Distillation

Hold both product purities of a 40-tray binary distillation column (Skogestad's Column A) with reflux and boilup. The two purities move together far more easily than apart, which makes the plant ill-conditioned. Only the two products are analysed, plus one tray temperature: the tray compositions that hold the column's memory, and the drifting feed composition, are hidden. The reward scores both purities.

import target_gym as tg

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

Action space	Box((2,)), all actions in [-1, 1]
Observation space	Box((7,))
Tracked variable(s)	yD (mole fraction), xB (mole fraction)
Episode length	200 steps of 60 s (3.33 h)
Cite as	distillation-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	L_raw	-1	1
1	V_raw	-1	1

Observation space

7 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], obs[1] against obs[5].

#	meaning
0	yD, light-component mole fraction in the distillate (top product)
1	xB, light-component mole fraction in the bottoms
2	reflux flow, fraction of its range (0 to 1)
3	boilup, fraction of its range (0 to 1)
4	target yD
5	target xB
6	T_15, stage 15's temperature (K)

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 7 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 200 steps.

Baselines

Recorded over 10 seeds of the 200-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	-8.299e+04	415
MPC	-2.467e+04	123.4

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("distillation", max_steps_in_episode=...).

parameter	value	unit
delta_t	1	min
max_steps_in_episode	200	steps
alpha	1.5	-
M_tray	0.5	kmol
M_drum	0.5	kmol
F	1	kmol/min
zF_nominal	0.5	-
qF	1	-
zF_noise_std	0.03	-
zF_min	0.4	-
zF_max	0.6	-
L_min	2.3	kmol/min
L_max	3.1	kmol/min
V_min	2.8	kmol/min
V_max	3.6	kmol/min
D_min	0.1	kmol/min
D_max	0.9	kmol/min
yD_floor	0.9	-
xB_ceiling	0.1	-
tracking_band	0.02	-
precision_floor	0.0001	-
boilup_cost_weight	0	-
time_unit_seconds	60	s
reward_version	2	-
e_floor_top	0.0001	-
e_floor_bottom	0.0001	-
e_tol	0	-
tracking_exponent	2	-
c_hold	3.282	kmol/min
running_weight	1	-
failure_cost	3.61e+06	reward
restart_steps	240	steps
rho_floor_tracking	8.53057e-05	reward
rho_floor	8.53057e-05	reward