CE 397: Control theory for smart infrastructure

Catalog Description

Introduction to control theory for civil engineers, with applications to structural, hydraulic, transportation, HVAC, electrical, and water/wastewater treatment systems. Presents mathematical methods for (i) modeling civil infrastructure systems, (ii) estimating system states from sensor data, and (iii) controlling system dynamics. Topics include differential equation-based models of civil infrastructure; time and frequency domain representations; linear spaces and linear operators; state-space models; modal analysis; controllability and observability; feedback control; state estimation; and system identification. Three lecture hours a week for one semester.

Prerequisites

Undergraduate-level differential equations and linear algebra. Programming experience with Python or MATLAB recommended.

Course objectives

The goal of this course is to teach students how to model, estimate, and control the dynamical behavior of civil infrastructure. After taking this class, students will be able to:

• Build differential equation-based models of civil infrastructure systems.
• Control the behavior of civil infrastructure in real-time to achieve operational goals.
• Estimate the internal states of civil infrastructure from imperfect or incomplete sensor data.
• Gain a graduate-level foundation in linear algebra and dynamical systems theory.
• Understand the fundamental properties of linear systems of differential equations, including their solutions, realizations, stability, controllability, and observability.

Required reference material

There is no required textbook for this class. All study material will be provided in the form of typed lecture notes, to be distributed over the duration of the class.

Optional reference material

Controls:

• Ogata, K. (2010). Modern Control Engineering. ISBN:978-0-13-615673-4.

Linear algebra:

• Strang, G. (2016). Introduction to Linear Algebra. ISBN:978-09802327-7-6
• Laub, A. J. (2005). Matrix Analysis for Scientists and Engineers. doi:10.1137/1.9780898717907

Linear systems theory:

• Chen, C.-T. (1999). Linear System Theory and Design (3rd ed.). ISBN:978-0195117776.

Grading policy

The approximate grade breakdown for the course is as follows:

Students will be graded on a curve. Letter grades will be assigned such that the median grade is at the borderline between an A- and a B+.

Homework

• Homework will be where the majority of your learning takes place, and thus homework will comprise the major part of your grade. Each homework assignment is worth roughly 5-6% of your overall grade–enough that you should take each assignment seriously, but not so much that you can’t afford to make mistakes.

• You are permitted and encouraged to discuss homework problems with your classmates. However, anything you turn in must be your own work. In other words, wholesale copying of your fellow students’ solutions or code is not permitted.

• Homework will be assigned weekly, and will be due each Thursday at 11:59 pm. The final homework assignment is an exception—this comprehensive final homework assignment will be worth twice as many points as a normal assignment, and you will be given two weeks to complete it.

• Your lowest homework score will be dropped (note that the final homework assignment cannot be dropped).

• Homework solutions will be posted promptly after each assignment due date; for this reason, late homework cannot be accepted.

Quizzes and participation

Quizzes will be administered during class to help reinforce lecture material. The participation portion of your grade will be primarily based on attendance. Opportunities for extra credit may be provided.

Class project

The class project will give you an opportunity to explore the topics presented in this course in greater detail. Your research topic must meet two basic requirements:

• It must relate to civil engineering in a substantive way.
• It must incorporate the material taught in class in a substantive way.

If you are unsure if a topic conforms to these requirements, please do not hesitate to talk with me. You may also incorporate additional methods and materials that are outside the scope of this class: for instance, by investigating advanced control-theoretic techniques like Kalman Filtering, or by implementing a real-world control system with embedded electronics (e.g. Arduinos). The class project will culminate in a written report, to be submitted on the last day of class.

Tentative class schedule