Heater Management Software

Description

This model implements a PID (Proportional-Integral-Derivative) feedback controller for Heaters in Thermal Management Systems. Given the error between a desired target temperature and the current temperature, the controller determines the required heater power output to minimize this error. The controller is tuned based on a set of gains ( $K$ , $K_{i}$ , $P$ ) and includes power limiting capabilities.

Example Use Cases

Closed Loop Thermal Control: Act as a controller for a heater in a thermal system, adjusting component temperature towards its ideal operating point via heater control in the same thermal network.
Analysis of Thermal and Electrical Systems Management: Model the dynamic impacts that heaters can have on electrical resources (e.g., battery charge during eclipse) within the simulation.

Module Implementation

This model assumes that the thermal dynamics of a controlled system can be managed through a PID control law. The temperature error for the current timestep is defined as:

e (t) = T_{t a r g e t} - T_{c u rre n t}

where $T_{t a r g e t}$ is the desired temperature and $T_{c u rre n t}$ is the measured temperature. The PID control law implemented determines the target heater power output $P_{h e a t er}$ via:

P_{h e a t er} = K \cdot e (t) + K_{i} \int_{t_{0}}^{t} e (τ) d τ + P \cdot \frac{d e ( t )}{d t}

Where:

$K$ is the proportional gain
$K_{i}$ is the integral gain
$P$ is the derivative gain
$e (t)$ is the temperature error at time $t$
$\int_{t_{0}}^{t} e (τ) d τ$ is the integral of temperature error over time
$\frac{d e ( t )}{d t}$ is the derivative of temperature error

The final power output is constrained to the operational limits set for the Heater Management Software:

P_{h e a t er} = clamp (P_{h e a t er}, P_{min}, P_{ma x})

where $P_{min}$ and $P_{ma x}$ are the minimum and maximum allowable heater power levels.

Integral Windup Protection

To prevent integral windup when the controller output saturates, the model implements two levels of protection:

Integral Limiting: The integral term $I$ is bounded by: $$

|I| \leq \frac{P_{max} - P_{min}}{|K_i|}

$$ 2. Saturation Protection: When the output is saturated, the integral accumulation is adjusted to prevent further windup: - If $P_{h e a t er} = P_{ma x}$ and $e (t) > 0$ : reduce integral accumulation - If $P_{h e a t er} = P_{min}$ and $e (t) < 0$ : reduce integral accumulation

Discrete Implementation

In the discrete-time implementation, the control law becomes:

P_{h e a t er} [k] = K \cdot e [k] + K_{i} \cdot i = 0 \sum k e [i] \cdot Δ t + P \cdot \frac{e [ k ] - e [ k - 1 ]}{Δ t}

where $k$ is the discrete time index and $Δ t$ is the simulation time step.

Assumptions/Limitations

A single instance of the Heater Management Software can only manage one heater towards one target temperature.
The controller operates in discrete time steps and requires proper tuning of PID gains for optimal performance.
Thermal system dynamics are not explicitly modelled; the controller assumes the heater is apart of a Thermal Network where the heater can influence the controlled temperature.

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