Cement Kiln¶

Hold the free lime in the clinker leaving a 3000 t/day rotary kiln with fuel and kiln speed. Free lime answers a fuel change only as material travels the kiln, half of it after about one residence time; kiln speed moves that delay itself; and eight readings stand in for 64 dynamic states. Overheating the kiln or letting it go cold trips it.

import target_gym as tg

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


Action space	`Box((2,))`, all actions in [-1, 1]
Observation space	`Box((8,))`
Tracked variable(s)	discharge free lime (%)
Episode length	700 steps of 30 s (5.83 h)
Cite as	`cement_kiln-v3`
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	-1	1
1	kiln_speed	-1	1

Observation space¶

8 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[7].

#	meaning
0	free lime at discharge (%)
1	burning-zone temperature, the hottest charge the pyrometer sees (K)
2	gas temperature at the kiln inlet (K)
3	material temperature at the back end (K)
4	`raw_meal` feed rate (kg/s), the disturbance
5	fuel, percent of its range
6	kiln speed, percent of its range
7	target free lime (%)

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 11 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. Both failure modes are irrecoverable in practice. See Reward shaping.

Truncation. After 700 steps.

Baselines¶

Recorded over 10 seeds of the 700-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	-1.275e+04	18.21
MPC	-110.7	0.1582

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("cement_kiln", max_steps_in_episode=...).

parameter	value	unit
`delta_t`	30	s
`max_steps_in_episode`	700	steps
`reward_version`	2	-
`e_floor`	0.0005	-
`e_tol`	0	-
`tracking_exponent`	2	-
`c_hold`	1.824	kg/s
`running_weight`	1	-
`failure_cost`	14112	reward
`restart_steps`	2880	steps
`rho_floor_tracking`	0.00956484	reward
`rho_floor`	0.00956484	reward
`diameter`	4	m
`length`	60	m
`slope`	0.035	-
`n_zones`	16	-
`w_bed_gas`	2.906	m
`w_wall_gas`	9.313	m
`w_wall_bed`	3.253	m
`refractory_thickness`	0.2	m
`rho_refractory`	2200	kg/m^3
`cp_refractory`	900	J/(kg K)
`U_shell`	4	W/(m^2 K)
`raw_meal_nominal`	53.82	kg/s
`caco3_fraction`	0.79	-
`calcination_upstream`	0.92	-
`cp_solid`	1000	J/(kg K)
`cp_gas`	1150	J/(kg K)
`bulk_density`	1400	kg/m^3
`angle_of_repose`	35	deg
`h_calcination`	1.78e+06	J/kg
`h_clinkerisation`	420000	J/kg
`A_calcination`	151990	1/s
`E_calcination`	170000	J/mol
`A_clinker`	4.7308e+06	1/s
`E_clinker`	280000	J/mol
`fuel_lhv`	2.6e+07	J/kg
`air_fuel_ratio`	10.5	-
`excess_air`	1.15	-
`flame_length`	15	m
`emissivity_gas`	0.25	-
`h_convective`	30	W/(m^2 K)
`h_wall_bed`	500	W/(m^2 K)
`T_feed`	1073	K
`T_secondary_air`	1373	K
`T_ambient`	300	K
`fuel_min`	1.2	kg/s
`precision_floor`	0.0005	-
`fuel_max`	2.4	kg/s
`rpm_min`	2	rpm
`rpm_max`	4.5	rpm
`fuel_nominal`	1.78	kg/s
`rpm_nominal`	3	rpm
`feed_noise_std`	2	kg/s
`lime_band`	0.006	-
`T_bz_max`	1900	K
`T_bz_min`	1620	K
`lime_max`	0.05	-
`fuel_weight`	0	-