BEIRUT ARAB UNIVERSITY
FACULTY OF ENGINEERING
DEPARTMENT OF MECHANICAL ENGINEERING
MCHE 511: DYNAMIC SYSTEMS CONTROL
Fall 2015-2016
TERM PROJECT- Design of a Controller
Antenna Azimuth: Position Control System Design
A position control system converts a position input command to a position output response. Position control systems find widespread applications in antennas, robot arms, and computer disk drives. The radio telescope antenna is one example of a system that uses position control systems. It may be used for communications with a satellite in a geostationary orbit for media or data transmissions, or communications with a deep-space human inhabited station, or even for the search of extraterrestrial life (SETI project).
An antenna azimuth position control system is shown in figure 1, with more details in figure 2 below. Its schematic diagram is shown in figure 3, and the resulting functional block diagram is in figure 4 below.
The purpose of this system is to have the azimuth angle output of the antenna, ?o(t), follow the input angle of the potentiometer, ?i(t). In other words, the input command is an angular displacement; the potentiometer converts the angular displacement into a voltage. In the same way, the output angular displacement is converted into a voltage by the potentiometer in the feedback path. The signal and power amplifiers boost the difference between input and output voltages. This amplified actuating signal (the error) drives the plant.
The system normally operates to drive the error to zero. When the input and output match, the error will be zero, and the motor will not turn. Thus, the motor is driven only when the output and input do not match. The greater the difference between input and output, the larger the motor input voltage, the faster the motor will turn. Nevertheless, one has to pay attention to the transient response of the system. Overshoot may be observed in the system along with some oscillations.
To solve the above problems, a controller with a dynamic response, a compensator, is used along with an amplifier. With this type of controller, it is possible to design both the required transient response and the required steady-state accuracy.
The uncompensated system can be modeled as a unity feedback system with a proportional controller and a plant:
Answer the following: a. Step Response
For K = 100, plot (using MATLAB®) the unit step response of the system.
Also calculate the closed-loop peak time, percent overshoot, and settling time. (You need to approximate the system as a second-order system and then check for the validity of your assumption).
b. Steady-State Error
Find the steady-state error in terms of the gain K, for step, ramp, and parabolic inputs. Find the value of gain K, to yield 1% error in the steady state.
c. Root-Locus
Draw the root-locus of the system using MATLAB©
d. Design via Gain Adjustment
Find the gain K required for 20% overshoot.
Plot the response of the system.
Repeat for 10% overshoot.
e. Controller Design
Design a cascade PD controller to meet the following requirements: • 20% overshoot
• 1.5 seconds settling time.
Plot the response and the root locus of the compensated system.
Suggest a physical realization of the controller.
f. Controller Design
Design a cascade controller to meet the following requirements: • 20% overshoot
• 1.5 seconds settling time.
• corresponding static-error constant equal to 20
Plot the response and the root locus of the compensated system. Suggest a physical realization of the controller.
g. Controller Design
Design a cascade controller to meet the following requirements:
• 10% overshoot
• 1 second settling time
• corresponding static-error constant equal to 30
Plot the response and the root locus of the compensated system.
REPORT
The report for this project is a technical report. Therefore, it should include a title page (containing the name of the university, the name of the faculty or department, the logo of the university, the name of the course and its code, the title of the project, the name of the instructor, your full name and ID number, and the date), a table of contents (with page numbers – start numbering after the page of contents), an introduction part, a theoretical analysis and background part stating all the assumptions, the answer to all questions with details and MATLAB® simulation, a discussion part, and a reference page.
The report should be typed and printed. The typeface you should use is Times New Roman, size 12 (Headings should be 14 and Bold, Sub-Headings should be 12 and Underline), and Font Color black. The paragraph alignment should be set to ‘Justify’. All the MATLAB® codes should be included in the report. All pictures and tables should be labeled with a number and description.
NOTES
• Deadline: January, 8, 2016, (firm deadline).
• This is an individual assignment.
• This assignment is optional.
• An oral examination will be done on January 8 (available time from 9:00 to 3:00) in my office. You may receive a bonus (up to 5 points) on the final grade.
• You should submit a CD with the word document and all MATLAB files. • Also you must hand the instructor a hard copy of the report.
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