MAE 461 Dynamics and Controls
Fall 2009
Course Description Syllabus Homework
(11/16): The test is on the day it was scheduled for! This is what you can expect on Test 3:
Question 1: FINDING MODES AND FREQUENCIES: You are given the equation of motion of a two degree-of-freedom mass-spring system acted on by applied forces. (a-10 pts) Determine the system's natural frequencies; (b-10 pts) Find the system's mode shapes; (c-5pts) normalize the mode shapes; (d-5 pts) Find the modal forces and modal initial conditions; (e-10 pts) Calculate the modal response; (f-5 pts) Calculate the physical response.
Question 2: FULL-DIMENSIONAL CONTROL OF TWO DEGREE-OF-FREEDOM SYSTEMS: You are given a figure of a two degree-of-freedom mass-spring system acted on by PID feedback and you are given a desirable dynamic performance: (a-15pts) Determine the equations of motion in matrix-vector form; (b-15 pts) Find the control gains.
Question 3: You are asked 4 true-false questions of 5 pts each. These questions evaluate your understanding of all of the material covered up to and including the chapter on feed forward control.
(10/26): The solution to test 2 is here.
(10/19): This is what you can expect in Test 2:
Question 1: You are given the equation of motion of a single degree-of-freedom mass-spring-damper system acted on by state feedback and you are given a desirable dynamic performance: (a-5pts) Determine the decay rate and the frequency of the closed-loop system; (b-10 pts) Find the control gains; (c-15pts) Find the closed-loop response given certain initial conditions.
Question 2: You are given the equation of motion of a single degree-of-freedom mass-spring-damper system acted on by PID feedback and you are given a desirable dynamic performance: (a-10pts) Determine the closed-loop characteristic equation; (b-15 pts) Find the vibration decay rate, steady-state decay rate and frequency of the closed-loop system; (c-10pts) Write down the general form of the closed-loop response.
Question 3: You are asked 6 true-false questions of 5 pts each. These questions evaluate your understanding of all of the material covered up to and excluding the chapter on multi-degree-of-freedom systems.
(10/5) Homework Clarification: In the upcoming homework assignment, plot M0 (the motor moment) as a function of time. Neglect the motor's mass and assume that the motor's radius is r = 3 inches.
(9/23): In HW 5-1 let T0 be a tenth of the fundamental period (the period associated with the system's damped frequency), and let A0 = 1.
(9/23): The solution to test 1 is here.
(9/10): There is no class on Monday, September 14.
(9/10): This is what you can expect in Test 1:
Question 1: You are given the equation of motion of a FREE single degree-of-freedom system: (a-5pts) determine whether it is un-damped, under-damped, etc.; (b-10 pts) Find the 2 roots of its characteristic equation; (c-10pts) Find the general form of the solution; (d-15 pts) Given some initial conditions, find the free response.
Question 2: You are given the equation of motion of a FORCED single degree-of-freedom system: (a-5pts) determine whether it is un-damped, under-damped, etc.; (b-20 pts) Find the steady-state (particular solutions) of the system; (c-10 pts) Find the general form of the transient (homogeneous) solution, (d-10 pts) Find the general form of the total solution, (e-10 pts) Given some initial conditions, find the forced response.
(8/25): Your teaching assistant for this class has been assigned. His name is "John" Joong-kyoo Park. His office hours are on Mondays at 10:00am-12:pm and on Fridays at 10:00am to 12:00pm in Broughton Hall, room no. 4170. His email address is jpark15@ncsu.edu. My office hours have changed to Mondays and Wednesdays at 4:00pm to 5:30pm. Your teaching assistant has asked you to make sure to come by his office prepared - with specific questions about the material or the homework, having read already the needed material in the notes. Also, please remember to make a copy of your homework before handing it in if you want to refer to it for the next homework assignment.
(8/19): Welcome to the web site for MAE 461 Dynamics and Controls. PLEASE BOOKMARK THIS PAGE!
All of the material that you'll need for the class is located here. You may want to start by reading over the course description, syllabus, and homework. Your homework deadlines are given in the syllabus and the tests dates in the course description.
In this class, you'll need a loose-leaf binder. Print out the Course Description, the Syllabus, the Homework, and the Class Notes below and put them in the loose-leaf binder. You won't need a separate book.
The homework problems will require that you program in MATLAB. An on-line MATLAB tutorial is offered at the AE Course Websites link located here.
Also, here's a SAMPLE HOMEWORK ASSIGNMENT. Your first homework assignment is due in a few days.
0. Preface
1. Complex Dynamics Simplified
2. Converting to the State Space
3. Types of Dynamical Systems, Control Problems and Control Strategies
4. Motion in a Stability Region (Part I)
5. Motion in a Stability Region (Part II)
6. Tracking the Reference Path
7. Regulating the Reference Path (Continuously-Acting Actuators)
8. Regulating the Reference Path (Discretely-Acting Actuators)
10. Treating Multi-Dimensional Systems
11. Regulating Multi-Dimensional Systems
12. Regulating Steady-State Behavior
14. Linear Algebraic Equations
15. State Estimation
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MAE 461 Dynamics and Controls
Fall 2008
Course Description Syllabus Homework
(12/8): The allowed formula sheet is here. Also, homework that has not been picked up is outside my office in a box. Any additional homework would be with the teaching assistant.
(12/3): This is what you can expect on the Exam:
Question 1: RESPONSE OF A 1DOF SYSTEM: You are given the equation of motion of a 1DOF mass-spring-damper system acted on by applied forces. (a--5 pts) Find the steady-state response; (b--5 pts) Find the form of the free response; (c--5 pts) Given initial conditions, find the total response.
Question 2: STATE ESTIMATION OF A 1DOF SYSTEM: You are given the equation of motion of a 1DOF system. (a--5 pts) Find the associated state equations of the system and of the observer; (b--5 pts) Find the characteristic equation of the error; (c--5 pts) Given a desirable settling time and frequency of the error, find the estimator gains.
Question 3: REGULATION OF THE STEADY-STATE RESPONSE OF A 2DOF SYSTEM: You are given a 2DOF system acted on by a harmonic excitation and a feed forward controller. (a--5 pts) Find the equations of motion; (b--5 pts) Find the complex steady-state response; (c--5 pts) Find the actual steady-state response.
Question 4: NON-FULL-DIMENSIONAL CONTROL OF A 2DOF SYSTEM: You are given a figure of a 2DOF system: (a--5pts) Find the equations of motion; (b--5 pts) Find the characteristic equation; (c--5 pts) Find the control gains.
Question 5: LINEAR ALGEBRAIC EQUATIONS: You are given a word statement. (a--5pts) Set up the problem in the form Ax = b (n > m); (b--5 pts) Solve for x; (c--5 pts) Find the errors in each of the equations.
Question 6: TRUE-FALSE QUESTIONS: Your are asked 5 true-false questions of 5 pts each. These questions evaluate your understanding of all of the material covered in the course.
(11/12): The solution to test 3 is here.
(11/12): This is what you can expect on Test 3:
Question 1: FINDING MODES AND FREQUENCIES: You are given the equation of motion of a two degree-of-freedom mass-spring system acted on by applied forces. (a-10 pts) Determine the system's natural frequencies; (b-10 pts) Find the system's mode shapes; (c-5pts) normalize the mode shapes; (d-5 pts) Find the modal forces and modal initial conditions; (e-10 pts) Calculate the modal response; (f-5 pts) Calculate the physical response.
Question 2: FULL-DIMENSIONAL CONTROL OF TWO DEGREE-OF-FREEDOM SYSTEMS: You are given a figure of a two degree-of-freedom mass-spring system acted on by PID feedback and you are given a desirable dynamic performance: (a-15pts) Determine the equations of motion in matrix-vector form; (b-15 pts) Find the control gains.
Question 3: You are asked 4 true-false questions of 5 pts each. These questions evaluate your understanding of all of the material covered up to and including the chapter on feed forward control.
(11/10): The solution to HW 10-1.
(10/22): The solution to test 2 is here.
(10/22): Solution to HW 5: PAGE 1 and PAGE 2
(10/16): Solution to HW 4: PAGE 1 and PAGE 2
(10/15): This is what you can expect in Test 2:
Question 1: You are given the equation of motion of a single degree-of-freedom mass-spring-damper system acted on by state feedback and you are given a desirable dynamic performance: (a-5pts) Determine the decay rate and the frequency of the closed-loop system; (b-10 pts) Find the control gains; (c-15pts) Find the closed-loop response given certain initial conditions.
Question 2: You are given the equation of motion of a single degree-of-freedom mass-spring-damper system acted on by PID feedback and you are given a desirable dynamic performance: (a-10pts) Determine the closed-loop characteristic equation; (b-15 pts) Find the vibration decay rate, steady-state decay rate and frequency of the closed-loop system; (c-10pts) Write down the general form of the closed-loop response.
Question 3: You are asked 6 true-false questions of 5 pts each. These questions evaluate your understanding of all of the material covered up to and excluding the chapter on multi-degree-of-freedom systems.
(10/14): Note for Homework 7-1 and 7-2 you can let c0 = 10 (instead of 100) to make the system less damped in which case the controllers INCREASE the damping in the system.
(9/29): The solutions to Problem 2-1 and Problem 2-2
(9/22): The solution to Test 1 is here.
(9/8): Here are some solutions that will help you on the next homework: solution to hw 1-2, solution to hw 1-3 (eqns. about 1st equil. only)
(9/6): This is what you can expect in Test 1:
Question 1: You are given the equation of motion of a FREE single degree-of-freedom system: (a-5pts) determine whether it is un-damped, under-damped, etc.; (b-10 pts) Find the 2 roots of its characteristic equation; (c-10pts) Find the general form of the solution; (d-15 pts) Given some initial conditions, find the free response.
Question 2: You are given the equation of motion of a FORCED single degree-of-freedom system: (a-5pts) determine whether it is un-damped, under-damped, etc.; (b-20 pts) Find the steady-state (particular solutions) of the system; (c-10 pts) Find the general form of the transient (homogeneous) solution, (d-10 pts) Find the general form of the total solution, (e-10 pts) Given some initial conditions, find the forced response.
(8/29): Your teaching assistant is Will Griffin. His office is located at BR 3172 and his email address is wfgriffin@gmail.com. He will be holding regular office hours on Tuesday, Thursday, and Friday from 9am-11am. My office hours have changed. They are now on Monday at 9am-10:30 (before class) and on Wednesday at 2:45pm-4:00pm (just after class). You teaching Assistant has asked you to make sure to come by the office prepared - with specific questions about the material or the homework.
(8/27): The solution to homework 1-1 is here.
(8/20): Welcome to the web site for MAE 461 Dynamics and Controls. PLEASE BOOKMARK THIS PAGE!
All of the material that you'll need for the class is located here. You may want to start by reading over the course description, syllabus, and homework. Your homework deadlines are given in the syllabus and the tests dates in the course description.
In this class, you'll need a loose-leaf binder. Print out the Course Description, the Syllabus, the Homework, and the On-Line Book below and put them in the loose-leaf binder. You won't need a separate book.
The homework problems will require that you program in MATLAB. An on-line MATLAB tutorial is offered at the AE Course Websites link located here.
Also, here's a SAMPLE HOMEWORK ASSIGNMENT. Your first homework assignment is due in a few days.
