m4:;-.mu:1xuhutzcamlmmnmmgu;
mt ~ .
3%
ChE 3015 Study Guide for Test # 3 to be held 5/5/14 (revised 4/28/14)
Test format
Students should bring: 1 page of notes (notes on the front and back are allowed)
a calculator
a ruler in case a graph needs to be read
Any special formulae will be provided.
ChE 3015 Study Guide for Test # 1 - revised 2/18/14
Test Conditions: Students should bring:
1 page of their own notes (notes on the front and back are allowed)
a calculator (essential!)
a ruler in case a graph needs to be read
at least one #2 pencil and
ChE 3015 2014 Tentative Grade Ranges revised 5/12/14
Note: The cumulative class scores in the table below are based on the current grades in ChE 3015 (test #s 1-3 +
homework/attendance). The 3 tests are equally weighted and count for a total of 92% of the
Demo
onstration of effect of deadtime on closed loop control d
d
p
demonstrate with gravi
e
ity
dra
ained tanks.
Start Gra
avity Drained tanks in op loop (OL mode at T
d
pen
L)
Tank 2 heigh = 4 m and CO = 70%. This
ht
d
.
is the des
sign level of operatio
14. Laplace Transforms
14.1 Laplace Transform Basics
Transforming functions from the time domain into the Laplace domain provides a convenient means
for manipulating and solving linear ODEs with constant coefficients. In particular, Laplace
transforms ena
Problem 17.2 in PPC: Showing all steps, use the direct synthesis method to derive the
controller tuning correlation for the case where the open loop process is described by a
first-order system without dead time equation (FO).
Showing all steps, use the d
How to Approximate a High Order Open Loop System with an FOPDT System Useful for Controller Tuning
Given a closed loop system described by Figure 16.3
and where the CLTF for a set point change is given
by:
Note: In Figure 16.3 above, we have assumed that
Flow Measurement mass & volumetric flow rates
Reading: pp.79-96 in Fundamentals of Instrumentation & Process Control
(FI & PC)
Fluid velocity or mass are typically not measured
directly.
directly
Measurements are affected by the properties of
y
p p
the fl
Thermocouple and Thermowell Sensor Model
from "Process Dynamics and Control" by Seborg, et al. (1989)
Objective: Develop a model for
relating fluid temperature to the
measured temperature that is
actually reported to the control
room in the form of a volt
What Temperature Instruments Do We Use
Temperature is one of the most common process
variables.
Temperature is most commonly measured by
Thermocouples
Resistance Temperature Devices (RTD)
Thermistors (may also be found embedded in some
control equipment)
Chapter 5 P-Only: The Simplest PID Controller
PV measured at intermediate values
The Gravity-Drained Tanks Control Loop
Measurement, computation and control action repeats every
loop sample time, T:
a sensor measures the liquid level process variable (PV)