👉 Controller math is a mathematical framework used to design and analyze control systems, particularly those involving feedback loops. It provides a systematic approach to understanding and synthesizing controllers by expressing the system dynamics in terms of a set of input-output relationships. The core idea is to represent the system's behavior using transfer functions, which describe how the system responds to different input signals. Controller math extends this by incorporating feedback mechanisms to stabilize and optimize system performance, allowing engineers to design controllers that can achieve desired dynamic characteristics such as stability, responsiveness, and robustness. This framework uses tools like pole placement, state-space representation, and optimal control techniques to derive controllers that effectively manage system behavior, making it a crucial tool in modern control theory and engineering applications.
