Keeping Things Stable: How Controllers Tackle Complexity in Modern Physics (Lecture 1)

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# Lecture

What do the LHC beamline, the International Space Stations orbit, and cryogenic detector temperatures have in common? They are *inherently unstable* and require precise, real-time control. Modern physics experiments and technologies depend on such controllers, and as systems grow more complex, controllers must not only *stabilize* but also *optimize* for performance, robustness and **computing efficiency**.

Every control system relies on a feedback loop: sensors measure states, a controller computes corrective actions, and actuators apply them — all under tight real-time constraints. At the LHC, for example, tiny beamline deviations must be detected and corrected through rapid calculations that keep the beam on track. Such high-precision, multi-input/multi-output systems push classical approaches like **PID** and **state-space controls** to their limit, especially when dealing with strong nonlinearities or frequent disturbances. That for, this lecture also introduces **ML-based strategies**, especially **reinforcement learning** (RL), which excels when system dynamics are complex, nonlinear, or difficult to model analytically. RL is especially promising for highly nonlinear or poorly understood dynamics, where traditional modeling becomes infeasible. Also RL can adapt in large or shifting parameter spaces and discover strategies beyond manual tuning.

The talk gives a concise overview of **modern control theory** in physics: from PID controllers and state-space methods (including LQR and MPC) to current challenges in controller synthesis and computing. By the end, participants will understand the main families of controllers, their strengths, and when each method is the right tool for demanding real-world physics applications.

# Hands-on Exercise

In the exercise participants will design a PID controller to stabilize a classical benchmark system: the **inverted pendulum**. In a simulation (provided as a python notebook) they must choose which PID…