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,  - . 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.
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.
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
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 , which has been expanded and improved upon in the new edition . 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.
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.
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