FINAL STEER REPORT
By Evelyn TorresRangel
Strengthen Teachers’ Education in Engineering and Research
(STEER) Program
California State University, Los Angeles
Summer 2003
TABLE OF CONTENTS
I.
Abstract
II.
Introduction
III.
Project Goals and Objectives
IV.
Implementing Curriculum Revisions
V.
Instructional Resources to be Used
VI.
Support Requirements and Budget
VII.
Student Outcomes
VIII.
References
IX. Appendix
In the Structures, Pointing, and Control Engineering (SPACE) lab at CSULA, student and faculty have designed and assembled a test bed model of the Next Generation Space Telescope (NGST), also known as the James Webb Space Telescope (JWST). My project was to develop a block diagram using the SIMULINK software program to perform simulations of a PID controller on the SPACE test bed model and to graph the results of the outputs using the MATLAB software.
I have been a high school mathematics and computer programming teacher for twenty five years and an advisor for the Mathematics, Engineering, Science, Achievement (MESA) program for eighteen years. The MESA program is designed to encourage students to pursue careers in mathematics, science, and engineering. For three years, I have also coached our high school robotics team in an afterschool program.
As a result of participating in the STEER program research, I gained much insight into the research done by students and professors in the SPACE lab. I have toured the SPACE lab several times in the past with my high school students. However, I’ve never had the chance to gain indepth knowledge of the actual work done in the lab. The STEER program offered the opportunity for me to learn about complex research being performed in the lab. A short range goal I have is to disseminate this information to my students. A long range goal that I have is to develop a robotics course for our high school, whereby students emulate the research methods practiced by the CSULA students.
The JWST is being developed by NASA to continue the research of the Hubble Space Telescope. The JWST is scheduled to be launched in 2011. The JWST has five main scientific themes of study:
1. The cosmology and structure of the universe.
2. The origin and evolution of galaxies.
3. The history of the Milky Way and its neighbors.
4. The birth and formation of stars.
5. The origin and evolution of planetary systems.
The JWST is a segmented mirror telescope, unlike the Hubble Telescope which consists of only one large mirror. In the CSULA SPACE lab, advanced technologies for precision pointing, shape control, vibration attenuation, fault identification, and controller reconfiguration are developed and experimentally validated on the test bed. These new technologies are of immediate interest to NASA, to the aerospace industry and the commercial sector.
Before students actually make physical changes to the SPACE lab system, it is important for the students to model the dynamic behavior of the system using simulation software. After the students model the behavior, and after they verify the results of the model, then the students translate their model into a C program which directly controls the telescope mechanism. It is imperative that the students test and retest their virtual model before applying the model to the physical one. This avoids the potential destruction of expensive components on the physical model.
(Photo property of SPACE
lab)
(Photo property of SPACE lab)
The SPACE test bed consists of six primary hexagonal mirrors surrounding one central reference mirror, forming a parabolic shape. At its focal point, a distance of 2.4 meters above the primary mirrors, is a secondary hexagonal mirror (see photo). Below the primary mirrors is a support structure consisting of 60 struts. The entire structure is supported by three bipods, which attach the test bed to the isolation platform.
Each hexagonal mirror is supported by three actuators to provide 3axis active control. Each mirror also has three collocated sensors. These actuators allow forces to be applied to the system while the sensors detect the resulting effect on the system.
To model a dynamic system, a statespace analysis is computed. The statespace equations are derived using input variables, output variables and state variables.
For my project, I was to examine the behavior of the primary mirrors in order to achieve shaping. The engineering students in the SPACE lab derived the mathematical model of the system. In developing the mathematical model, the students had to consider the actuator points and the truss points (see diagram below) for each actuator. These are the internal disturbance points needed to model the system. The students drew the model using the NASTRAN software and extracting the information from the output file of the model.
actuator point
truss point
(Diagram property
of SPACE lab)
My project was to develop two block diagrams using the SIMULINK software program to perform simulations on the SPACE test bed model. One diagram was to model an open loop system; the other was to model a closed loop system. In an open loop system, an input is applied to the system but the output has no effect on the system, i.e. there is no feedback to the system. In a closed loop system, the output is applied back to the system, compared with the desired result, and then reapplied to the system so as to reduce the error and bring the output of the system to the desired value.
OPEN LOOP SYSTEM
Here is my SIMULINK block diagram of the open loop system:
The inputs on the left are the values input into the six primary mirror panel actuators and the secondary mirror actuators. The outputs on the right are the resulting values of the corresponding sensors. Below is a more detailed diagram of the inputs (left) and the outputs (right). Again, I used SIMULINK to create these diagrams.
I used the MATLAB software to plot the output from each of the three sensors from one of the panels. The graphs are shown below. Each actuator was given a different initial reference input. Actuator 14 was given an input step of 5, actuator 15 was given an input of 4 and actuator 13 was given a reference input of 3. These were arbitrary values I selected. Note that each actuator took about six seconds to settle to the desired reference value.
I wrote a MATLAB program to generate these graphs. Below is the program:
subplot (3,1,1);plot(tout,simout14);
grid
ylabel('ACTUATOR 14')
xlabel('time in seconds')
subplot (3,1,2);plot(tout,simout15);
grid
ylabel('ACTUATOR 15')
xlabel('time in seconds')
subplot (3,1,3);plot(tout,simout13);
grid
ylabel('ACTUATOR 13')
xlabel('time in seconds')
CLOSED LOOP SYSTEM
For the second block diagram, PID controllers were added to close the loop. PID controllers allow the user to input the values for Proportional gain, Integral and Derivative to allow adjustments to the system. A closed loop allows for feedback into the system to reduce the error and bring the output of the system to the desired value.
My SIMULINK diagram of the closed loop system:
Each of the six panels has three PID controllers. The six panels are shown below on the left. A detailed view of a PID controller is shown below on the right.
My goal was to achieve a maximum overshoot (vertical height) of 15%, a settling time less than 5 seconds and a steady state error of 0.1. I experimented with various values of P, I and D and finally managed to attain the desired results with P = 10, I = 2000, D = 200.
The results were again graphed using the program I wrote using MATLAB.
In conclusion, I discovered that increasing the values of P, I and D resulted in the following changes to the system:

Overshoot 
Settling Time 
SteadyState Error 
P (proportional gain) 
increase 
little change 
decrease 
I (integral) 
increase 
increase 
eliminate 
D (derivative) 
decrease 
decrease 
little change 
In order to complete this project I had to first become familiar with the MATLAB and SIMULINK software programs and the test bed itself. In particular, I had to:
1. Understand the use of vectors and matrices in MATLAB.
2. Learn how to plot graphs using MATLAB.
3. Understand the various block structures available in SIMULINK.
4. Understand the SPACE test bed model, i.e. the details of the relationship between the mirror panels and the actuators and sensors of the model.
5. Become acquainted with Power Point.
6. Learn how to write a paper based on scientific research.
My experiences in the SPACE lab have greatly affected my appreciation for the intense training and perseverance required of electrical engineering students. Students in the CSULA SPACE lab have been afforded the unique opportunity to work handson with stateoftheart equipment with direct application to the scientific community. This opportunity also places a unique responsibility on their shoulders, i.e. they are expected to report periodically on their progress. My experiences will affect my teaching in the following ways:
1. During my units on vectors and matrices, I will provide my students with real world examples of these data structures as used by the CSULA students in the SPACE lab.
2. I will work with our high school mathematics teachers to ensure that students appreciate the use of matrices in future scientific work.
3. My curriculum will include discussions on the process where CSULA engineering students design a virtual control system and then translate this design into a C program that directly controls the space telescope in the SPACE lab.
4. I will assign one programming project to students at the end of the year where they will present their results in a technical paper and a Power Point presentation..
5.
During
the Engineering and Technology Open House event, my students will tour the SPACE
lab as well as other labs at CSULA.
For the past three years, I have
coached a robotics team as an extra curricular, after school program. I would like to develop a robotics course,
whereby students can receive high school credit. This course will be inquiry based. A formal robotics course will enable students to work in a much
more structured environment.
The past three years that I have coached the robotics teams, I have acquired six robotics kits. In order to teach a robotics course, I will need to purchase additional robotics kits.
The success of my goals will be measured by the strength of my students’ research projects and the number of students that enroll in the robotics course the following year.