Handbook of Pi And Pid Controller Tuning Rules

by O'Dwyer, Aidan

• ISBN13: 9781860946226
• ISBN10: 1860946224
• Edition: 2nd
• Format: Hardcover
• Copyright: 2006-04-30
• Publisher: World Scientific Pub Co Inc

Summary

The vast majority of automatic controllers used to compensate industrial processes are of PI or PID type. This book comprehensively compiles, using a unified notation, tuning rules for these controllers proposed over the last seven decades (1935-2005). The tuning rules are carefully categorized and application information about each rule is given. The book discusses controller architecture and process modeling issues, as well as the performance and robustness of loops compensated with PI or PID controllers. This unique publication brings together in an easy-to-use format material previously published in a large number of papers and books. This wholly revised second edition extends the presentation of PI and PID controller tuning rules, for single variable processes with time delays, to include additional rules compiled since the first edition was published in 2003. Contents: Controller Architecture; Tuning Rules for PI Controllers; Tuning Rules for PID Controllers; Performance and Robustness Issues in the Compensation of FOLPD Processes with PI and PID Controllers. Key Features Addresses the needs of a niche market where no comparable book is available A comprehensive compilation of PI and PID controller tuning rules Makes the tuning rules easily accessible to researchers and practitioners through unified notation Highlights the marked increase in the number of tuning rules compiled, from 600 in the first edition to 1,134 in this second edition Readership: Control engineering researchers in academia and industry with an interest in PID control and control engineering practitioners using PID controllers. The book also serves as a reference for postgraduate and undergraduate students.

Table of Contents

Preface	vii
1. Introduction	1	(4)
1.1 Preliminary Remarks	1	(1)
1.2 Structure of the Book	2	(3)
2. Controller Architecture	5	(21)
2.1 Introduction	5	(1)
2.2 PI Controller Structures	6	(1)
2.3 PID Controller Structures	7	(13)
2.3.1 Ideal PID controller structure and its variations	7	(4)
2.3.2 Classical PID controller structure and its variations	11	(1)
2.3.3 Non-interacting PID controller structure and its variations	12	(5)
2.3.4 Other PID controller structures	17	(2)
2.3.5 Comments on the PID controller structures	19	(1)
2.4 Process Modelling	20	(4)
2.5 Organisation of the Tuning Rules	24	(2)
3. Tuning Rules for PI Controllers	26	(128)
3.1 FOLPD Model	26	(41)
3.1.1 Ideal controller – Table 3	26	(35)
3.1.2 Ideal controller in series with a first order lag – Table 4	61	(1)
3.1.3 Ideal controller in series with a second order filter – Table 5	62	(1)
3.1.4 Controller with set-point weighting – Table 6	63	(2)
3.1.5 Controller with proportional term acting on the output 1 – Table 7	65	(1)
3.1.6 Controller with proportional term acting on the output 2 – Table 8	66	(1)
3.2 FOLPD Model with a Positive Zero	67	(2)
3.2.1 Ideal controller – Table 9	67	(1)
3.2.2 Ideal controller in series with a first order lag – Table 10	68	(1)
3.3 FOLPD Model with a Negative Zero	69	(1)
3.3.1 Ideal controller in series with a first order lag – Table 11	69	(1)
3.4 Non-Model Specific	70	(6)
3.4.1 Ideal controller – Table 12	70	(5)
3.4.2 Controller with set-point weighting – Table 13	75	(1)
3.5 IPD Model	76	(13)
3.5.1 Ideal controller – Table 14	76	(7)
3.5.2 Ideal controller in series with a first order lag – Table 15	83	(1)
3.5.3 Controller with set-point weighting – Table 16	84	(1)
3.5.4 Controller with proportional term acting on the output 1 – Table 17	85	(2)
3.5.5 Controller with proportional term acting on the output 2 – Table 18	87	(1)
3.5.6 Controller with a double integral term – Table 19	88	(1)
3.6 FOLIPD Model	89	(13)
3.6.1 Ideal controller – Table 20	89	(3)
3.6.2 Controller with set-point weighting – Table 21	92	(2)
3.6.3 Controller with proportional term acting on the output 1 – Table 22	94	(7)
3.6.4 Controller with proportional term acting on the output 2 – Table 23	101	(1)
3.7 SOSPD Model	102	(20)
3.7.1 Ideal controller – Table 24	102	(18)
3.7.2 Controller with set-point weighting – Table 25	120	(2)
3.8 SOSIPD Model – Repeated Pole	122	(1)
3.8.1 Controller with set-point weighting – Table 26	122	(1)
3.9 SOSPD Model with a Positive Zero	123	(2)
3.9.1 Ideal controller – Table 27	123	(2)
3.10 SOSPD Model (repeated pole) with a Negative Zero	125	(1)
3.10.1 Ideal controller in series with a first order lag – Table 28	125	(1)
3.11 Third Order System plus Time Delay Model	126	(4)
3.11.1 Ideal controller – Table 29	126	(2)
3.11.2 Controller with set-point weighting – Table 30	128	(2)
3.12 Unstable FOLPD Model	130	(11)
3.12.1 Ideal controller – Table 31	130	(5)
3.12.2 Controller with set-point weighting – Table 32	135	(2)
3.12.3 Controller with proportional term acting on the output 1 – Table 33	137	(3)
3.12.4 Controller with proportional term acting on the output 2 – Table 34	140	(1)
3.13 Unstable FOLPD Model with a Positive Zero	141	(4)
3.13.1 Ideal controller – Table 35	141	(1)
3.13.2 Ideal controller in series with a first order lag – Table 36	142	(1)
3.13.3 Controller with set-point weighting – Table 37	143	(2)
3.14 Unstable SOSPD Model (one unstable pole)	145	(2)
3.14.1 Ideal controller – Table 38	145	(2)
3.15 Unstable SOSPD Model with a Positive Zero	147	(2)
3.15.1 Ideal controller – Table 39	147	(1)
3.15.2 Controller with set-point weighting – Table 40	148	(1)
3.16 Delay Model	149	(3)
3.16.1 Ideal controller – Table 41	149	(3)
3.17 General Model with a Repeated Pole	152	(1)
3.17.1 Ideal controller – Table 42	152	(1)
3.18 General Model with Integrator	153	(1)
3.18.1 Ideal controller – Table 43	153	(1)
4. Tuning Rules for PID Controllers	154	(308)
4.1 FOLPD Model	154	(81)
4.1.1 Ideal controller – Table 44	154	(27)
4.1.2 Ideal controller in series with a first order lag – Table 45	181	(2)
4.1.3 Ideal controller in series with a second order filter – Table 46	183	(2)
4.1.4 Ideal controller with weighted proportional term – Table 47	185	(1)
4.1.5 Ideal controller with first order filter and set-point weighting 1 – Table 48	186	(1)
4.1.6 Controller with filtered derivative – Table 49	187	(6)
4.1.7 Blending controller – Table 50	193	(1)
4.1.8 Classical controller 1 – Table 51	194	(14)
4.1.9 Classical controller 2 – Table 52	208	(1)
4.1.10 Series controller (classical controller 3) – Table 53	209	(2)
4.1.11 Classical controller 4 – Table 54	211	(1)
4.1.12 Non-interacting controller 1 – Table 55	212	(1)
4.1.13 Non-interacting controller 2a – Table 56	213	(2)
4.1.14 Non-interacting controller 2b – Table 57	215	(2)
4.1.15 Non-interacting controller based on the two degree of freedom structure 1 – Table 58	217	(5)
4.1.16 Non-interacting controller based on the two degree of freedom structure 2 – Table 59	222	(1)
4.1.17 Non-interacting controller based on the two degree of freedom structure 3 – Table 60	223	(1)
4.1.18 Non-interacting controller 4 – Table 61	224	(2)
4.1.19 Non-interacting controller 5 – Table 62	226	(1)
4.1.20 Non-interacting controller 6 (I-PD controller) – Table 63	227	(3)
4.1.21 Non-interacting controller 7 – Table 64	230	(1)
4.1.22 Non-interacting controller 11 – Table 65	231	(1)
4.1.23 Non-interacting controller 12 – Table 66	232	(1)
4.1.24 Industrial controller – Table 67	233	(2)
4.2 Non-Model Specific	235	(24)
4.2.1 Ideal controller – Table 68	235	(6)
4.2.2 Ideal controller in series with a first order lag – Table 69	241	(2)
4.2.3 Ideal controller in series with a second order filter – Table 70	243	(2)
4.2.4 Ideal controller with weighted proportional term – Table 71	245	(1)
4.2.5 Controller with filtered derivative – Table 72	246	(6)
4.2.6 Ideal controller with set-point weighting 1 – Table 73	252	(1)
4.2.7 Classical controller 1 – Table 74	253	(1)
4.2.8 Series controller (classical controller 3) – Table 75	254	(1)
4.2.9 Classical controller 4 – Table 76	255	(1)
4.2.10 Non-interacting controller based on the two degree of freedom structure 1 – Table 77	256	(1)
4.2.11 Non-interacting controller 4 – Table 78	257	(1)
4.2.12 Non-interacting controller 9 – Table 79	258	(1)
4.3 IPD Model	259	(20)
4.3.1 Ideal controller – Table 80	259	(3)
4.3.2 Ideal controller in series with a first order lag – Table 81	262	(1)
4.3.3 Ideal controller with first order filter and set-point weighting 2 – Table 82	263	(1)
4.3.4 Controller with filtered derivative – Table 83	264	(1)
4.3.5 Controller with filtered derivative and dynamics on the controlled variable – Table 84	265	(1)
4.3.6 Classical controller 1 – Table 85	266	(2)
4.3.7 Classical controller 2 – Table 86	268	(1)
4.3.8 Classical controller 4 – Table 87	269	(1)
4.3.9 Non-interacting controller based on the two degree of freedom structure 1 – Table 88	270	(2)
4.3.10 Non-interacting controller based on the two degree of freedom structure 3 – Table 89	272	(1)
4.3.11 Non-interacting controller 4 – Table 90	273	(1)
4.3.12 Non-interacting controller 6 (I-PD controller) – Table 91	274	(2)
4.3.13 Non-interacting controller 8 – Table 92	276	(1)
4.3.14 Non-interacting controller 10 – Table 93	277	(1)
4.3.15 Non-interacting controller 12 – Table 94	278	(1)
4.4 FOLIPD Model	279	(30)
4.4.1 Ideal controller – Table 95	279	(3)
4.4.2 Ideal controller in series with a first order lag – Table 96	282	(2)
4.4.3 Ideal controller with weighted proportional term – Table 97	284	(1)
4.4.4 Controller with filtered derivative – Table 98	285	(1)
4.4.5 Controller with filtered derivative with set-point weighting 1 – Table 99	286	(1)
4.4.6 Controller with filtered derivative with set-point weighting 3 – Table 100	287	(2)
4.4.7 Ideal controller with set-point weighting 1 – Table 101	289	(1)
4.4.8 Classical controller 1 – Table 102	290	(2)
4.4.9 Classical controller 2 – Table 103	292	(1)
4.4.10 Series controller (classical controller 3) – Table 104	293	(1)
4.4.11 Classical controller 4 – Table 105	294	(1)
4.4.12 Non-interacting controller based on the two degree of freedom structure 1 – Table 106	295	(2)
4.4.13 Non-interacting controller 4 – Table 107	297	(1)
4.4.14 Non-interacting controller 6 (I-PD controller) – Table 108	298	(5)
4.4.15 Non-interacting controller 8 – Table 109	303	(1)
4.4.16 Non-interacting controller 11 – Table 110	304	(1)
4.4.17 Non-interacting controller 12 – Table 111	305	(1)
4.4.18 Industrial controller – Table 112	306	(1)
4.4.19 Alternative controller 1 – Table 113	307	(1)
4.4.20 Alternative controller 2 – Table 114	308	(1)
4.5 SOSPD Model	309	(65)
4.5.1 Ideal controller – Table 115	309	(23)
4.5.2 Ideal controller in series with a first order lag – Table 116	332	(4)
4.5.3 Ideal controller in series with a first order filter — Table 117	336	(1)
4.5.4 Ideal controller in series with a second order filter — Table 118	337	(1)
4.5.5 Controller with filtered derivative — Table 119	338	(1)
4.5.6 Controller with filtered derivative in series with a second order filter — Table 120	339	(1)
4.5.7 Ideal controller with set-point weighting 1 — Table 121	340	(1)
4.5.8 Ideal controller with set-point weighting 2 — Table 122	341	(1)
4.5.9 Classical controller 1 — Table 123	342	(9)
4.5.10 Classical controller 2 — Table 124	351	(1)
4.5.11 Series controller (classical controller 3) — Table 125	352	(2)
4.5.12 Non-interacting controller 1 — Table 126	354	(9)
4.5.13 Non-interacting controller based on the two degree of freedom structure 1 — Table 127	363	(5)
4.5.14 Non-interacting controller 4 — Table 128	368	(2)
4.5.15 Non-interacting controller 5 — Table 129	370	(1)
4.5.16 Non-interacting controller 6 — Table 130	371	(1)
4.5.17 Alternative controller 4 — Table 131	372	(2)
4.6 I²PD Model	374	(7)
4.6.1 Controller with filtered derivative with set-point weighting 2 — Table 132	374	(2)
4.6.2 Controller with filtered derivative with set-point weighting 4 — Table 133	376	(2)
4.6.3 Series controller (classical controller 3) — Table 134	378	(1)
4.6.4 Non-interacting controller based on the two degree of freedom structure 1 — Table 135	379	(1)
4.6.5 Industrial controller — Table 136	380	(1)
4.7 SOSIPD Model (repeated pole)	381	(2)
4.7.1 Non-interacting controller based on the two degree of freedom structure 1 — Table 137	381	(2)
4.8 SOSPD Model with a Positive Zero	383	(9)
4.8.1 Ideal controller — Table 138	383	(2)
4.8.2 Ideal controller in series with a first order lag — Table 139	385	(1)
4.8.3 Controller with filtered derivative — Table 140	386	(1)
4.8.4 Classical controller 1 — Table 141	387	(1)
4.8.5 Series controller (classical controller 3) — Table 142	388	(1)
4.8.6 Classical controller 4 — Table 143	389	(1)
4.8.7 Non-interacting controller 1 — Table 144	390	(1)
4.8.8 Non-interacting controller based on the two degree of freedom structure 1 — Table 145	391	(1)
4.9 SOSPD Model with a Negative Zero	392	(6)
4.9.1 Ideal controller – Table 146	392	(1)
4.9.2 Controller with filtered derivative – Table 147	393	(1)
4.9.3 Classical controller 1 – Table 148	394	(1)
4.9.4 Classical controller 4 – Table 149	395	(1)
4.9.5 Non-interacting controller 1 – Table 150	396	(1)
4.9.6 Non-interacting controller based on the two degree of freedom structure 1 – Table 151	397	(1)
4.10 Third Order System plus Time Delay Model	398	(5)
4.10.1 Ideal controller – Table 152	398	(1)
4.10.2 Ideal controller in series with a first order lag – Table 153	399	(1)
4.10.3 Controller with filtered derivative – Table 154	400	(1)
4.10.4 Non-interacting controller based on the two degree of freedom structure 1 – Table 155	401	(2)
4.11 Unstable FOLPD Model	403	(24)
4.11.1 Ideal controller – Table 156	403	(5)
4.11.2 Ideal controller in series with a first order lag – Table 157	408	(2)
4.11.3 Ideal controller with set-point weighting 1 – Table 158	410	(4)
4.11.4 Classical controller 1 – Table 159	414	(1)
4.11.5 Series controller (classical controller 3) – Table 160	415	(1)
4.11.6 Non-interacting controller based on the two degree of freedom structure 1 – Table 161	416	(4)
4.11.7 Non-interacting controller 3 – Table 162	420	(1)
4.11.8 Non-interacting controller 8 – Table 163	421	(2)
4.11.9 Non-interacting controller 10 – Table 164	423	(2)
4.11.10 Non-interacting controller 12 – Table 165	425	(2)
4.12 Unstable SOSPD Model (one unstable pole)	427	(15)
4.12.1 Ideal controller – Table 166	427	(3)
4.12.2 Ideal controller in series with a first order lag – Table 167	430	(1)
4.12.3 Ideal controller with set-point weighting 1 – Table 168	431	(1)
4.12.4 Classical controller 1 – Table 169	432	(1)
4.12.5 Series controller (classical controller 3) – Table 170	433	(1)
4.12.6 Non-interacting controller 3 – Table 171	434	(5)
4.12.7 Non-interacting controller 8 – Table 172	439	(3)
4.13 Unstable SOSPD Model (two unstable poles)	442	(3)
4.13.1 Ideal controller – Table 173	442	(2)
4.13.2 Ideal controller with set-point weighting 1 – Table 174	444	(1)
4.14 Unstable SOSPD Model with a Positive Zero	445	(4)
4.14.1 Ideal controller in series with a first order lag – Table 175	445	(2)
4.14.2 Non-interacting controller based on the two degree of freedom structure 1 – Table 176	447	(2)
4.15 Delay Model	449	(3)
4.15.1 Ideal controller – Table 177	449	(1)
4.15.2 Ideal controller in series with a first order lag – Table 178	450	(1)
4.15.3 Classical controller 1 – Table 179	451	(1)
4.16 General Model with a Repeated Pole	452	(2)
4.16.1 Ideal controller – Table 180	452	(1)
4.16.2 Ideal controller in series with a first order lag – Table 181	453	(1)
4.17 General Stable Non-Oscillating Model with a Time Delay	454	(1)
4.17.1 Ideal controller – Table 182	454	(1)
4.18 Fifth Order System plus Delay Model	455	(7)
4.18.1 Ideal controller – Table 183	455	(2)
4.18.2 Controller with filtered derivative – Table 184	457	(3)
4.18.3 Non-interacting controller 7 – Table 185	460	(2)
5. Performance and Robustness Issues in the Compensation of FOLPD Processes with PI and PID Controllers	462	(23)
5.1 Introduction	462	(1)
5.2 The Analytical Determination of Gain and Phase Margin	463	(6)
5.2.1 PI tuning formulae	463	(3)
5.2.2 PID tuning formulae	466	(3)
5.3 The Analytical Determination of Maximum Sensitivity	469	(1)
5.4 Simulation Results	470	(5)
5.5 Design of Tuning Rules to Achieve Constant Gain and Phase Margins, for all Values of Delay	475	(9)
5.5.1 PI controller design	475	(5)
5.5.1.1 Processes modelled in FOLPD form	475	(2)
5.5.1.2 Processes modelled in IPD form	477	(3)
5.5.2 PID controller design	480	(3)
5.5.2.1 Processes modelled in FOLPD form – classical controller 1	480	(2)
5.5.2.2 Processes modelled in SOSPD form – series controller	482	(1)
5.5.2.3 Processes modelled in SOSPD form with a negative zero – classical controller 1	482	(1)
5.5.3 PD controller design	483	(1)
5.6 Conclusions	484	(1)
Appendix 1 Glossary of Symbols Used in the Book	485	(8)
Appendix 2 Some Further Details on Process Modelling	493	(14)
Bibliography	507	(28)
Index	535