The Control Systems group at Ohio State has for many years been
recognized as a leader in the area of laboratory instruction;
see for example, [1] - [7]. The fundamental focus in development
of this undergraduate control systems laboratory was to provide
an appropriate atmosphere for instruction as well as for
independent learning. While there may be many ways to achieve
these objectives, we feel this goal is best achieved by imposing
a limit of two students at each laboratory station, and limiting
the total number of stations to optimize the amount of contact
the instructor has with the students. Thus, the control laboratory
we describe has five fully equipped laboratory stations. A picture
of the laboratory is shown below.
Station Hardware
The heart of the laboratory station is the Pentium-based PC,
operating at 120 MHz with 24Mbyte RAM, Windows 3.11 operating
system, and 1Gbyte storage capacity. The Metrabyte DAS-20 high-speed
data acquisition card in each computer has 16 digital I/O channels
and eight differential input channels with 12 bit resolution,
and is capable of 100 KHz A/D conversion rates. The purpose of
this configuration is to provide a functionally complete measurement
and test system when interfaced with the programmable instrumentation.
A letter-quality dot-matrix printer accompanies each computer.
In order to connect all the programmable instruments with the
computer, we use the General Purpose Interface Bus (GPIB) as it
is defined in IEEE standard 488-1978. The GPIB cable has 24 lines,
16 assigned to specific signals (data, management, handshake)
and eight to shields and grounds. Instruments can be connected
to the GPIB bus in linear or star configuration or in a combination
of both. Interface with the computer is accomplished via a card
and Tekware from Tektronix.
The instruments at each station include:
Tektronix AFG5101 Programmable Function Generator. This
is an analog signal source for sine, triangle, arbitrary and dc
signals. The AFG5101 is designed to operate in three compartments
of a TM500 Series power module. It can be operated manually using
front panel keys or programmed via the GPIB. For standard waveform
functions, the AFG5101 operates within a frequency range of 0.02
Hz to 12 MHz. For all waveform functions, output amplitude is
from 10mV to 9.99V.
Tektronix 2424L Digital Oscilloscope. This is a portable,
dual-channel instrument with a maximum digitizing rate of 25 megasamples
per second. Several features make the instrument versatile and
easy to operate. Most front-panel buttons call up menus on the
screen, then menu buttons on the CRT bezel select among the displayed
control functions. Cursors allow direct measurement of amplitude,
time frequency and other waveform parameters which are also displayed
on the screen of the oscilloscope. Information about any front-panel
control can be displayed on the screen using the HELP feature.
Tektronix HC100 Plotter. This is a sophisticated, yet easy
to operate plotter, configured as only-listener and can plot waveforms
from the screen of the digital oscilloscope.
Tektronix CPS250 Triple Output Power Supply. This power
supply has a fixed five volt output and two variable outputs (0
to 20 volts @ 500mA), configured to supply +15 volts.
Station Software
Operation in analysis and design of control systems in this
laboratory is carried out via two primary software packages. For
"on-line"' test and analysis, the Tektronix EZ-TEST
package provides easy interface with the digital oscilloscope
and waveform generator. For "off-line"' analysis and
design, the Mathworks, Inc. MATLAB package provides computer-aided
design capabilities. Finally, the QuickBasic language is utilized
for digital controller implementation.
The Tektronix EZ-TEST program is a software development tool for
use on a PC with a GPIB interface card. Used with GPIB-programmable
test instruments, this system configuration allows us to generate
and run automated test procedures. There are several menu driven
programs such as: a generator program which sets up instruments,
learns/executes procedures, and obtains test data; a translator
program which converts test procedures into QuickBasic source
code; a utility program that manipulates the test data (list,
plot, or print test results); and, a test execution program which
runs test procedures produced with the translator.
MATLAB is a powerful, programmable matrix calculator with
graphics. It can solve complex, large-scale matrix problems that
are encountered in a variety of engineering problems. This package
was chosen for this laboratory course for these reasons, and primarily
because it is easy to use and understand. The accompanying manual
is invaluable in describing operation and functionality. The package
provides ease in designing control systems via root locus, Bode
and Nyquist analysis tools. Interactive graphics routines provide
excellent means by which a theoretical analysis and design may
be developed for implementation on real analog plants in the laboratory.
On-line HELP is extensive, and a menu-driven demonstration is
provided.
Ohio State operates under the quarter system with 10 week terms.
After a standard two-course sequence in signals and systems, students
interested in control systems may elect to take the first course
in control systems, followed by the laboratory course described
below.
Philosophy
Students spend approximately four hours in each Lab (weekly
meeting), and are required to prepare brief written reports, some
for single Labs, or for groups of Labs as appropriate (generally
five or six reports throughout the term). The descriptions and
procedures for the course have been written in textbook form and
published as a low cost laboratory manual sold at the university
bookstore; previously, the book used was [2], which has been expanded
and improved upon in the new edition [3]. Most often the course
is taught entirely by a qualified graduate student teaching assistant,
where 15 to 30 minutes of lecture precedes each Lab meeting. Because
the text is available, students are able to prepare prior to the
meeting with short "pre-Lab" exercises.
A feature of the laboratory course is the utilization of computer-controlled
instrumentation over the GPIB. Although only the first few Labs
make explicit use of this feature, it is expected that the students
continue throughout the course to use the tools developed early
on for analysis and design. Although many educators today are
utilizing software which emulates instrumentation such
as the digital storage scope and waveform generator, we felt that
the benefit of exposing students to the actual instrumentation
(facilitating the "hands-on" atmosphere) far outweighed
any convenience afforded by those software tools. Of course, the
Tektronix equipment donation enabled us to realize this objective.
Another important feature is the use of a commercially available
software package for computer-aided analysis and design. Also,
the introduction of concepts from sampled-data systems and digital
control broadens the scope and treatment of the course material.
A characteristic immediately evident in each of the Labs is that
none involve "real"' physical plants such as a motor
or heater, although each does involve an analog plant in the form
of an operational amplifier circuit implemented on the Comdyna
analog computer. There are basically two reasons for this:
(1) A goal was to keep the nature of each Lab as generic as possible;
thus, a "real plant"' could be substituted, without
any loss of continuity, in most of the procedures (and, this has
been done on occasion).
(2) Many students move on to take more advanced control laboratory
courses (such as EE 757 Control Laboratory I
or EE 758 Control Laboratory II) which
involve physical plants such as motors, heaters, process control
tanks, a flexible robot, and so on.
This philosophy represents a trade-off, with regard to cost, since
analog circuits are typically more reliable, more robust to day-to-day
usage (and abuse), and are certainly easier (and cheaper) to maintain.
It also tends to focus attention on fundamentals being taught
in the course structure, rather than on making an apparatus and
its accompanying electronics perform properly.
Course Structure
The Labs and their objectives are as follows:
Lab #1: Instrumentation and Software
The objective of this Lab is to become familiar with the laboratory
computer, programmable measurement instruments, instrument controller
software and the GPIB, and sophisticated software for computer-aided
control system design and analysis. Also, the relationship between
the transient response and the pole-zero location of a transfer
function is explored.
Lab #2: Analog Simulation
Toward a better understanding of analog simulation, this Lab has
four objectives: 1) To demonstrate how to obtain the differential
equations for a mass and spring system; 2) To find an analog simulation
for a given differential equation using op-amps; 3) To analyze
the damping for a system; 4) To witness the effect of noise when
determining the frequency response of a syste.
Lab #3: Introduction to Digital Signal Processing
The objective of this Lab is to offer a brief introduction to
digital signal processing. The effects of sampling an analog signal
using an analog to digital (A/D) converter and then reconstructing
this analog signal using a digital to analog (D/A) converter are
analyzed. As a result, the effects of aliasing and quantization
errors are demonstrated. This Lab also reviews the basics of Fourier
series analysis, examines the sampling of finite and infinite
bandwidth signals, and briefly addresses discrete-time equivalent
approximation of continuous-time filters.
Lab #4: Gain Compensation and Feedback
The objective of this Lab is to employ cascade gain compensation
in a unity feedback configuration to adjust the damping of a closed-loop
system. Choice of compensating gains are determined via computer-aided
design using root locus and frequency response techniques.
Lab #5: Lag Compensation
The objective of this Lab is to utilize computer-aided design
tools, with techniques from Bode design methods and root locus
design methods, to design and subsequently implement lag compensation
in a unity feedback configuration to achieve desirable stability
and time response characteristics for a given plant.
Lab #6: Lead Compensation
The objective of this Lab is to utilize computer-aided design
tools, with techniques from Bode design methods and root locus
design methods, to design and subsequently implement lead compensation
in a unity feedback configuration to achieve desirable stability
and time response characteristics for a given plant.
Lab #7: Compensation for Sampled Data Systems
In this Lab two design techniques are utilized in order to
develop a compensator for a sampled-data system, which is defined
here as a system with a continuous-time analog plant with a discrete-time
controller. In the first case, a discrete design of a gain compensator
is carried out using Z-plane root locus. Secondly, discrete
equivalents are found for the continuous-time lag and lead compensators
designed using the root locus in Labs #5 and #6, and implemented
for the continuous time plant.
Lab #8: Tuning an Analog PID Controller
The objective of this Lab is to investigate the Proportional-Integral-Derivative
(PID) type of control law. The Ziegler-Nichols tuning rules are
investigated for designing a PID controller for a linear plant
with modeled or unmodeled dynamics.
Lab #9: Tuning a Digital PID Controller
The objective of this Lab is to investigate the discrete-time
version of the PID controller, and to implement classical tuning
rules for the digital control system.
Typically, the tenth week is reserved for a "lab practical"'
examination, testing the students' understanding of analysis and
design procedures which exercise the instrumentation and software.
[1] S. Yurkovich, Guest Editor, Special Issue on Advances in Control
Education, IEEE Control Systems, Vol. 12, No. 3, 1992.
[2] S. Yurkovich, Control Systems Laboratory, Kendall/
Hunt Pub. Co., Dubuque, Iowa, 1991.
[3] S. Yurkovich, D. J. Clancy and J. K. Hurtig, Control Systems
Laboratory, Simon & Schuster Custom Publishing Co., Needham
Heights, MA, 1998.
[4] U. Ozguner, "Three-Course Control Laboratory Sequence,"
IEEE Control Systems, Vol. 8, No. 3, 1989, pp. 14-18.
[5] S. Yurkovich, U. Ozguner and K. M. Passino, "Control System Testbeds and Toys: Serendipitous or Suspect?," in Proceedings of the American Control Conference, Albuquerque, NM, June 4-6, 1997.
[6] S. Yurkovich and K.M. Passino, "A Laboratory Course for Teaching Intelligent Control," Proceedings of the 1996 Conference on Decision and Control, Kobe, Japan, Dec 1996.
[7] S. Yurkovich and K.M. Passino, "An Intelligent Control
Laboratory Course," Proceedings of the 1996 IFAC World
Congress, San Francisco, CA, July 1996.