Dynamics, Systems, and Controls Q Guidelines

This document is not field policy and has not been subject to field vote. It is a working document provided as a good-faith attempt to describe the current shared viewpoint of the DSC faculty. Per field rules, the exam committee decides the scope of the exam and questions are at the discretion of the committee.

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Q exam name: Dynamics, Systems, and Controls

Field(s) to which it applies: AE, ME

Core physical principles covered: the DSC Q exam tests examinees in the sub-disciplines of applied mathematics, dynamics, and controls, exemplified by the content in MAE4730/5730: Intermediate Dynamics and MAE4780/5780: Feedback Control Systems. Courses such as MAE 5790: Nonlinear Dynamics and Chaos, MAE 5910: Model Based Systems Engineering, MAE 6700: Advanced Dynamics, MAE 6720: Advanced Astrodynamics, MAE 6750: Nonlinear Vibrations, MAE 6760: Model-Based Estimation, MAE 6770: Formal Methods for Robotics, MAE 6780:
Multivariable Control Theory and MAE 6790: Intelligent Sensor Planning and Control build on these principles, and students may find that taking a subset of these courses helps in preparing for the exam.

The exam committee decides the scope of the exam and questions are at the discretion of the committee; however, this list is provided as a good-faith outline of topics covered as a way to frame students’ broad study of dynamics, systems, and controls as a discipline.

Recommended textbooks for study: no textbooks are currently specified by the DSC faculty.

Classes required before Q exam: none

Classes strongly recommended before Q exam: MAE 4730/5730: Intermediate Dynamics and MAE4780/5780: Feedback Control Systems

Classes deemed helpful but not always taken before Q exam: MAE6700: Advanced Dynamics, MAE 6760: Model-Based Estimation, and MAE 6780: Multivariable Control Theory

Typical Format: Field rules specify a format (see Q exam rules on this website) but afford the committee flexibility with many details within that format.  Students are urged to inquire with their exam committee with questions about format, because the DGS can enforce field rules only, they cannot control whether an individual committee structures a Q exam in a manner similar to the way it has in the past.  ASK THE DGS TO TELL YOU THE COMMITTEE CHAIR’S NAME AND TALK TO THAT PERSON IF YOU WANT TO KNOW WHAT THE FORMAT WILL BE.

With these caveats, the committee conducting the Q-Exam for Dynamics and Controls has typically used a format as follows:

  1. Each student’s exam lasts one hour.
  2. Each student is examined by a committee of three or more faculty members in the DSC area.
  3. The format and questions for all students examined by a specific Q committee are the same.
  4. The exam consists of:
    1. A prepared presentation of 10 minutes in length, or less, followed by 5 minutes of questioning about the presentation or related material. The faculty may also ask questions during the presentation for clarification.
    2. Three oral questions, or sets of questions, given by the committee members one at a time, lasting 15 minutes each.

Prepared Presentation
The presentation and the student’s answers to the committee’s questions about the presentation are meant to indicate how well the student understands material that they have had time to prepare, without the pressure of an oral exam. The presentation can be about any topic of the student’s choosing that involves skills and ideas covered by this qualifying exam, as listed below. The presentation topic will not be set by the committee at any time. It should be prepared and given at a level that other top first-year DSC students can understand. The topic can be a new idea or a standard problem. The student should be prepared to answer questions involving the assumptions, the detailed aspects of the presentation, and possible extensions or extrapolations. Students will be stopped in their presentation at the ten minute mark.

Oral Questions
Oral questions cover the areas of Applied Math, Feedback Control, and Dynamics. They can range from very subject-specific to more philosophical and exploratory. Each member of the committee poses a question verbally or in written form. The student has 15 minutes to answer each question, which includes time for possible hints from the committee or follow-up questions on related topics. Good performance on this portion of the exam involves demonstrating the ability to apply a broad base of knowledge to new and potentially unfamiliar questions. The committee is most interested in a student’s ability to attack a brand new problem in sensible and effective ways and to make use of appropriate tools. Students taking the exam may not discuss its content with anyone until after the end of the final exam period.

Exam Content

The list below is representative of the topics that may be covered during the exam. Not all topics will appear on any one exam, but no questions will be asked outside of these topics. For each topic we list reference material. This material is a suggestion – other reference may be used to prepare for the exam.

References

  • Goldstein, H.; Poole, C. P.; Safko, J. L. (2001). Classical Mechanics (3rd ed.). Addison-wesley. ISBN 9780201657029.
  • Ogata, K. (2003). System dynamics (4th Ed.), Prentice Hall. ISBN 9780131424623.
  • Kane, T; Levinson, D. (1985). Dynamics: Theory and Applications. McGraw-Hill. https://ecommons.cornell.edu/bitstream/1813/638/10/Dynamics-Theory_opt.pdf
  • Mazourek, D.; Johnston, E.; Beer, F.; Cornwell, F. (2015). Vector Mechanics for Engineers (11th ed.). McGraw Hill. ISBN 9780073398136
  • Astrom, K. J., and Murray, R. M. (2008). Feedback systems: An introduction for scientists and engineers. Princeton University Press.
  • Franklin G. F., J. D. Powell, A, Enami-Naeini “Feedback Control of Dynamic Systems”
  • Tongue, B. H. (2005) Dynamics: Analysis and Design of Systems in Motion (2nd ed.). John Wiley & Sons, Inc. ISBN 978-0470-23789-2
  • Kasdin, N. J. and Paley, D. A. (2011) Engineering Dynamics: A Comprehensive Introduction. Princeton University Press ISBN 978-0-691-13537-3
  • Riley, K.F.; Hobson, M.P.; Bence, S.J. (2006). Mathematical methods for physics and engineering. Cambridge University Press. ISBN 9780521861533
  • Classes at Cornell : MAE 2030, MAE 5730, MAE 6700, MAE 3260, MAE 5780, MATH 2930, MATH 2940, MAE 6810

Topics

Applied Math (Classes : MATH 2930, MATH 2940, MAE 3260, MAE 6810)

  • Basis functions and vector spaces, including infinite-dimensional spaces Riley 8.1
  • Laplace Transform, Fourier transform, and Fourier series Riley 12, 13
  • Initial-value, final-value, and boundary-value problems Riley 5, 14, 15
  • Probability and statistics (PDF, CDF, moments, conditional and marginal probabilities, law of total probability, mean, expectation, variance, covariance); Bayes’s Theorem, statistical distributions (e.g. Gaussian, Poisson, binomial, etc.) Riley 30, 31
  • Matrix transformations (e.g., SVD, QR decomposition, eigenvalues, eigenvectors, matrix inverse, pseudoinverse, characteristic equation) Riley 8.3 through 8.12
  • Linear Algebra (e.g., rank, null space, range space, rank-nullity theorem, definiteness, matrix exponential eAt ) Riley 1, 7, 8
  • Differential equations (ODEs, PDEs) Riley 14-17
  • Vector calculus (e.g., div, grad, curl, tangent planes) Riley 2, 10
  • Functions of complex variables Riley 3, 24.1
  • Optimization (identification and classification of critical points, Lagrange multipliers) Riley 5.8, 5.9
  • Numerical methods (e.g., Newton-Raphson iteration, root finding,  finite differences) Riley 27
  • Numerical integration (quadrature, error control, Euler’s method for ODEs) Riley 27.4
  • Linearization of nonlinear equations
  • Equilibria and stability

Feedback Control (Classes: MAE 3260, MAE 5780)

System Dynamics
  • Time-domain solutions of equations of motion for single degree-of-freedom linear systems Franklin Ch 3; Ogata, Ch. 6-1, 6-2, 6-3, 6-4
  • Simple harmonic oscillators Ogata, Ch. 3-1, 3-2, 3-3, 3-4, 3-5, 4-4
  • Performance parameters for linear systems: rise time, settling time, overshoot Ogata, Ch. 8-4, 8-5, 8-6
  • Linear single degree-of-freedom dynamical systems in the frequency domain Franklin Ch 3; Ogata, Ch. 2-1, 2-2, 2-3, 2-4; 7-1, 7-2
  • Initial value and final-value theorems Ogata, Ch. 2-3
  • State-space representations; transforming between state space and transfer functions Ogata, Ch. 10
  • Discrete-time vs. continuous-time systems (e.g. z transform and s transform) Ogata, Ch. 11
Single-Input, Single-Output Systems
  • Concept of sensors, actuators, and plant Ogata Ch. 8-1, 8-2
  • Transfer function and impulse response Ogata Ch. 8
  • Feedback-control block diagrams Ogata Ch. 8
  • Graphical methods (root-locus plots, Bode plots) Franklin Ch. 5; Ogata Ch. 8; 9-2
  • Stability (eigenvalues, characteristic-polynomial roots, Routh array) Ogata Ch. 9-1, 9-2, 9-4, 9-6
  • Phase and gain margin Ogata Ch. 8; 9-1 – 9-6
  • Feedback control synthesis Franklin Ch. 4; Ogata Ch. 8; 9-1 – 9-6
  • Compensation: P, PI, PD, PID, Lead, Lag Franklin Ch 6; Ogata Ch. 8; 9
Multiple-Input, Multiple-Output Systems
  • General time-domain solutions Astrom and Murray, Ch. 5
  • Stability (eigenvalues, characteristic-polynomial roots) Astrom and Murray, Ch. 4.3, 8.2
  • State space representation and feedback Franklin Ch 4 and Ch 7

Dynamics (Classes: MAE 2030, MAE 5730, MAE 6700)

Kinematics
  • Degrees of freedom Goldstein Ch. 1; Kasdin Ch. 2; Tongue Ch. 2
  • Coordinate systems and generalized coordinates in two and three dimensions Goldstein Ch. 1, 5; Kasdin Ch. 1-2, 10, 13; Tongue Ch. 2, 5, 6,8
  • Frames of reference Kane Ch. 2, 6; Kasdin Ch. 3, 10-11
  • Vector mechanics: scalar, vector, and tensor products Goldstein Ch. 4, 5; Kasdin Appendix B; Kane Ch. 1
  • Vector kinematics (derivatives), including the Transport Equation (also known as the Transport Theorem, Q dot formula or the Great Kinematic Identify). Kane Ch. 1; Kasdin Ch. 8; Tongue Ch. 6, 8
  • Center of mass, mass moment of inertia, parallel-axis theorem, and moment transport Kane Ch. 3; Tongue Ch. 8; Kasdin Ch. 10, 11
  • Planar and 3D rigid body kinematics Goldstein Ch. 4; Tongue Ch. 6,8; Kasdin Ch. 9-11
Formulation of equations of motion for point masses, planar objects, and rigid bodies
  • Free-body diagrams Mazourek Ch. 4; Tongue Ch. 1
  • Forces and moments in statically determinate structures Mazourek Ch. 6
  • Impulse, momentum, and angular momentum Mazourek Ch. 12, 13, 16; Tongue Ch 3; Kasdin Ch 2-4
  • Impacts, friction, and stiction Kasdin Ch. 6; Tongue Ch. 3
  • Central-force problems Goldstein Ch. 3; Kasdin Ch 4, 7
  • Work, kinetic energy, and potential energy Tongue Ch. 4; Kasdin Ch. 5, Kane Ch. 5
  • Newton’s laws Kasdin Ch. 1-2; Tongue Ch 1-2; Kane Ch. 6
  • Lagrange’s equations Goldstein Ch. 2
  • Hooke’s Law, Newton’s law of Gravitation, Friction, and other specific models of common physical phenomena Tongue Ch. 3; Kasdin Ch. 2-3; Goldstein Ch. 4
Vibrations
  • Dynamics of discrete structures: natural frequencies and modes (eigenvalues/eigenvectors) Kasdin Ch. 12; Tongue Ch. 9
  • Forced and unforced response of oscillators Kasdin Ch. 2, 12; Tongue Ch. 9