A tuning method for decentralized PID controllers was developed based on probabilistic robustness for multi-input-multi-output plants, whose parameters vary in a determinate area. The advantage of this method is that the entire uncertainty parameter space can be considered for controller designing. According to model uncertainties, the probabilities of satisfaction for every item of dynamic performance requirements were computed and synthesized as the cost function of genetic algorithms, which was used to optimize the parameters of decentralized PID controllers. Monte Carlo experiments were used to test the control system robustness. Simulations for five multivariable chemical processes were carried out. Comparisons with a standard design method based on nominal conditions indicate that the method presented in this paper has better robustness, and the systems can satisfy the design requirements in a maximal probability.

References

References
1.
Monica
,
T. J.
,
Yu
,
C. C.
, and
Luyben
,
W. L.
,1998, “
Improved Multiloop Single-Input/Single-Output (SISO) Controllers for Multivariable Processes
,”
Ind. Eng. Chem. Res
,
27
, pp.
969
973
.
2.
Hovd
,
M.
and
,
S.
, 1994, “
Sequential Design of Decentralized Controllers
,”
Automatica
,
30
, pp.
1601
1607
.
3.
Lee
,
J.
, and
Edgar
,
T. F.
, 2000, “
Phase Conditions for Stability of Decentralized Control Systems
,”
Comput. Chem. Eng.
,
23
, pp.
1623
1630
.
4.
Huang
,
H -P.
,
Jeng
,
J -C.
,
Chiang
,
C -H.
, and
Pan
,
W.
, 2003, “
A Direct Method for Decentralized PI/PID Controller Design
,”
J. Process Control
,
13
, pp.
769
786
.
5.
Huang
,
X.
, and
Huang
,
B.
, 2004, “
Multi-Loop Decentralized PID Control Based on Covariance Control Criteria: An LMI Approach
,”
ISA Trans.
,
43
(
1
), pp.
49
59
.
6.
He
,
M.-J.
,
Cai
,
W.-J.
, and
Wu
,
B.-F.
, 2006, “Design of Decentralized IMC-PID Controller Based on dRI Analysis”
AIChE J
,
52
(
11
), pp.
3852
3863
.
7.
Lee
,
J.
,
Cho
,
W.
, and
Edgar
,
T. F.
, 1998, “
Multiloop PI Controller Tuning for Interacting Multivariable Processes
,”
Comput. Chem. Eng.
,
22
, pp.
1711
1723
.
8.
Li
,
D.
,
Gao
,
F.
,
Xue
,
Y.
, and
Lu
,
C.
, 2007, “
Optimization of Decentralized PI/PID Controllers Based on Genetic Algorithm
,”
Asian J. Control
,
9
, pp.
306
316
.
9.
Braatz
,
R. D.
,
Morari
,
M.
, and
,
S.
, 1994, “
Robust Reliable Decentralized Control
,”
Proceedings of the American Control Conference,
pp.
3384
3388
.
10.
Günde
,
A. N.
, and
Desoer
,
C. A.
, 1990,
Algebraic Theory of Linear Feedback Systems With Full and Decentralized Compensators (Lecture Notes in Control Information Sciences)
,
Springer, Berlin
, Vol.
142
.
11.
Tan
,
X. L.
,
Siljak
,
D. D.
, and
Ikeda
,
M.
, 1992, “
Reliable Stabilization via Factorization Methods
,”
IEEE Trans. Autom. Control
,
37
(
2
), pp.
1786
1791
.
12.
Barmish
,
B. R.
, 1992, “
A Probabilistic Robustness Result for a Multilinearly Parameterized H Norm
,”
Proceedings of the American Control Conference
pp.
1
6
.
13.
Calafiore
,
G. C.
,
Dabbene
,
F.
, and
Tempo
,
R.
, 2000, “
Randomized Algorithms for Probabilistic Robustness With Real and Complex Structured Uncertainty
,”
IEEE Trans. Autom. Control
,
45
, pp.
2218
2235
.
14.
Chen
,
X.
,
Aravena
,
J. L.
, and
Zhou
,
K.
, 2005, “
Risk Analysis in Robust Control—Making the Case for Probabilistic Robust Control
,”
2005 American Control Conference,
pp.
1533
1538
15.
Calafiore
,
G.
,
Dabbene
,
F.
, and
Tempo
,
R.
, 2007, “
A Survey of Randomized Algorithms for Control Synthesis and Performance Verification
,”
J. Complex.
,
23
, pp.
301
316
.
16.
Niederreiter
,
H.
, 1992,
Random Number Generation Quasi-Monte Carlo Methods
,
SIAM
,
.
17.
Wu
,
H.
, and
Cai
,
K.
, 2004, “
Probabilistic Robust Analysis of Uncertain Control Systems Using Adaptive Importance Sampling
,”
Control Theory Appl
.,
21
, pp.
812
816
.
18.
Chen
,
X.
,
Aravena
,
J. L.
, and
Zhou
,
K.
, 2006, “
Sample Reuse Techniques for Probabilistic Robust Control
,”
Control Uncertain Syst
.,
329
, pp.
417
429
.
19.
Wang
,
Q.
, and
Robert
,
F. S.
, 2002, “
Robust Control of Nonlinear Systems With Parametric Uncertainty
,”
Automatica
,
38
, pp.
1591
1599
.
20.
Tempo
,
R.
,
Calafiore
,
G.
,
Dabbene
,
F.
, 2005,
Randomized Algorithms for Analysis and Control of Uncertain Systems
,
Springer-Verlag
,
London, UK
.
21.
Wang
,
Q.
, and
Robert
,
F. S.
, 2005, “
Robust Nonlinear Flight Control of a High-Performance Aircraft
,”
IEEE Trans. Control Syst. Technol.
,
13
, pp.
15
26
.
22.
Nohtomi
,
S.
,
,
K.
, and
Horiuchi
,
S.
, 2004, “
Application of Analytic Hierarchy Process to Stochastic Robustness Synthesis of Integrated Vehicle Controllers
,”
Veh. Syst. Dyn.
,
42
, pp.
3
21
.
23.
Edmunds
,
J. M.
, 1998, “
Input and Output Scaling and Reordering for Diagonal Dominance and Block Diagonal Dominance
,”
IEE Proc.: Control Theory Appl.
,
145
, pp.
523
530
.
24.
,
H. L.
, 1997, “
Inverted Decoupling: A Neglected Technique
,”
ISA Trans
,
36
, pp.
3
10
.
25.
Massart
,
P.
, 1990,
The Tight Constant in the D.K.W. Inequality
,
Ann. Probab.
,
18
, pp.
1269
1283
.
26.
Chen
,
X.
,
Zhou
,
K.
, and
Aravena
,
J. L.
, 2003, “
Fast Universal Algorithms for Robustness Analysis
,”
Proceeding of the 42nd IEEE Conference on Decision and Control,
Maui
, pp.
1926
1931
.
27.
Holland
,
J. H.
, 1975,
Adaptation in Natural and Artificial Systems,
University Michigan Press
.
Ann Arbor, MI
.
28.
Lunze
,
J.
, 1989,
Robust Multivariable Feedback Control
,
Prentice Hall International UK Ltd
,
London, UK
.
29.
Xue
,
Y.
, 2005,
Multivariable Control Systems Optimization for Thermal Power Process
,
Tsinghua University
.
30.
Wang
,
C.
,
Li
,
D.
,
Li
,
Z.
, and
Jiang
,
X.
, 2009, “
Optimization of Controllers for Gas Turbine Based on Probabilistic Robustness
,”
Trans. ASME: J. Engineering Gas Turbines Power, September
,
131
, 054502.
You do not currently have access to this content.
{"ft_lang_label":"__label__en","ft_lang_prob":0.7818527,"math_prob":0.69616693,"size":4230,"snap":"2019-43-2019-47","text_gpt3_token_len":1013,"char_repetition_ratio":0.115475625,"word_repetition_ratio":0.14162348,"special_character_ratio":0.21702127,"punctuation_ratio":0.16643357,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.95790637,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2019-10-22T06:25:46Z\",\"WARC-Record-ID\":\"<urn:uuid:1f43f085-744c-465a-8286-632b2da4b57f>\",\"Content-Length\":\"127995\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:969fdce2-0dde-4c41-9e9a-d9fe1cbdfa1b>\",\"WARC-Concurrent-To\":\"<urn:uuid:b4c760f4-b278-40ce-86cf-121120b9c0b1>\",\"WARC-IP-Address\":\"173.254.190.160\",\"WARC-Target-URI\":\"https://asmedigitalcollection.asme.org/dynamicsystems/article-abstract/133/6/061015/471147/Decentralized-PID-Controllers-Based-on?redirectedFrom=fulltext\",\"WARC-Payload-Digest\":\"sha1:EZRO2AXQOATAV3PMJ6NCNTPEMDRAIRN7\",\"WARC-Block-Digest\":\"sha1:BQMY6JL2ICMNDTIJFGTXAWA4FDMV5NIB\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2019/CC-MAIN-2019-43/CC-MAIN-2019-43_segments_1570987803441.95_warc_CC-MAIN-20191022053647-20191022081147-00210.warc.gz\"}"}