Bonus Day 8: First-Order Response Intuition — Why Model 4 Feels Like Real HVAC скачать в хорошем качестве

Bonus Day 8: First-Order Response Intuition — Why Model 4 Feels Like Real HVAC

In this bonus lesson, we shift gears from linear algebra and regression into physics intuition. Today is all about first-order response — the core idea behind PNNL Model 4. Instead of thinking in “degrees per minute,” we start thinking in percentages. A first-order model says something very simple but very powerful: every time step, the temperature error shrinks by the same ratio. That’s it. If you’re 8°F away from setpoint, you make big progress early. If you’re 1°F away, progress slows down. This perfectly matches how real HVAC systems behave as they approach setpoint. In this video, we build the mental model slowly and clearly. No equations up front. No libraries. Just intuition. We cover: • What “error” really means in heating and cooling • Why first-order response is about percentage improvement, not fixed slope • Why HVAC systems slow down near setpoint • What the decay factor c actually represents • How this directly maps to Model 4 in the PNNL paper • Why this model often feels more realistic than linear or quadratic models We also walk through a tiny Python example (no NumPy) to simulate how error shrinks minute by minute, so you can literally watch the behavior happen. This lesson is foundational. Once first-order response clicks, the logarithmic time equation used in Model 4 suddenly makes sense instead of feeling abstract. Lesson reference https://github.com/bbartling/hvac-opt... Vibe Coding (Niagara Program Objects) https://github.com/bbartling/niagara4... HVAC Optimal Start Math Playground https://github.com/bbartling/hvac-opt... #hvac #optimalstart #buildingautomation #niagaraframework #smartbuildings #hvacmath #FirstOrderSystems #controlsystems #engineeringeducation #vibecoding #smarthvac