# Atmel Software Framework

oven_plant.c File Reference

Class B Oven Simulation plant.

#include <asf.h>
#include "oven.h"
#include "oven_ui.h"
#include "oven_plant.h"

## Macros

Physical properties of the model
#define C_POT   20.0
Pot heat capacity. More...

#define C_PLATE   2.0
Plate heat capacity. More...

#define K_POT   7
Pot heat conductivity. More...

#define K_PLATE   2
Plate heat conductivity. More...

#define ENV_TEMP   25
Environment temperature. More...

## Functions

float oven_plant_get_state_temp (uint8_t no)
Read the internal simulation states. More...

void oven_plant_init (void)
Initialize the oven's physical state. More...

void oven_plant_sim_step (enum pot_t pot)
Perform a simulation step. More...

Internal functions
Read the period of the frequency signal capture. More...

static float oven_plant_calculate_u_from_period (uint16_t p)
Map the signal period to a power level for the simulation plant. More...

## Variables

static float state [2] = {20 * C_PLATE, 20 * C_POT}
State variables for the simulation: Plate and Pot temperature. More...

 #define C_PLATE   2.0

Plate heat capacity.

Referenced by oven_plant_get_state_temp(), oven_plant_init(), and oven_plant_sim_step().

 #define C_POT   20.0

Pot heat capacity.

Referenced by oven_plant_get_state_temp(), oven_plant_init(), and oven_plant_sim_step().

 #define ENV_TEMP   25

Environment temperature.

Referenced by oven_plant_sim_step().

 #define K_PLATE   2

Plate heat conductivity.

Referenced by oven_plant_sim_step().

 #define K_POT   7

Pot heat conductivity.

Referenced by oven_plant_sim_step().

 static float oven_plant_calculate_u_from_period ( uint16_t p )
static

Map the signal period to a power level for the simulation plant.

In effect, this function acts as the induction coil in the oven.

Its return value reflects wattage as used in the controller and the user interface.

Parameters
 p Period of frequency signal, from oven_plant_read_signal_period()
Returns
Float value mapping captured signal period to energy

Referenced by oven_plant_sim_step().

 float oven_plant_get_state_temp ( uint8_t no )

Parameters
 no The state variable to get, 0 for plate and 1 for pot
Returns
Temperature of the selected state variable

References C_PLATE, C_POT, and state.

Referenced by main_execute_simulation_step().

 void oven_plant_init ( void )

Initialize the oven's physical state.

References C_PLATE, C_POT, and state.

Referenced by main().

 static uint16_t oven_plant_read_signal_period ( void )
static

Read the period of the frequency signal capture.

Returns
A value representing the power with which the plate element is actuated.

Referenced by oven_plant_sim_step().

 void oven_plant_sim_step ( enum pot_t pot )

Perform a simulation step.

This function first reads the received frequency signal representing the power level the plate element is actuated with, then performs a simulation step and outputs the simulated temperature of the plate element as an analog value via DACB on the pin marked ADC2.

The simulation plant is a discretized version of the continuous system: $$\dot{x} = \mathbf{F}*\vec{x} + \mathbf{B}*\vec{u}$$, where:

$\begin{array}{c} \mathbf{F} = \left[ \begin{array}{c c} \frac{-1}{C_\textnormal{plate} * K_\textnormal{plate}} & 0 \\ \\ 0 & \frac{-1}{C_\textnormal{pot} * K_\textnormal{pot}} \end{array} \right] \\ \vec{x} = \left[ \begin{array}{c} E_\textnormal{plate} \\ \\ E_\textnormal{pot} \end{array} \right] \\ \mathbf{B} = \left[ \begin{array}{c c} 1 & 0 \\ \\ 0 & 1 \end{array} \right] \\ \vec{u} = \left[ \begin{array}{c} \frac{T_\textnormal{environment}}{K_\textnormal{plate}} \\ \\ \frac{T_\textnormal{environment}}{K_\textnormal{pot}} \end{array} \right] \end{array} \\$

in the case when the pot is OFF the plate.

This corresponds to the plate and the pot cooling separately by Newton's law of cooling because no power can be induced when the pot is not on the plate.

When the pot is ON the stove, the system is similar, but F is modified by adding heat transfer between the plate and the contents of the pot, and disregarding heat loss from the plate to the environment. Likewise u is modified by adding energy induction into the bottom of the pot, simplified here as being the same point as the plate:

$\begin{array}{c} \mathbf{F} = \left[ \begin{array}{c c} \frac{-1}{C_\textnormal{plate}* K_\textnormal{plate}} & \frac{1}{C_\textnormal{pot}* K_\textnormal{plate}} \\ \\ \frac{1}{C_\textnormal{plate}* K_\textnormal{plate}} & \frac{-1}{C_\textnormal{pot}* K_\textnormal{plate}} - \frac{1}{C_\textnormal{pot} * K_\textnormal{pot}} \end{array} \right] \\ \vec{u} = \left[ \begin{array}{c} \delta E_\textnormal{induced} \\ \\ \frac{T_\textnormal{environment}}{K_\textnormal{pot}} \end{array} \right] \end{array}$

Parameters
 pot Whether the pot is on or off the plate.

Referenced by main_execute_simulation_step().

 float state[2] = {20 * C_PLATE, 20 * C_POT}
static

State variables for the simulation: Plate and Pot temperature.