Glass Furnace¶

Hold the crown temperature of a regenerative float-glass furnace on a slowly walking setpoint by setting the fuel flow. The crown is read through a lagging thermocouple, the glass and regenerator temperatures are hidden, the firing side reverses on a fixed cycle, and the furnace responds over hours, so a few instruments have to steer a large, slow plant.

import target_gym as tg

env, params = tg.make("glass_furnace")


Action space	`Box((1,))`, all actions in [-1, 1]
Observation space	`Box((5,))`
Tracked variable(s)	crown temperature (K)
Episode length	1600 steps of 30 s (13.3 h)
Cite as	`glass_furnace-v2`
Physics	contract

Action space¶

Actions are normalised to [-1, 1] and mapped onto the plant's real actuator range inside the environment.

#	meaning	min	max
0	fuel rate	-1	1

Observation space¶

5 values in the plant's own units. The space declares no bounds (it spans the float32 range), so scale them before training. The reward scores obs[0] against obs[4].

#	meaning
0	crown temperature as the thermocouple reads it (°C); it lags the true crown temperature the reward scores
1	combustion air preheat temperature (°C)
2	fuel flow, percent of maximum
3	regenerator phase: 0 while regenerator A preheats the air, 1 while B does
4	target crown temperature (°C)

Rewards¶

See the environment's compute_reward.

Every environment in this suite scores on one contract. The reward is minus the sum of three non-negative costs, -(tracking_cost + running_cost + failure_cost). The running cost charges consumption and the failure cost charges trips out of the operating envelope. The reward is never positive, and its scale differs by orders of magnitude between plants. Some plants are priced in dollars or euros and the rest are dimensionless; the per-plant summary says which. See Reward shaping for how each cost is built.

Starting state¶

reset samples the initial condition and the target; state has 16 fields.

Episode end¶

Termination. None by default. Leaving the operating envelope trips the plant: the step that leaves it is charged the trip cost and sets info["tripped"] and info["trip_cost"], and the plant restarts as reset_env would while the episode clock keeps running. Episodic use is optional: with continuing = False the plant is lost and terminated is raised on that step instead. See Reward shaping.

Truncation. After 1600 steps.

Baselines¶

Recorded over 10 seeds of the 1600-step episode (see Baseline results). The reward is a cost, so a return closer to zero is better.

controller	mean return	cost per step
PID	-1878	1.174
MPC	-499.9	0.3125

The MPC beats the PID on 10 of 10 seeds and does not trip the plant on any of them.

Arguments¶

The scored configuration, which tg.make returns. A keyword argument changes one field, as in tg.make("glass_furnace", max_steps_in_episode=...).

parameter	value	unit
`delta_t`	30	s
`max_steps_in_episode`	1600	steps
`LHV`	5e+07	J/kg
`AFR`	17	-
`excess_air`	0.1	-
`c_p_air`	1150	J/(kg K)
`c_p_gas`	1200	J/(kg K)
`fuel_min`	0.513	kg/s
`fuel_max`	0.698	kg/s
`flame_rad_fraction`	0.55	-
`C_regen_node`	3e+07	J/K
`eps_regen_node`	0.8	-
`reversal_period`	1500	s
`reversal_dead_time`	40	s
`reversal_firing_floor`	0.05	-
`tau_thermocouple`	120	s
`charge_period`	300	s
`charge_duty`	0.3	-
`charge_mass_jitter`	0.15	-
`U_regen`	0.3	W/(m^2 K)
`A_regen`	300	m^2
`m_pull`	5.79	kg/s
`batch_yield`	0.83	-
`T_batch_in`	25	degC
`dH_fusion`	800000	J/kg
`m_batch_full`	39000	kg
`batch_shield`	0.85	-
`m_pull_noise_std`	0.4	kg/s
`C_gas`	240000	J/K
`C_crown`	2.5e+08	J/K
`C_melt`	7.8e+08	J/K
`C_work`	7.8e+08	J/K
`c_p_glass_a`	900	J/(kg K)
`c_p_glass_b`	0.35	J/(kg K^2)
`eps_rad`	0.8	-
`A_crown`	200	m^2
`A_melt`	200	m^2
`A_work`	10	m^2
`h_conv`	30	W/(m^2 K)
`U_wall`	1	W/(m^2 K)
`A_wall_crown`	200	m^2
`A_wall_melt`	200	m^2
`A_wall_work`	200	m^2
`UA_work_cooling`	3000	W/K
`T_ambient`	25	degC
`T_crown_min`	1427	degC
`tracking_band`	10	K
`precision_floor`	1	K
`T_crown_max`	1677	degC
`T_glass_min`	900	degC
`T_glass_max`	1727	degC
`fuel_cost_weight`	0	-
`target_T_crown_trim`	6	K
`initial_T_crown_offset`	4	K
`initial_T_gas_offset`	31	K
`initial_T_melt_offset`	-35	K
`initial_T_work_offset`	-151	K
`initial_T_regen_hot`	1383	degC
`initial_T_regen_cold`	544	degC
`initial_m_batch`	10753	kg
`reward_version`	2	-
`e_floor`	1	K
`e_tol`	0	K
`tracking_exponent`	2	-
`c_hold`	0.59	kg/s
`running_weight`	1	-
`failure_cost`	66978	reward
`restart_steps`	40320	steps
`rho_floor_tracking`	0.00376996	reward
`rho_floor`	0.00376996	reward