Chapter 2: Dynamic Systems and Feedback Control

Modeling, analysis, and feedback ideas needed for control co-design

A controller can only improve a system through the dynamics of the plant it acts on. To do control co-design well, we must understand those dynamics clearly.

Control co-design (CCD) is fundamentally about dynamic systems. A plant is not just a static object with dimensions and mass. It moves, stores energy, dissipates energy, responds to disturbances, and interacts with sensors and actuators over time. Controllers also act over time: they measure, decide, and command. Because both the plant and controller affect time-domain behavior, CCD requires fluency in dynamic-system modeling and feedback ideas.

This chapter develops that foundation. We begin with physical system modeling and the language of states, inputs, outputs, and disturbances. We then introduce state-space representation, discuss open- and closed-loop systems, explain stability, and show how feedback modifies system behavior. The chapter closes by connecting these ideas back to plant design: changing stiffness, mass, damping, geometry, inertia, or actuator placement changes the system dynamics, which in turn changes what controller is best.

Learning objectives¶

After completing this chapter, you should be able to:

1. explain why dynamic-system models are needed in control co-design;

2. identify states, inputs, outputs, and disturbances for a physical system;

3. derive a state-space model from differential equations;

4. distinguish open-loop and closed-loop systems;

5. explain equilibrium, stability, and asymptotic stability for linear systems;

6. show how feedback changes closed-loop dynamics; and

7. explain how plant design choices modify the dynamic model and therefore influence control design.

Chapter roadmap¶

Physical model $\rightarrow$ States and signals $\rightarrow$ State space $\rightarrow$ Feedback $\rightarrow$ Stability $\rightarrow$ Plant–control interaction