Unstable CSTR

Hold the concentration of A in a jacketed exothermic reactor on its open-loop unstable middle steady state, commanding the coolant through a lagging jacket while the feed temperature drifts unmeasured. Left alone the reactor runs away within tens of seconds, and the target steps five times per episode, so every move crosses the unstable region under control. A trip costs an hour of restart.

import target_gym as tg

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

Action space	Box((1,)), all actions in [-1, 1]
Observation space	Box((4,))
Tracked variable(s)	C_a (mol/L)
Episode length	1200 steps of 3 s (60 min)
Cite as	unstable_cstr-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	coolant command	-1	1

Observation space

4 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[3].

#	meaning
0	C_a, concentration of A (mol/L)
1	T, reactor temperature (K)
2	T_j, jacket temperature (K)
3	target C_a, the current block's level (mol/L)

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 1200 steps.

Baselines

Recorded over 10 seeds of the 1200-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	-7.312e+07	6.093e+04
MPC	-4.74e+06	3950

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("unstable_cstr", max_steps_in_episode=...).

parameter	value	unit
delta_t	0.05	min
max_steps_in_episode	1200	steps
q	100	L/min
V	100	L
rho	1000	g/L
C	0.239	J/(g*K)
deltaHr	-50000	J/mol
EA_over_R	8750	K
k0	7.2e+10	1/min
UA	50000	J/(min*K)
Ti	350	K
Caf	1	mol/L
precision_floor	0.0001	mol/L
time_unit_seconds	60	s
T_c_min	290	K
T_c_max	310	K
tau_j	0.1	min
T_trip	365	K
T_valid_min	250	K
Ti_sigma	2	K
Ti_tau	10	min
Ti_dev_reset_clip	3	-
block_steps	200	steps
initial_CA_offset	0.01	mol/L
initial_T_offset	1.5	K
reward_version	2	-
e_floor	0.0001	mol/L
e_tol	0	mol/L
tracking_exponent	2	-
CA_error_max	0.55	mol/L
failure_cost	6.05e+07	reward
restart_steps	1200	steps
rho_floor_tracking	0.00395641	reward
rho_floor	0.00395641	reward