graph LR idea_07a8c39b_efcf_4827_8612_9cea99444047["Ziegler-Nichols Open-Loop (Reaction Curve) Rules"] idea_086f2598_38a2_428c_b06a_3ae204be88ac["Proportional Band vs Proportional Gain"] idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed["Choosing P, PI, PD or PID for a Loop"] idea_0a290845_fa58_4ff3_b9d6_5207691684e9["Derivative Kick"] idea_12bbfda1_b102_4b82_8208_723cad7237c7["Finding the Ultimate Gain and Period with a Closed-Loop Test"] idea_1521ba9b_c32a_4382_aefa_524a11912fec["Feedforward Control"] idea_284a60a7_df13_4b59_b97c_4ea75b7e8352["Relay Auto-Tuning"] idea_28c7370e_5572_4b74_be11_e7ddaa806483["Manual PID Tuning Heuristics"] idea_2a6ff42a_edac_4df3_a190_18a30c35c699["Output Deadband and Hysteresis"] idea_2db1cffb_8650_48e2_8d00_dc6b5f6d7544["Fine-Tuning After a Tuning Formula"] idea_3076f2d3_9ecd_4e40_974b_6624b9d13758["Tune the Inner Loop First in Cascade Control"] idea_331e62b3_94f6_4873_8cbc_70c7c026fe17["Setpoint"] idea_3b05d99d_1643_4f91_b8e9_cb1302a5cbd8["Setpoint Weighting"] idea_3f6d71dc_8fcb_4190_8fbc_ff5f73c74d17["Error Signal"] idea_40cf522c_2c48_49d1_91db_1c655e09d08a["Tuning a PID for an Integrating Process (Level Control)"] idea_4531fa68_5cf1_4501_b723_be77496539e2["Derivative Filtering"] idea_48498729_585e_48d3_81cd_0cd830a3d0c5["Read Gain, Time Constant and Dead Time from a Step Response Plot"] idea_495f5a8e_2bad_46a4_bf26_63001753ff0b["Derivative Control Action"] idea_4a6f14b4_afab_400a_baa7_8f82d9812c0d["Process Variable"] idea_4a922882_de8d_49fa_b579_f6d33dfcaba1["Steady-State Error"] idea_5c0da3c1_f2f5_4517_b819_a94c68e57132["Cascade Control"] idea_5e4689c8_5f83_441c_8cc1_815163ea7c31["Aggressive vs Robust Tuning Trade-off"] idea_5ecc2ded_b545_4b3f_acca_e011be7524f5["Filtering a Noisy Measurement Before the PID"] idea_622e1fe7_3895_4bf1_b527_6f82e0303d67["Dead Time to Time Constant Ratio Decides Tuning Difficulty"] idea_6f890e67_f1ef_45ea_bc18_788a04066c24["Integral Error Indices (IAE, ISE, ITAE)"] idea_6f9c77c1_f418_4beb_afa9_edee2f0f25a5["Bumpless Transfer Between Manual and Auto"] idea_70147834_410f_4113_bd9b_55f3ddade0fb["Step Response Performance Metrics"] idea_70ec24b5_e526_47aa_b11b_ea077ba6b0a6["Closed-Loop Stability"] idea_78ff0c1d_27e2_439c_9f13_5116dfa4f6f3["Choosing the PID Sample Time"] idea_8140b0ab_c250_43b5_99f0_12618424d7f8["Self-Regulating vs Integrating Process"] idea_83904bc3_82e1_4a62_b90e_d499c8ae1cbe["When Auto-Tuning Gives Bad Gains"] idea_86c79c12_d3fe_4f40_b0cd_e85f400a4e81["Cohen-Coon Tuning Rules from a Step Test"] idea_8d4d0638_a99c_485e_bff1_57a3c4a3d1ca["Valve Stiction and Backlash"] idea_900e5b78_c677_467e_914e_e479e9b984cf["Diagnose a Loop Oscillation from Its Period"] idea_92532848_fdc3_442b_b679_0d25b4fc317e["Proportional Gain"] idea_98874bc5_3546_4d4d_8e84_032659d30a4e["Process Nonlinearity and Why One Tuning Doesn't Fit All Loads"] idea_9b03a115_3d77_4d7f_b749_ffaa292745eb["Proportional Control Action"] idea_9f185acd_0cc6_4613_9dd9_708d6f985f6a["Manual Mode vs Automatic Mode on a Controller"] idea_a0a5db5b_d47c_4856_8d7d_a1819db6934e["Negative Feedback Loop"] idea_a56f7cd9_2481_4a05_affd_03f119650d9a["Tuning a PID Temperature Control Loop"] idea_a5933868_ef63_405c_9172_3a4a2b65152e["Tuning a Drone PID Rate Loop"] idea_a8d331d6_ff89_4207_abbe_07efae6b84bb["Noisy Controller Output from Too Much Derivative"] idea_af908d90_220b_47a7_a4d0_b2ec0d526edb["Actuator Saturation"] idea_b0f1170b_0d88_4fc4_b169_07bc731092e7["SIMC Tuning Rules for Slow Processes"] idea_b0f8ebe6_684b_44d9_844d_739b9903af17["Integral Windup"] idea_b1596d14_638b_4636_b509_6d66598b2803["Controller Output and the Manipulated Variable"] idea_cd9d6e9a_3ec0_432f_aa3f_9c7fa1460432["Ultimate Gain"] idea_d0443aed_062d_4086_a346_ed007d7aa76b["Direct Acting vs Reverse Acting Controller"] idea_d5265d02_1ac4_4546_88d0_479aa8d39edd["What Good PID Tuning Looks Like"] idea_e0e676aa_bd22_4dad_9528_301ed295d5f3["Measurement Noise"] idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0["Integral Anti-Windup"] idea_ea7310ee_03db_4133_8522_0c78b49a3ffc["Tuning a DC Motor Speed Loop with PID"] idea_ec720b2a_b4d8_405b_a85d_014885863ef3["Integral Control Action"] idea_f141ad73_e843_43cb_9618_422eed0210ae["Lambda Tuning (IMC) Picks the Closed-Loop Time Constant"] idea_f1477f0b_fd7d_49d2_8fef_a100b31c0e41["Disturbance Rejection"] idea_f47af757_3897_4a46_8087_0a8e6e02999e["Gain Scheduling Across Operating Points"] idea_70147834_410f_4113_bd9b_55f3ddade0fb --> idea_6f890e67_f1ef_45ea_bc18_788a04066c24 idea_495f5a8e_2bad_46a4_bf26_63001753ff0b --> idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed idea_f141ad73_e843_43cb_9618_422eed0210ae --> idea_b0f1170b_0d88_4fc4_b169_07bc731092e7 idea_4a6f14b4_afab_400a_baa7_8f82d9812c0d --> idea_d5265d02_1ac4_4546_88d0_479aa8d39edd idea_3b05d99d_1643_4f91_b8e9_cb1302a5cbd8 --> idea_a56f7cd9_2481_4a05_affd_03f119650d9a idea_2db1cffb_8650_48e2_8d00_dc6b5f6d7544 --> idea_3076f2d3_9ecd_4e40_974b_6624b9d13758 idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0 --> idea_a56f7cd9_2481_4a05_affd_03f119650d9a idea_3f6d71dc_8fcb_4190_8fbc_ff5f73c74d17 --> idea_6f890e67_f1ef_45ea_bc18_788a04066c24 idea_622e1fe7_3895_4bf1_b527_6f82e0303d67 --> idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed idea_9f185acd_0cc6_4613_9dd9_708d6f985f6a --> idea_6f9c77c1_f418_4beb_afa9_edee2f0f25a5 idea_5e4689c8_5f83_441c_8cc1_815163ea7c31 --> idea_f47af757_3897_4a46_8087_0a8e6e02999e idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0 --> idea_6f9c77c1_f418_4beb_afa9_edee2f0f25a5 idea_b0f8ebe6_684b_44d9_844d_739b9903af17 --> idea_6f9c77c1_f418_4beb_afa9_edee2f0f25a5 idea_e0e676aa_bd22_4dad_9528_301ed295d5f3 --> idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed idea_28c7370e_5572_4b74_be11_e7ddaa806483 --> idea_a56f7cd9_2481_4a05_affd_03f119650d9a idea_e0e676aa_bd22_4dad_9528_301ed295d5f3 --> idea_83904bc3_82e1_4a62_b90e_d499c8ae1cbe idea_8d4d0638_a99c_485e_bff1_57a3c4a3d1ca --> idea_2a6ff42a_edac_4df3_a190_18a30c35c699 idea_4a922882_de8d_49fa_b579_f6d33dfcaba1 --> idea_d5265d02_1ac4_4546_88d0_479aa8d39edd idea_622e1fe7_3895_4bf1_b527_6f82e0303d67 --> idea_a56f7cd9_2481_4a05_affd_03f119650d9a idea_5c0da3c1_f2f5_4517_b819_a94c68e57132 --> idea_3076f2d3_9ecd_4e40_974b_6624b9d13758 idea_1521ba9b_c32a_4382_aefa_524a11912fec --> idea_ea7310ee_03db_4133_8522_0c78b49a3ffc idea_5ecc2ded_b545_4b3f_acca_e011be7524f5 --> idea_ea7310ee_03db_4133_8522_0c78b49a3ffc idea_0a290845_fa58_4ff3_b9d6_5207691684e9 --> idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed idea_cd9d6e9a_3ec0_432f_aa3f_9c7fa1460432 --> idea_12bbfda1_b102_4b82_8208_723cad7237c7 idea_f141ad73_e843_43cb_9618_422eed0210ae --> idea_40cf522c_2c48_49d1_91db_1c655e09d08a idea_f1477f0b_fd7d_49d2_8fef_a100b31c0e41 --> idea_d5265d02_1ac4_4546_88d0_479aa8d39edd idea_70ec24b5_e526_47aa_b11b_ea077ba6b0a6 --> idea_12bbfda1_b102_4b82_8208_723cad7237c7 idea_331e62b3_94f6_4873_8cbc_70c7c026fe17 --> idea_d5265d02_1ac4_4546_88d0_479aa8d39edd idea_48498729_585e_48d3_81cd_0cd830a3d0c5 --> idea_86c79c12_d3fe_4f40_b0cd_e85f400a4e81 idea_98874bc5_3546_4d4d_8e84_032659d30a4e --> idea_f47af757_3897_4a46_8087_0a8e6e02999e idea_28c7370e_5572_4b74_be11_e7ddaa806483 --> idea_a5933868_ef63_405c_9172_3a4a2b65152e idea_a8d331d6_ff89_4207_abbe_07efae6b84bb --> idea_a5933868_ef63_405c_9172_3a4a2b65152e idea_92532848_fdc3_442b_b679_0d25b4fc317e --> idea_086f2598_38a2_428c_b06a_3ae204be88ac idea_9b03a115_3d77_4d7f_b749_ffaa292745eb --> idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed idea_a0a5db5b_d47c_4856_8d7d_a1819db6934e --> idea_d0443aed_062d_4086_a346_ed007d7aa76b idea_b1596d14_638b_4636_b509_6d66598b2803 --> idea_2a6ff42a_edac_4df3_a190_18a30c35c699 idea_b1596d14_638b_4636_b509_6d66598b2803 --> idea_d0443aed_062d_4086_a346_ed007d7aa76b idea_8140b0ab_c250_43b5_99f0_12618424d7f8 --> idea_40cf522c_2c48_49d1_91db_1c655e09d08a idea_a0a5db5b_d47c_4856_8d7d_a1819db6934e --> idea_d5265d02_1ac4_4546_88d0_479aa8d39edd idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0 --> idea_ea7310ee_03db_4133_8522_0c78b49a3ffc idea_900e5b78_c677_467e_914e_e479e9b984cf --> idea_12bbfda1_b102_4b82_8208_723cad7237c7 idea_4531fa68_5cf1_4501_b723_be77496539e2 --> idea_a5933868_ef63_405c_9172_3a4a2b65152e idea_8140b0ab_c250_43b5_99f0_12618424d7f8 --> idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed idea_8140b0ab_c250_43b5_99f0_12618424d7f8 --> idea_83904bc3_82e1_4a62_b90e_d499c8ae1cbe idea_78ff0c1d_27e2_439c_9f13_5116dfa4f6f3 --> idea_ea7310ee_03db_4133_8522_0c78b49a3ffc idea_28c7370e_5572_4b74_be11_e7ddaa806483 --> idea_ea7310ee_03db_4133_8522_0c78b49a3ffc idea_8d4d0638_a99c_485e_bff1_57a3c4a3d1ca --> idea_83904bc3_82e1_4a62_b90e_d499c8ae1cbe idea_af908d90_220b_47a7_a4d0_b2ec0d526edb --> idea_a56f7cd9_2481_4a05_affd_03f119650d9a idea_ec720b2a_b4d8_405b_a85d_014885863ef3 --> idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed idea_07a8c39b_efcf_4827_8612_9cea99444047 --> idea_86c79c12_d3fe_4f40_b0cd_e85f400a4e81 idea_284a60a7_df13_4b59_b97c_4ea75b7e8352 --> idea_83904bc3_82e1_4a62_b90e_d499c8ae1cbe style idea_92532848_fdc3_442b_b679_0d25b4fc317e fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_4531fa68_5cf1_4501_b723_be77496539e2 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_5c0da3c1_f2f5_4517_b819_a94c68e57132 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_1521ba9b_c32a_4382_aefa_524a11912fec fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_5ecc2ded_b545_4b3f_acca_e011be7524f5 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_ec720b2a_b4d8_405b_a85d_014885863ef3 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_622e1fe7_3895_4bf1_b527_6f82e0303d67 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_f47af757_3897_4a46_8087_0a8e6e02999e fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_b0f8ebe6_684b_44d9_844d_739b9903af17 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_f1477f0b_fd7d_49d2_8fef_a100b31c0e41 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_9b03a115_3d77_4d7f_b749_ffaa292745eb fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_086f2598_38a2_428c_b06a_3ae204be88ac fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_70ec24b5_e526_47aa_b11b_ea077ba6b0a6 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_6f9c77c1_f418_4beb_afa9_edee2f0f25a5 fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_a8d331d6_ff89_4207_abbe_07efae6b84bb fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_40cf522c_2c48_49d1_91db_1c655e09d08a fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_284a60a7_df13_4b59_b97c_4ea75b7e8352 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_a0a5db5b_d47c_4856_8d7d_a1819db6934e fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_5e4689c8_5f83_441c_8cc1_815163ea7c31 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_9f185acd_0cc6_4613_9dd9_708d6f985f6a fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_095d81a0_0a7b_4c08_93f5_e3c0097650ed fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_28c7370e_5572_4b74_be11_e7ddaa806483 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_b0f1170b_0d88_4fc4_b169_07bc731092e7 fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_a5933868_ef63_405c_9172_3a4a2b65152e fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_2a6ff42a_edac_4df3_a190_18a30c35c699 fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_495f5a8e_2bad_46a4_bf26_63001753ff0b fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_af908d90_220b_47a7_a4d0_b2ec0d526edb fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_d5265d02_1ac4_4546_88d0_479aa8d39edd fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_f141ad73_e843_43cb_9618_422eed0210ae fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_2db1cffb_8650_48e2_8d00_dc6b5f6d7544 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_3076f2d3_9ecd_4e40_974b_6624b9d13758 fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_48498729_585e_48d3_81cd_0cd830a3d0c5 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_3b05d99d_1643_4f91_b8e9_cb1302a5cbd8 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_4a6f14b4_afab_400a_baa7_8f82d9812c0d fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_07a8c39b_efcf_4827_8612_9cea99444047 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_4a922882_de8d_49fa_b579_f6d33dfcaba1 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_0a290845_fa58_4ff3_b9d6_5207691684e9 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_6f890e67_f1ef_45ea_bc18_788a04066c24 fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_e0e676aa_bd22_4dad_9528_301ed295d5f3 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_86c79c12_d3fe_4f40_b0cd_e85f400a4e81 fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_3f6d71dc_8fcb_4190_8fbc_ff5f73c74d17 fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_70147834_410f_4113_bd9b_55f3ddade0fb fill:#fef3c7,stroke:#f59e0b,color:#92400e style idea_331e62b3_94f6_4873_8cbc_70c7c026fe17 fill:#fef3c7,stroke:#f59e0b,color:#92400e style 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idea_83904bc3_82e1_4a62_b90e_d499c8ae1cbe fill:#e5e7eb,stroke:#9ca3af,color:#374151 style idea_78ff0c1d_27e2_439c_9f13_5116dfa4f6f3 fill:#fef3c7,stroke:#f59e0b,color:#92400e