State Space

This series introduces control techniques built on state-space equations, the model representation of choice for modern control.

We will provide some intuition around how to think about state variables and why this representation is so powerful. We’ll walk through a simple but effective feedback controller called pole placement, or full state feedback, and show how it is able to move the eigenvalues of your system.

We’ll also describe the concepts of controllability and observability. Finally, we’ll look at the Linear Quadratic Regulator (LQR), a popular MIMO control technique, and show how you can use it to find optimal eigenvalue locations based on weighting criteria.

Part 1: Introduction to State-Space Equations Let’s introduce the state-space equations, the model representation of choice for modern control. This video will provide some intuition around how to think about state variables and why this representation is so powerful.

Part 2: Pole Placement This video provides an intuitive understanding of pole placement, also known as full state feedback. This is a control technique that feeds back every state to guarantee closed-loop stability and is the stepping stone to other methods like LQR.

Part 3: A Conceptual Approach to Controllability and Observability This video helps you answer two really important questions that come up in control systems engineering: Is your system controllable? And is it observable? In this video, we’re going to approach the answers from a conceptual and intuitive direction.

Part 4: What is LQR Control? LQR is a type of optimal control based on state-space representation.