State-space model

Classic loop design treats a system as one input and one output. A state-space model instead tracks the internal quantities that define the system at any instant (positions, velocities, temperatures, currents) and writes equations for how inputs change them and how sensors observe them. It handles multiple inputs and outputs naturally and is the foundation for state feedback, observers, Kalman filters and model predictive control.

Why it matters for a product: when actuators interact (two heaters in one chamber, the axes of a gimbal, a vehicle's steering and speed), separate single loops can fight each other. A model-based design accounts for the coupling. The cost is that you need a credible model and more engineering time; for simple, decoupled loops a well-tuned PID is usually the better trade.