Teaching Control to High School Students

COSMOS Cluster 11 Course: Feedback Control

The California State Summer School for Mathematics and Science (COSMOS) at UC Santa Cruz is a 4-week summer residential program for high school scholars with demonstrated interest and achievement in math and science.

The California State Legislature established COSMOS with a mission to motivate the most creative minds of the new generation of prospective scientists, engineers, and mathematicians so that they may actively participate in the business and higher educational sectors of the State of California.

The course will introduce the students to the basic principles of feedback control. The focus will be on introducing concepts such as input, output, disturbance, uncertainty, sensing, decision making, actuation, using examples. We will use historical case studies to introduce the concepts such as stability and stabilization. Students will learn how to draw block diagrams, their interconnections, and reason about practical systems from engineering and biology. The aim is to expose the students to the idea that problems from different disciplines can be thought of in a unified way. The topics will include how to balance a stick on hand, how to fly an airplane, cruise control of a car, and how to treat diabetes. The main learning outcome for the students is to appreciate the idea that these seemingly different problems can be addressed using the common language of feedback control.

Instructor: Prof. Abhishek Halder (Dept. of Applied Mathematics, School of Engineering, UC Santa Cruz)

Comments received from the COSMOS 2021 students at the end of the course

Comments received from the COSMOS 2022 students at the end of the course

My interview in Macrocosm magazine for COSMOS 2022

2021 Course Slides

Lecture 01: Introduction to Control

Lecture 02: Understanding Block Diagrams

Lecture 03: Signals in Control Systems

Lecture 04: Dynamics in Control Loops

Lecture 05: Stability and Stabilization

Lecture 06: Fixed Points and Stability

Lecture 07: Oscillation   [Some calculation details for slides 11 and 12]

Lecture 08: Linear versus Nonlinear

Lecture 09: State Space

Lecture 10: Control Objectives

Lecture 11: Linear Feedback

Lecture 12: Controllability

Lecture 13: Modeling Control Systems

Lecture 14: Uncertainties in Control Systems

Lecture 15: Probabilistic Uncertainties and State Estimation

Lecture 16: Filtering

Lecture 17: Control Education and Careers

Lecture 18: Course Review

Discovery Lecture

[July 19, 2021] Uncertainties and Feedback Control in Mars Entry-Descent-Landing