Control Systems I

Abstract

Analysis and synthesis for linear time-invariant control systems with one input and one output signal (SISO). State-space models, time response, stability conditions. Transfer functions and frequency response. Stability analysis under feedback: Root Locus, Bode plots, Nyquist condition. Feedback control synthesis: time- and frequency-domain specifications, PID lead/lag compensation, loop shaping.

Objective

The course addresses dynamic control systems, i.e., systems that (i) evolve over time, and (ii) have control inputs and measured outputs. The main objective is to learn how to design the control inputs in such a way that the measured outputs have some desirable properties. For example, for an advanced driver assistance system, how to control acceleration so that the speed remains constant, and how to control the steering angle so that the car remains in the center of the lane. In order to pursue this objective, the course is organized into three main parts: 1) Modeling: learn how to represent a dynamic control system in such a way that it can be treated effectively using comutational and mathematical tools. This will include learning how to use computer tools like Matlab to simulate dynamic control systems. 2) Analysis: understand the basic characteristics of a system, such as its (internal and external) stability, performance, and robustness, and how the input affects the output. We will also learn to analyze systems obtained as interconnections (e.g., feedback) of two or more other systems. In particular, we will focus on tools that allow to understand how a system will behave under feedback control (i.e., closed-loop behavior), based only on its open-loop behavior. 3) Synthesis: the last part of the course will concentrate on how to design feedback control laws, in order to change the behavior of the system in a desirable way. In this course, we will concentrate on systems that can be modeled by Ordinary Differential Equations (ODEs), and that satisfy certain other technical conditions, such as linearity and time-invariance. In addition, we will focus on systems with a Single Input and a Single Output (SISO). This will allow us to use "classical control" tools that are very powerful and easy to use (i.e., mostly graphical), and which are really laying the foundation of any followup work on more challenging control problems. In addition to paper-and-pencil techniques, we will leverage modern computational tools for control design, such as Python and/or Matlab.

Resources