NE 351: Nuclear Reactor System Dynamics and Control (New)

Course Description and Goals:

The objective of this course is to study the principles of system modeling, control design, nuclear reactor dynamics, and control. The course presents the development of mathematical models of dynamic systems, transient analysis, transfer functions, frequency response, stability, state space methods, and control design. Nuclear reactor kinetics, nodal modeling of primary side components, and their control actions are discussed. Students are required to work on mini-projects during the semester using MATLAB™ and SIMULINK™.

Prerequisite: NE 301

Text: Introduction to Dynamics and Control
 Authors: B.R. Upadhyaya

References:

1. J.J. Distefano, III, A.R. Stubberud and I.J. Williams, Feedback and Control Systems, Schaum’s Outline Series, McGraw-Hill, New York, 1995.
2. C.L. Phillips and R.D. Harbor, Feedback Control Systems, Prentice-Hall, Englewood Cliffs, NJ 1988.
3. B.C. Kuo, Control Systems, Prentice-Hall, Englewood Cliffs, NJ, 1991.
4. J.J. Duderstadt and L.J. Hamilton, Nuclear Reactor Analysis, John Wiley, New York, 1976.
5. D.L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, La Grange, Park, 1993.
6. M. Naghedolfeizi and B.R. Upadhyaya, Dynamic Modeling of a Pressurized Water Reactor Plant for Diagnostics and Control, Research Report, DOE/NE/88ER12824-02, June 1991.
7. Using MATLAB, The MathWorks, Inc., 1999.
8. D. Hanselman and B. Littlefield, Mastering MATLAB, Prentice-Hall, Upper Saddle River, NJ, 1996.

Course Outline:

The following topics are presented during the semester.  The course format consists of lectures and laboratory demonstrations.  Students will work on two mini-projects, using MATLAB™ and its Toolboxes.

1.  Introduction

• Course overview.
• Evolution of system dynamic analysis and control design technology.
• Control system terminology.

• Introduction to system modeling and examples.
• Some definitions.
• The perturbation equation.
• Linear systems versus nonlinear systems.
• Linearization of nonlinear models.
• State space models.*
• Empirical or data-driven models.

3.  Nuclear Plant Systems

• Major systems in a Pressurized Water Reactor (PWR).
• Major systems in a Boiling Water Reactor (BWR).
• CANDU (CANadian-Deuterium-Uranium) pressured heavy water reactor (PHWR).*
• High-Temperature Gas-Cooled Reactor (HTGR).*

4.  Transient Analysis (this is studied along with Laplace Transforms)

• Analytical solutions of ordinary differential equations.
• Exponential form of response of a linear system.
• Standard forcing functions in process simulation.
• Examples of first order system responses.
• Numerical solutions of differential equations.
• Matrix exponential solutions for linear state space models.*
• Eigenvalues and eigenvectors.*

• Definition of the Laplace transform.
• Laplace transforms of standard functions.
• Solutions of differential equations using the Laplace transform.
• Some transform pairs.
• The method of residues and the inverse Laplace transform.
• Step response of a second order system.
• Laplace transform and linear state space models.*
• Initial value theorem and final value theorem.
• Transfer functions of linear time-invariant systems.
• The impulse response function.
• The convolution integral.
• Time delay systems.

• Concept of frequency response of linear systems.
• System transfer functions.
• Frequency response function.
• Examples of frequency response computation.
• Bode plots and linear system examples.
• Minimum and nonminimum phase functions.*
• Frequency response of multivariate linear systems (state space models).*

• Definition of stability.
• Stability of inear systems.
• Nonlinear systems and stability in the small.*
• Stability analysis using frequency response methods; Nyquist stability criterion.*
• Relative stability; gain and phase margins.

• Response characteristics of dynamic systems.
• System transfer function.
• Various control actions.
• Design methods for proportional-integral controllers.
• Example of application to a water level control problem.
• Temperature control laboratory.

• Point reactor kinetics equations.
• Power reactor dynamics and feedback effects.
• Modeling reactor core dynamics and simulation.
• Primary system model of a PWR.
• SIMULINK model of a PWR plant.
• Control strategies in a PWR.
• Control rod reactivity estimation.

10.  Instrumentation in typical PWRs.

• Process sensors and neutron detectors.

11. Presentation by Guest Speakers

12. Presentation by Student Projects

Student Projects

Each student will work on 2-3 mini-projects during the semester as defined by the instructor. The projects are related to reactor system simulation, control design, and operation. Students are required to prepare short reports with appropriate data and results. The students would use computational tools, such as MATLAB™ and SIMULINK™, and Toolboxes. The projects are assigned in order to reinforce the material covered during the semester.

Report Format

• Abstract
• Introduction: background and objectives
• Body of the report (including discussion of results)
• Summary and conclusions
• References
• Appendices

Nuclear System Dynamics and Control (NE 351): Classroom Activities (The sequence in which the topics are presented may be changed)
 

Return to ABET Course Listing

Return to NE Homepage