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A bilevel optimisation framework is proposed to find the proportional–integral–derivative (PID) controller with balanced performance in terms of transient response, actuator preservation and robustness. In the lower level problem, the transient performance is optimised so that the balanced controller can be designed with minimal controller output variation in the upper level problem, where the requirement on transient performance is relaxed to a pre-specified extent. The robustness of the system is guaranteed by constraints on the maximum sensitivity in both problems. The trade-off between transient performance and actuator preservation is controlled uniformly for diverse process dynamics by a single parameter, which characterises the uniformness of relaxation in transient performance. By choosing different values of this parameter, tuning rules are provided for first order plus time delay (FOPTD) processes for set point following and load disturbance rejection, respectively. The efficiency of these tuning rules is demonstrated by examples covering the whole plant family set.
References
-
-
1)
-
K.J. Astrom ,
T. Hagglund
.
(2005)
Advanced PID control.
-
2)
-
K.J. Astrom ,
T. Hagglund
.
The future of PID control.
Control Eng. Pract.
,
11 ,
1163 -
1175
-
3)
-
A.V. Oppenheim ,
A.S. Willsky ,
S.H. Nawab
.
(1983)
Signals & systems.
-
4)
-
D.E. Rivera ,
M. Morari ,
S. Skogestad
.
Internal model control 4. PID controller design.
Ind. Eng. Chem. Process. Des. Dev.
,
1 ,
252 -
265
-
5)
-
A. Visioli
.
Optimal tuning of PID controllers for integral and unstable processes.
IEE Proc. Control Theory Appl.
,
2 ,
180 -
184
-
6)
-
Shi, D.W., Wang, J.Z., Ma, L.L., Zhao, J.B.: `Design of plant-friendly PID controllers based on constrained optimization', Proc. IEEE Int. Conf. on Automation and Logistics, 2009, Shenyang, China, p. 337–342.
-
7)
-
Klan, P., Gorez, R.: `PI controller design for actuator preservation', Proc. 17th IFAC World Congress, 2008, Seoul, Korea.
-
8)
-
Balestrino, A., Landi, A., Medaglia, M., Satler, M.: `Performance indices and tuning in process control', Proc. 14th Mediterranean Conf. on Control and Automation, 2006, Ancona, Italy, p. 1–6.
-
9)
-
B. Colson ,
P. Marcotte ,
G. Savard
.
Bilevel programming: a survey.
4OR: Q. J. Oper. Res.
,
2 ,
87 -
107
-
10)
-
C.R. Madhuranthakam ,
A. Elkamel ,
H. Budman
.
Optimal tuning of PID controllers for FOPTD, SOPTD and SOPTD with lead processes.
Chem. Eng. Process.
,
2 ,
251 -
264
-
11)
-
Klan, P., Gorez, R.: `On aggressiveness of PI control', Proc. 16th IFAC World Congress, 2005, Praha, Czech.
-
12)
-
E.N. Goncalves ,
R.M. Palhares ,
R.H.C. Takahashi
.
A novel approach for H2/H∞ robust PID synthesis for uncertain systems.
J. Process. Control
,
1 ,
19 -
26
-
13)
-
G. Buckbee
.
Poor controller tuning drives up valve costs.
Control Mag.
,
47 -
51
-
14)
-
R. Vilanova
.
IMC based robust PID design: tuning guidelines and automatic tuning.
J. Process. Control
,
1 ,
61 -
70
-
15)
-
Y.J. Huang ,
Y.-J. Wang
.
Robust pid tuning strategy for uncertain plants based on the kharitonov theorem.
ISA Trans.
,
4 ,
419 -
431
-
16)
-
W.K. Ho ,
K.W. Lim ,
W. Xu
.
Optimal gain and phase margin tuning for PID controllers.
Automatica
,
8 ,
1009 -
1014
-
17)
-
M. Zhuang ,
D.P. Atherton
.
Automatic tuning of optimum PID controllers.
IEE Proc. Control Theory Appl.
,
3 ,
216 -
224
-
18)
-
K.J. Astrom ,
T. Hagglund
.
Revisiting the Ziegler–Nichols step response method for PID control.
J. Process. Control
,
6 ,
635 -
650
-
19)
-
M. Ge ,
M.S. Chiu ,
Q.G. Wang
.
Robust PID controller design via LMI approach.
J. Process Control
,
3 -
13
-
20)
-
K.J. Åström ,
H. Panagopoulos ,
T. Hägglund
.
Design of PI controllers based on non-convex optimization.
Autom.
,
5 ,
585 -
601
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2009.0561
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