Lecture 44.ppt, Wednesday, April
25, 214 Kb
This lecture concludes the discussion
of nyquist stability analysis for systems containing 1/s^2 and
a discussion of Nyquist's argument principle that explains the
frequency domain stability criteria.
Lecture 43.ppt, Monday, April
23, 176 Kb
This lecture explains the closing of the
nyquist contour when the open-loop system includes a 1/s component
(like all our PI controlled systems have.)
Lecture 42.ppt, Friday April
20, 160 Kb
This lecture completes an example of Nyquist
stability analysis of open loop unstable systems, and then applies
it to Proportional control of Marlin's CSTR at an unstable equilibrium
point. These initial examples are systems that do not include
a 1/s component.
Wednesday the 18th of April was used for questions in preparation for the 3rd exam on the 19th
Lecture 40.ppt, Monday April
16, 169 Kb
This lecture introduces the Nyquist stability
criteria with a first example of control for 125/[(s+5)^2(s-1)].
A one-page summary of frequency domaing stability criteria includind
Bode, Simplified Nyquist and Nyquist criteria is distributed in
class.
Friday the 13th of April was used to exercise the Homework 14 software assignment.
Lecture 38.ppt, Wednesday April
11, 353 Kb
This lecture concludes the discussion
of Bode Diagram sketching and analysis through the contribution
of the derivative mode of a PID controller to 1/(s(s+1)^2)).
Lecture 37.ppt, Monday April
9, 159 Kb
This lecture presents examples of Bode
Diagram sketching for PI control of (-s+1)/(s+1) and (-1)/(s(s+1)^2)).
These two systems were previously used in the root locus examples
of Lecture 32.ppt.
Lecture 36.ppt, Friday April
6, 242 Kb
This lecture summarizes frequency domain
guidelines and explains a complete set of rules for sketching
Bode Diagrams
of systems with arbitrary order.
There is a second page to the sketching
rules that provides a graphical summary. The second page will
be included in the in-class handout; but since it is an old File
in Macintosh graphics format, I can't link to it from the web
or view under Windows Word.
Lecture 35.ppt, Wednesday April
4, 373 Kb
This lecture summarizes time-domain, s-domain,
and frequency-domain design guidelines and then disposes of PI
and PID empirical relations from Chapter 9 on Ciacone and Chapter
10's Ziegler Nichols.
Lecture 34 on Monday, April 2, covered the PID portion of the Lecture 32 overheads and then went through a SIMULINK simulation of Bode Stability criteria of Section 10.6. Updated SIMULINK programs for this demonstration are in the frintro folder in e48\grubby\new stuff. Set path and enter frintro to matlab.
On Friday March 30, Ananth will return the 2nd exam and address your questions regarding homework 11.
Lecture 32.ppt, Wednesday March
28, 292Kb
This lecture uses 5 examples to demonstrate
the behavior of root locus plots for PI, and PID controller design.
A one-page summary of 5 rules
for root locus plots supplements Marlin's book. Marlin glosses
over the importance of root-locus because, in his opinion, chemical
plants have a lot of delays and root-locus requires polynomials.
However, in my opinion, 2nd order Pade approximations of delays
are excellent approximations that enable root locus analysis for
plants with delays.
Lecture 31.ppt, Monday March
26, 261Kb
This lecture completes a presentation
on P, PI, and PID control from Sections 8.4 through 8.7 using
the Example 7.2 3 tank mixing model.
Lectures 28,29, and 30 covered a demonstration of how to do the s-function exercise of homework 10.2, review for the 2nd exam, and a demonstration of homework 10.3 for linearization of the 10.2 model. At the end of Friday, some of the overheads leftover from lecture 27 were covered.
Lecture 27.ppt, Friday March
16, 212Kb
This lecture discusses the use of Integral-Mode
of a controller to fix the offset problem of proportional mode
control. Marlin's example 7.2 model of three mixing tanks in series
is then introduced. This mixing tank model is used in subsequent
chapters to exemplify control principles. Today, the model allows
the discussion of disturbance rejection and how integral-mode
control is needed for no-offset due to disturbances. And, now
seemed to be a good time to briefly mention Section's 10.6 discussion
of Phase Margin and Gain Margin specifications for obtaining good
closed-loop responses.
Lecture 26.ppt, Wednesday, March
14, 191Kb
This lecture continues the preview of
Section 10.5 on stability analysis of control systems with proportional
control of the relatively complex Example 7.1 system that requires
numerical root-locus to analyze. Then a simpler 1st order plant
with sensor delay with proportional control is introduced and
analyzed with both analytic and numerical procedures. Next, there
is a return to Chapter 7 to continue with performance specifications.
The offset specification is then address by adding integral control
as described in Sections 8.4 and 8.5.
Lecture 25.ppt, Monday, March
12 , 172Kb
This lecture starts in Chapter 7 on the
feedback loop, picks up a little bit of Chapter 8 on block diagram
of the feedback loop, warps up to catch a preview of Chapter 10
on stability analysis of feedback systems, and then returns to
Chapter 7 to continue with the performance specifications (or
assessments) of feedback systems.
Class was not held on Friday, March 2nd, as partial compensation for the extra time involved in evening exams.
Lecture 23.ppt, Wednesday, February
28, 87Kb
The ppt presentation discuses empirical
model estimation presented in the first part of Chapter 6 in Marlin.
It then demonstrates the Pade approximation of a delay. After
the presentation, homework 10's
software exercise will be introduced. Two tutorial documents provide
step-by-step instructions on how
to use SIMULINK to linearize a model of a CSTR and step-by-step
instructions on how to modify
the CSTR s-function to add additional dynamic equations.
Lecture 22.ppt, Monday, February
26, 95Kb
The ppt presentation discuses Marlin's
section on staged processes and introduces a SIMULINK model of
a Binary distillation column whose hydraulic model and other parameters
were obtained from a book by Luyben, 1990, on Process Modeling
Simulation and Control for Chemical Engineers. (Luybens book is
very good on modeling, but all the well-worked examples are FORTRAN-based.)
The files distillation..mdl, distillation_setup.m, distillation_sf.m,
and distillation_sf.doc have been placed in the grubby\e48\new
stuff directory. distillation_sf.doc highlights the changes needed
to adapt the s-function template file to this application. The
mdl file requires SIMULINK 3.0 available in the CAC labs (not
compatible with FENSKE lab version 2.0).
Lecture 21.ppt, Friday, February
23, 102Kb
The ppt presentation discuses Marlin's
sections on recycle structures and Multiple Input and Multiple
Output systems. The last three slides were added after class as
help for homework 8.
Lecture 20.ppt, Wednesday, February
21, 162Kb
The ppt presentation reviews a series
of two first order systems as a second order system, and then
goes into a series of 20 first order systems using a SIMULINK
model to construct data for Marlin's Figure 5-5. The most useful
result of Chapter 6 for approximating a series of first order
systems as a delay and 1st order system is presented. Frequency
response of a delay and 2nd order Pade approximation are used
to introduce inverse response (identifiable when numerator zeros
have positive real parts). Marlin's presentation of parallel structures
is presented and the rosetta program was used to demonstrate the
effect of numerator zeros on system response.
Lecture 19.ppt, Monday, February
19th, 217Kb
The ppt presentation covers 1st and 2nd
order system responses presented in Chapter 5 of Marlin. It additionally
covers more detail on the characteristics of 2nd order system
complex roots, including Appendix C Equation 15 for a CSTR. Finally
it looks at a series of two first order systems as a second order
system. Some MATLAB/SIMULINK statements and examples in the presentation
use additional example programs that are stored in my "new
stufff" folder on grubby\e48. rosetta.m is an m-file
that correlates damping factor, with pole plots, with expected
time responses. AppC_Eq15.mdl is a SIMULINK model to demonstrate
App C. Eq 15 open-loop and closed-loop system responses.
Lecture 18.ppt, Friday, February
16th, 236Kb
The ppt presentation helps explain answers
to parts of homework 6 in regards to linear model accuracy and
Euler numerical integration. The presentation next reviewed bode
diagram characteristics and then demonstrated time responses using
SIMULINK. The next part of the presentation drugged-up the seldom
used momentum equation and applied it to a manometer behavior
(in support of further explanation of response of second order
systems in Chapter 5.)
Lecture 17, Wednesday,February
14, went through the steps to complete homework
6 problems 1 through 3.
Lecture 16, Monday, February 12,
took questions regarding topics for the exam. And then went through
a derivation on the board on for bode magnitude and phase plots
characteristics when plotted on log-log scales.
Lecture 15.ppt, Friday, February
9th, 162 Kb and UPDATED 2/10/2001 at 3:30 PM!
The ppt presentation presents the derivation
of the frequency response of a transfer function. After the ppt
presentation, some features of MATLAB and SIMULINK that support
frequency response analysis was presented.
Lecture 14.ppt, Wednesday, February
7th, 59 Kb
The ppt presentation presents a brief
summary of inverse Laplace for a 1/s system driven by a sinusoidal
input. The preferred form of the inverse due to the complex poles
with the sinusoid response with a phase angle was noted. Examples
of the use MATLAB to generate plots is presented. After the ppt
presentation, the definition and use of transfer functions in
Section 4.3 and 4.4 was introduced.
Lecture 13.ppt, Monday, February
5th, 114 Kb
The ppt presentation presents a modified
derivation of the non-isothermal reactor in Appendix C. The modification
includes an additional inlet flow stream, similar to what you
need in homework set 5. After the power point presentation, I
went over an example of applying Inverse Laplace of a 1/s system
to a sinusoidal input. Also distributed in class was a copy Marlin's
software laboratory workbook that will be involved with homework
6.
Lecture 12.ppt, Friday, February
2nd, 170 Kb
The ppt presentation presents examples
Inverse Laplace using partial fraction expansion. Marlin's text
does not cover this material. I have provided a one-page summary
updated as of 2/2/201 as a supplement for the text. Additional
examples of using the procedure are covered in class.
Lecture 11.ppt, Wednesday, January
31, 145 Kb
The ppt presentation first summarizes
the results from Monday's additional Laplace techniques. Then
the application to solving coupled sets of differential equations
is completed. Partial Fraction expansion techniques are then introduced.
After the ppt presentation, an example of using partial fraction
expansion to solve Marlin's table 4.1 entry 10 was presented on
the board.
Lecture 10.ppt, Monday, January
29, 51 Kb
The ppt presentation summarizes Friday's
introduction to Laplace. The rest of the lecture covered 1) Laplace
of pulse, impulse, and time delays, 2) the final value theorem,
and 3) began application of Laplace to solving coupled sets of
differential equations, such as the non-isothermal reactor of
Appendix C.
Lecture 9.ppt, Friday, January
26, 84 Kb
The ppt presentation summarizes the stirred
tank heater example 3.7 and the Section 3.6 and Appendix C Non-isothermal
reactor. The rest of the lecture began review of Laplace
transforms in Chapter 4 through example 4.1.
Lecture 8, Wednesday, January
24, continuation of modeling and linearization with the stirred
tank heater example 3.7.
Lecture 7, Monday, January 22, energy
equation and example 3.4, setup for homework problem 3.2; 1st
example of linearization for setting up homework problem 3.3 (similar
to example 3.6). Check example 3.5 on your own.
Lecture 6, Friday, January 19, completed
example 3.2 and 3.2
Lecture 5, Wednesday, January 17,
integrating factor approach to solving differential equations
like that developed in example 3.1; began example 3.2
Lecture 4, Monday, January
15, began Chapter 3 by going over modeling of example 3.1
Lecture 3.ppt, Friday, January
12, 10,500Kb
All of Chapter 2
Lecture 2.ppt, Wednesday, January
10, 3,000Kb
The rest of Marlin Chapter 1.
Lecture 1.ppt, Monday, January
8, 1,600Kb
Course syllabus, Marlin
Chapter 1, Sections 1.1-1.2