graph LR idea_07f4a745_2f52_4a04_afc1_1f1377fa29c9["Step Response"] idea_0a290845_fa58_4ff3_b9d6_5207691684e9["Derivative Kick"] idea_1521ba9b_c32a_4382_aefa_524a11912fec["Feedforward Control"] idea_152700af_77f1_46de_b73f_22a2e7ccc075["Ziegler-Nichols Tuning"] idea_18bbad9c_a218_4f4e_8c48_c3555bcb449e["PID Control Law"] idea_1c116978_5df3_431c_9b80_8c5602223be3["Overshoot"] idea_1ed1eed8_37cf_4427_b8ff_1fc753f547bb["Time Constant"] idea_252f3bdf_7eda_49cb_af01_271b3967dab1["Low-Pass Filter"] idea_284a60a7_df13_4b59_b97c_4ea75b7e8352["Relay Auto-Tuning"] idea_28c7370e_5572_4b74_be11_e7ddaa806483["Manual PID Tuning Heuristics"] idea_2ad915fd_1701_43ff_9cff_0b9fc6a1613a["Poles of a Transfer Function"] idea_2f8507af_d549_4437_b577_cfbf7e6f74a6["Finite Difference Approximation"] idea_2fa29f8e_6b5f_44ba_8133_ade5fa6f4cf0["Derivative"] idea_331e62b3_94f6_4873_8cbc_70c7c026fe17["Setpoint"] idea_3b05d99d_1643_4f91_b8e9_cb1302a5cbd8["Setpoint Weighting"] idea_3f6d71dc_8fcb_4190_8fbc_ff5f73c74d17["Error Signal"] idea_4531fa68_5cf1_4501_b723_be77496539e2["Derivative Filtering"] idea_495f5a8e_2bad_46a4_bf26_63001753ff0b["Derivative Control Action"] idea_4a922882_de8d_49fa_b579_f6d33dfcaba1["Steady-State Error"] idea_4c172522_f59e_48fb_add6_145ff6dcdcc0["Dead Time"] idea_5c0da3c1_f2f5_4517_b819_a94c68e57132["Cascade Control"] idea_70147834_410f_4113_bd9b_55f3ddade0fb["Step Response Performance Metrics"] idea_70ec24b5_e526_47aa_b11b_ea077ba6b0a6["Closed-Loop Stability"] idea_88634765_8c73_4373_bb9b_cdf5bc87379f["Settling Time"] idea_92532848_fdc3_442b_b679_0d25b4fc317e["Proportional Gain"] idea_9b03a115_3d77_4d7f_b749_ffaa292745eb["Proportional Control Action"] idea_a0a5db5b_d47c_4856_8d7d_a1819db6934e["Negative Feedback Loop"] idea_a1a1d61c_dae3_4e7e_bc27_99e8a7048530["Integral"] idea_a42b6001_c10e_4927_9e7d_83a3289de097["Nyquist-Shannon Sampling Theorem"] idea_af908d90_220b_47a7_a4d0_b2ec0d526edb["Actuator Saturation"] idea_b0f8ebe6_684b_44d9_844d_739b9903af17["Integral Windup"] idea_b2a5b8fa_c9ec_4386_a196_3ee165e2c834["Damping Ratio"] idea_c0754b70_01eb_49b7_9294_f67864819483["Process Gain"] idea_ccea946f_0fdf_493b_a2e4_ba2cf92aa29b["Discrete-Time PID Implementation"] idea_cd9d6e9a_3ec0_432f_aa3f_9c7fa1460432["Ultimate Gain"] idea_d49b313f_ae8f_4563_9d80_0ac1656b3b49["Transfer Function"] idea_e0401852_0729_4fcb_a72a_ae91c83bb948["First-Order Plus Dead Time Model"] idea_e0e676aa_bd22_4dad_9528_301ed295d5f3["Measurement Noise"] idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0["Integral Anti-Windup"] idea_ec720b2a_b4d8_405b_a85d_014885863ef3["Integral Control Action"] idea_ecdac4cb_e209_4915_a9d6_5b125706683c["Rise Time"] idea_f1477f0b_fd7d_49d2_8fef_a100b31c0e41["Disturbance Rejection"] idea_2f8507af_d549_4437_b577_cfbf7e6f74a6 --> idea_ccea946f_0fdf_493b_a2e4_ba2cf92aa29b idea_af908d90_220b_47a7_a4d0_b2ec0d526edb --> idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0 idea_9b03a115_3d77_4d7f_b749_ffaa292745eb --> idea_28c7370e_5572_4b74_be11_e7ddaa806483 idea_18bbad9c_a218_4f4e_8c48_c3555bcb449e --> idea_152700af_77f1_46de_b73f_22a2e7ccc075 idea_0a290845_fa58_4ff3_b9d6_5207691684e9 --> idea_3b05d99d_1643_4f91_b8e9_cb1302a5cbd8 idea_f1477f0b_fd7d_49d2_8fef_a100b31c0e41 --> idea_5c0da3c1_f2f5_4517_b819_a94c68e57132 idea_f1477f0b_fd7d_49d2_8fef_a100b31c0e41 --> idea_1521ba9b_c32a_4382_aefa_524a11912fec idea_70147834_410f_4113_bd9b_55f3ddade0fb --> idea_28c7370e_5572_4b74_be11_e7ddaa806483 idea_a1a1d61c_dae3_4e7e_bc27_99e8a7048530 --> idea_ec720b2a_b4d8_405b_a85d_014885863ef3 idea_b0f8ebe6_684b_44d9_844d_739b9903af17 --> idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0 idea_3f6d71dc_8fcb_4190_8fbc_ff5f73c74d17 --> idea_9b03a115_3d77_4d7f_b749_ffaa292745eb idea_af908d90_220b_47a7_a4d0_b2ec0d526edb --> idea_284a60a7_df13_4b59_b97c_4ea75b7e8352 idea_3f6d71dc_8fcb_4190_8fbc_ff5f73c74d17 --> idea_18bbad9c_a218_4f4e_8c48_c3555bcb449e idea_331e62b3_94f6_4873_8cbc_70c7c026fe17 --> idea_5c0da3c1_f2f5_4517_b819_a94c68e57132 idea_ec720b2a_b4d8_405b_a85d_014885863ef3 --> idea_e6d6e61d_47d4_4857_bbd8_968ff998ebd0 idea_d49b313f_ae8f_4563_9d80_0ac1656b3b49 --> idea_1521ba9b_c32a_4382_aefa_524a11912fec idea_3f6d71dc_8fcb_4190_8fbc_ff5f73c74d17 --> idea_495f5a8e_2bad_46a4_bf26_63001753ff0b idea_1ed1eed8_37cf_4427_b8ff_1fc753f547bb --> idea_e0401852_0729_4fcb_a72a_ae91c83bb948 idea_ec720b2a_b4d8_405b_a85d_014885863ef3 --> idea_28c7370e_5572_4b74_be11_e7ddaa806483 idea_18bbad9c_a218_4f4e_8c48_c3555bcb449e --> idea_3b05d99d_1643_4f91_b8e9_cb1302a5cbd8 idea_e0401852_0729_4fcb_a72a_ae91c83bb948 --> idea_152700af_77f1_46de_b73f_22a2e7ccc075 idea_a0a5db5b_d47c_4856_8d7d_a1819db6934e --> idea_5c0da3c1_f2f5_4517_b819_a94c68e57132 idea_152700af_77f1_46de_b73f_22a2e7ccc075 --> idea_284a60a7_df13_4b59_b97c_4ea75b7e8352 idea_cd9d6e9a_3ec0_432f_aa3f_9c7fa1460432 --> idea_152700af_77f1_46de_b73f_22a2e7ccc075 idea_ecdac4cb_e209_4915_a9d6_5b125706683c --> idea_70147834_410f_4113_bd9b_55f3ddade0fb idea_495f5a8e_2bad_46a4_bf26_63001753ff0b --> idea_28c7370e_5572_4b74_be11_e7ddaa806483 idea_4a922882_de8d_49fa_b579_f6d33dfcaba1 --> idea_70147834_410f_4113_bd9b_55f3ddade0fb idea_c0754b70_01eb_49b7_9294_f67864819483 --> idea_1521ba9b_c32a_4382_aefa_524a11912fec idea_cd9d6e9a_3ec0_432f_aa3f_9c7fa1460432 --> idea_284a60a7_df13_4b59_b97c_4ea75b7e8352 idea_2fa29f8e_6b5f_44ba_8133_ade5fa6f4cf0 --> idea_18bbad9c_a218_4f4e_8c48_c3555bcb449e idea_a1a1d61c_dae3_4e7e_bc27_99e8a7048530 --> idea_18bbad9c_a218_4f4e_8c48_c3555bcb449e idea_495f5a8e_2bad_46a4_bf26_63001753ff0b --> idea_4531fa68_5cf1_4501_b723_be77496539e2 idea_92532848_fdc3_442b_b679_0d25b4fc317e --> idea_9b03a115_3d77_4d7f_b749_ffaa292745eb idea_a0a5db5b_d47c_4856_8d7d_a1819db6934e --> idea_18bbad9c_a218_4f4e_8c48_c3555bcb449e idea_9b03a115_3d77_4d7f_b749_ffaa292745eb --> idea_ec720b2a_b4d8_405b_a85d_014885863ef3 idea_e0e676aa_bd22_4dad_9528_301ed295d5f3 --> idea_495f5a8e_2bad_46a4_bf26_63001753ff0b idea_2fa29f8e_6b5f_44ba_8133_ade5fa6f4cf0 --> idea_495f5a8e_2bad_46a4_bf26_63001753ff0b idea_2ad915fd_1701_43ff_9cff_0b9fc6a1613a --> idea_70ec24b5_e526_47aa_b11b_ea077ba6b0a6 idea_88634765_8c73_4373_bb9b_cdf5bc87379f --> idea_70147834_410f_4113_bd9b_55f3ddade0fb idea_07f4a745_2f52_4a04_afc1_1f1377fa29c9 --> idea_e0401852_0729_4fcb_a72a_ae91c83bb948 idea_b2a5b8fa_c9ec_4386_a196_3ee165e2c834 --> idea_70ec24b5_e526_47aa_b11b_ea077ba6b0a6 idea_331e62b3_94f6_4873_8cbc_70c7c026fe17 --> idea_3b05d99d_1643_4f91_b8e9_cb1302a5cbd8 idea_4a922882_de8d_49fa_b579_f6d33dfcaba1 --> idea_ec720b2a_b4d8_405b_a85d_014885863ef3 idea_07f4a745_2f52_4a04_afc1_1f1377fa29c9 --> idea_70147834_410f_4113_bd9b_55f3ddade0fb idea_e0e676aa_bd22_4dad_9528_301ed295d5f3 --> idea_4531fa68_5cf1_4501_b723_be77496539e2 idea_d49b313f_ae8f_4563_9d80_0ac1656b3b49 --> idea_70ec24b5_e526_47aa_b11b_ea077ba6b0a6 idea_252f3bdf_7eda_49cb_af01_271b3967dab1 --> 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