E250: Feedback Control for Linear Systems

This course provides a brief overview of the basic concepts in linear systems and feedback control. The course begins with an exploration of the feedback control problem and its applications in various fields: robotics, manufacturing, traffic, etc. We will present the unifying mathematical formulation of the problem, as well as its fundamental concepts: equilibrium and stability. We then explore the application of these concepts to linear systems and the role of linear algebra. With a grasp of the range of possible behaviors of linear time-invariant systems, we proceed to the design of feedback controllers. In the second session of the course we talk about output feedback techniques. We consider the influence of proportional and integral action, and we put these together in a worked example using PID control. This example illustrates the limits of PID and motivates the third session on state feedback methods. In the third session we describe the pole placement approach to state feedback, and couple it with the analogous state estimator. We briefly discuss observability and controllability as prerequisites for this design approach. We end the course by solving the example of the previous session with state feedback techniques, and motivating other advanced topics in control theory.