pH neutralisation

Hold the pH of a stirred tank, where strong acid meets strong base in a carbonate buffer, at a target by setting the base flow. The titration curve makes the process gain swing by more than an order of magnitude across the range, and the buffer flow that moves the curve drifts unmeasured, so the same pH reading can call for very different moves.

import target_gym as tg

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

Action space	Box((1,)), all actions in [-1, 1]
Observation space	Box((3,))
Tracked variable(s)	pH
Episode length	300 steps of 5 s (25 min)
Cite as	ph_neutralization-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	base flow	-1	1

Observation space

3 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[2].

#	meaning
0	pH
1	base flow valve, percent of its range
2	target pH

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 300 steps.

Baselines

Recorded over 10 seeds of the 300-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	-4.48e+04	149.3
MPC	-1594	5.313

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("ph_neutralization", max_steps_in_episode=...).

parameter	value	unit
delta_t	5	s
max_steps_in_episode	300	steps
V	2900	mL
q1	16.6	mL/s
Wa1	0.003	mol/L
Wb1	0	mol/L
q2_nominal	0.55	mL/s
q2_noise_std	0.35	mL/s
q2_min	0	mL/s
q2_max	2.5	mL/s
Wa2	-0.03	mol/L
Wb2	0.03	mol/L
q3_min	10	mL/s
q3_max	22	mL/s
Wa3	-0.00305	mol/L
Wb3	5e-05	mol/L
pK1	6.35	-
pK2	10.25	-
pH_min	2	pH
precision_floor	0.01	pH
pH_max	12	pH
tracking_band	1	pH
reagent_cost_weight	0	-
reward_version	2	-
e_floor	0.01	pH
e_tol	0	pH
tracking_exponent	2	-
c_hold	16.24	mL/s
running_weight	1	-
failure_cost	3.1e+06	reward
restart_steps	720	steps
rho_floor_tracking	0.0169	reward
rho_floor	0.0169	reward