{"artifact_id":"L1-434","layer":"L1","title":"PID Controller Tuning","domain":"Control Theory","sub_domain":"Classical control","physics_fingerprint":{"L_DAG":2.0,"title":"PID Controller Tuning","domain":"Control Theory","carrier":"N/A","primitives":["N.pointwise","S.zn.tuning_rule","O.iae.integral_criterion"],"sub_domain":"Classical control","noise_model":"gaussian","problem_class":"parameter_estimation","solution_space":"PID_parameter_vector","difficulty_delta":3,"integration_axis":"time","sensing_mechanism":"closed_loop_step_response"},"observable_profile":{"metric":"IAE_integral_absolute_error","regime":"Existence of the recovered PID_parameter_vector is guaranteed within the declared Omega bounds. Uniqueness holds on the measurement-supported subspace; out-of-support modes are controlled by declared priors. Stability is conditionally stable (kappa_eff ~= 10); plant_gain_variation dominates the stability cliff; the remaining mismatch parameters contribute higher-order bias terms. Gaussian sets the irreducible data-fidelity floor.","secondary":"overshoot_percent"},"size_tiers":{"center_spec":{"omega":{"plant_K":1.0,"plant_L":0.1,"plant_tau":1.0,"desired_PM_deg":45},"input_format":"measurement_only","problem_class":"parameter_estimation","forward_operator":"closed_loop_step_response","epsilon_fn_center":"0.3 IAE_integral_absolute_error"},"omega_bounds":{"plant_K":[0.1,10.0],"plant_L":[0.001,10.0],"plant_tau":[0.01,100.0],"desired_PM_deg":[30,70]},"epsilon_bounds":{"IAE_integral_absolute_error":[0.05,2.0]},"allowed_problem_classes":["parameter_estimation"],"allowed_omega_dimensions":["plant_K","plant_tau","plant_L","desired_PM_deg"],"allowed_forward_operators":["closed_loop_step_response"]},"hardness_fn":{"type":"epsilon_fn","delta":3,"kappa":200,"metric":"IAE_integral_absolute_error"},"initiator_dataset":[{"name":"primary","weight":1.0,"ipfs_cid":null,"license_hash":null}],"status":"testnet","staked_pwm":0.0,"chain_hash":"0x4c6477238f4388535011959bfca70d1a63e1ca808d7addb600173e33dce8bb79","chain_tx_hash":"0x4f8b46faf1b793eb6437471a64e3238a1392f3e209b75afea7b58207e93f0525","chain_block":41555257}