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Introduction

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Modeling Prediction

Modeling Prediction

Modeling Framework for Predictive Systems

Definitions

Architecture of digital model

  • If the digital model architecture involves real sensors as system inputs for the integration of observers or discrepancy models, these must first be disabled
  • The predictive architecture works exclusively in open-loop

Definition of the sampling time of the digital model

  • Ts = Sampling time of the digital model

Definition of the cycle time of the microcontroller

  • Tcycle = Cycle time of the microcontroller

Model Classification

Condition
Classification
Behavior
Ts = Tcycle
Real-time model
System operates in sync with real-world time
Ts > Tcycle
Predictive model
System predicts ahead of real-world time

Mathematical Steps for Determining Model Discretization

Objective: Calculate the correct discretization time (Ts) for the digital model given:

  1. Tcycle = Cycle time of the task where the prediction model runs
  2. Tpred = Prediction time (how far into the future the model is estimating)
  3. Tinter = Time interval at which you will read/access the model prediction

Key Variables

  • Tcycle = Cycle time of the microcontroller/task
  • Ts = Discretization time of the digital model (what we're solving for)
  • Tpred = Desired prediction horizon (e.g., 60 seconds into the future)
  • Tinter = Interval at which predictions are read/accessed

Formula to calculate Ts:

Ts = Tcycle × (Tpred / Tinter)

Example

  • If Tcycle = 0.001s (1ms)
  • Tpred = 60s (want to predict 60 seconds into the future)
  • Tinter = 2s (read prediction results every 2 seconds)
  • Then: Ts = 0.001s × (60s / 2s) = 0.03s

This means the model should use a discretization time of 0.03s to achieve the desired prediction horizon when operating within the given task cycle and reading interval. You can better visualize the concept in the figure below.

image

This predictive capability is crucial for thermal management systems. By knowing the future temperature trend, control systems can take proactive measures to prevent overheating, optimize cooling resources, and maintain optimal operating conditions well before critical thresholds are reached.

Speed Factor

  • The ratio Ts/Tcycle determines if the model is real-time or predictive
  • For example: if Ts = 0.01s and Tcycle = 0.001s
  • Then the model is 10× faster than real-time
  • In 1 second of real-time computing, we predict 10 seconds ahead

Note: This framework helps determine the appropriate discretization time to achieve desired prediction horizons while ensuring the system operates correctly within your task's timing constraints.