Course Description       Syllabus       Homework

Note to Students (12/3):  The following describes what to expect on the FINAL:

Question 1 (15pts) - Equations of Motion of a 2DOF System: You are given a drawing of a 2DOF System and asked to a) draw its free-body diagrams, b) write down the 2 equations of motion, and c) find the corresponding mass and stiffness matrices.

Question 2 (15pts) - The Eigenvalue Problem: You are given the equations of motion of a 2DOF system and asked to a) find the associated characteristic equation and the corresponding natural frequencies, and b) find the naturla modes of the system.

Question  3(20pts) - System Response: You are given the equations of motion of a 2DOF system, its frequencies, and mode shapes and asked to a) Find the modal forces, b) find the modal displacements, and c) find the system response.

Question 4 (20pts) - Full-Dimensional Control: You are given the equations of motion of a 2DOF system and a desirable closed-loop performance and asked to a) find the system's closed-loop frequencies and decay rates, and b) determine the control gain matrices G, H, and I.

Question 5 (20pts) -Non-Full-Dimensional Control: You are given the equations of motion of a 2DOF system, a  general form of a controller,  and a desirable closed-loop performance and asked to a) find the system's closed-loop frequencies and decay rates, b) the desirable characteristic equation, and c) the control gains.        

Note to Students (12/1):  The solution to test 3 is here.

Note to Students (11/26):  Matrix inverses of  2 x 2 and 3 x 3 matrices are shown how to be performed here.

Note to Students (11/19):  Test 3 has been moved to Wednesday, November 28. The following describes what you can expect on TEST 3:

Question 1(30 pts) - Regulating Steady-State Behavior: You are given a 1DOF system with base excitation and a control force and want to perform either inertial position control or relative position control. a) Derive the system's equations of motion. b) Assuming a complex harmonic excitation, find the complex control force. c) Assuming a real harmonic excitation, find the real control force. 

Question 2 (30 pts) -Linear Algebraic Equations: You are given a set of linear algebraic equations. a) Find the least squares (or minimum norm) solution, b) find the minimum squared norm (or the least square error). 

Question 3 (30 pts) - State Estimation: You are given a 2nd-order system and want to design an observer to estimate either the position or the velocity. a) Rewrite the equations in the state space, and write down the corresponding state equations for the state estimator and for the error. b) Find the characteristic equation for the error. c) Given a prescribed performance for the error, find the estimator's gains.       

Note to Students (10/31):  The solution to test 2 is here.

Note to Students (10/17):  The following describes what you can expect on TEST 2:

Question 1(35 pts) - State Feedback: You are given a 1DOF system and asked to design a controller to dampen the motion in a certain time and to reduce peak overshoot by a certain factor. a) Calculate the alpha and beta, b) find the control gains g and h, determine the systems closed-loop response x(t).

Question 2 (40 pts) - PID of a 1DOF System: You are given a 1DOF system acted on by a constant force and are given the PID controller. a) solve the characteristic equation for the closed-loop system, b) find the closed-loop steady-state decay rate, closed-loop vibration decay rate, and closed-loop frequency  c) Find the system's response.

Question 3 (25 pts) - Performance and Cost: You are asked 5 True-False questions about performance and cost. These test your understanding of the concepts.  

Note to Students (9/26):  The solution to test 1 is here.

Note to Students (8/28):  Your Teaching Assistant for this class is Wesley Boyette (wrboyett@ncsu.edu). His office hours are:

BROUGHTON HALL, ROOM 4167 (Diesel Wing)

Mondays at 3:00pm to 4:00pm & Tuesday & Thursdays at  2:00pm to 4:00pm

He asks that your homework be 1) very neat, 2) on engineering paper, and 3) includes all MATLAB programs stapled to the back.  Also, he will be entertaining questions about the grades you receive up to one week after the homework is returned. 

Note to Students (8/23):  Note that the 1st Homework is due on the 3rd day of class on August 29. (The syllabus and homework sheets incorrectly stated that day 2 was August 29 and day 3 was August 31).

Note to Students (8/22):  Welcome to the web site for MAE 461 Dynamics and Control.  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 test dates and homework deadlines are given in the syllabus.

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. Please print them out and put them in the loose-leaf  binder.  You won't need a separate book.

In a few weeks, the homework problems will require that you program in MATLAB. It can be helpful, if needed, to practice ahead of time. For those interested, here's a MATLAB TUTORIAL. 

Also, here's a SAMPLE HOMEWORK ASSIGNMENT. You are expected to hand in neat homework assignments like the sample.

CONTROL OF DYNAMICAL SYSTEMS: AN INTRODUCTORY APPROACH

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