Abstract

This paper is concerned with the problem of proportional-integral tracking control of a two-stage chemical reactor system subject to time delays, disturbances, uncertainties, and input quantization. In this work, an improved equivalent-input-disturbance estimator is incorporated into the proportional-integral tracking control system to compensate for the disturbances in the addressed model. Moreover, to minimize the communication congestion in the control networks, the quantized control input signals are considered while designing the controller. Further, a robust stability condition for the addressed system is established in the form of linear matrix inequalities by employing asymmetric Lyapunov–Krasovskii functional and Jensen's integral inequalities. Moreover, in accordance with the derived conditions, the control and observer gain matrices are determined. Finally, a numerical example is provided to demonstrate the validity of the proposed control scheme.

References

1.
Sui
,
S.
, and
Chen
,
C. P.
,
2019
, “
Adaptive Output-Feedback Finite-Time Stabilisation of Stochastic Non-Linear Systems With Application to a Two-Stage Chemical Reactor
,”
IET Control Theory Appl.
,
13
(
4
), pp.
534
542
.10.1049/iet-cta.2018.5431
2.
Zhai
,
J.
,
2019
, “
Dynamic Output-Feedback Control for Nonlinear Time-Delay Systems and Applications to Chemical Reactor Systems
,”
IEEE Trans. Circuits Syst. II: Express Briefs
,
66
(
11
), pp.
1845
1849
.10.1109/TCSII.2018.2890654
3.
Bzioui
,
S.
, and
Channa
,
R.
,
2020
, “
Robust Tracking Control for the Non-Isothermal Continuous Stirred Tank Reactor
,”
Int. J. Bioautomation
,
24
(
2
), pp.
131
142
.10.7546/ijba.2020.24.2.000615
4.
Mukherjee
,
A.
, and
Sengupta
,
A.
,
2021
, “
Robust Reference Tracking and Transient Response Shaping of a Class of Nonlinear Systems
,”
Int. J. Control
,
94
(
7
), pp.
1970
1981
.10.1080/00207179.2019.1690688
5.
Yan
,
X.
,
Chen
,
M.
,
Feng
,
G.
,
Wu
,
Q.
, and
Shao
,
S.
,
2021
, “
Fuzzy Robust Constrained Control for Nonlinear Systems With Input Saturation and External Disturbances
,”
IEEE Trans. Fuzzy Syst.
,
29
(
2
), pp.
345
356
.10.1109/TFUZZ.2019.2952794
6.
Dehri
,
K.
,
Messaoud
,
A.
, and
Ben Abdennour
,
R.
,
2022
, “
A Discrete Output Feedback 2-SMC Using Linear Matrix Inequalities and Adaptive Switching Gain Approaches: Real Application on a Chemical Reactor
,”
J. Vib. Control
,
29
(
9–10
), pp.
2116
2128
.10.1177/10775463221075113
7.
Franco de los Reyes
,
H. A.
, and
Lvarez
,
J.
,
2018
, “
Anti-Windup Scheme for PI Temperature Control of an Open-Loop Unstable Chemical Reactor
,”
IFAC-Papersonline
,
51
(
4
), pp.
491
496
.10.1016/j.ifacol.2018.06.143
8.
Vlahakis
,
E.
, and
Halikias
,
G.
,
2019
, “
Temperature and Concentration Control of Exothermic Chemical Processes in Continuous Stirred Tank Reactors
,”
Trans. Inst. Meas. Control
,
41
(
15
), pp.
4274
4284
.10.1177/0142331219855591
9.
Li
,
Y.
,
Tang
,
G.
,
Ji
,
L.
, and
Zhao
,
D.
,
2021
, “
Identifying Chemical Kinetics Contributions to Unstable Behaviours of a Methane-Burnt Combustion System
,”
Int. J. Hydrogen Energy
,
46
(
7
), pp.
5812
5823
.10.1016/j.ijhydene.2020.11.093
10.
Pourdehi
,
S.
, and
Karimaghaee
,
P.
,
2018
, “
Stability Analysis and Design of Model Predictive Reset Control for Nonlinear Time-Delay Systems With Application to a Two-Stage Chemical Reactor System
,”
J. Process Control
,
71
, pp.
103
115
.10.1016/j.jprocont.2018.09.010
11.
Pourdehi
,
S.
, and
Karimaghaee
,
P.
,
2020
, “
Reset Observer-Based Fault Tolerant Control for a Class of Fuzzy Nonlinear Time-Delay Systems
,”
J. Process Control
,
85
, pp.
65
75
.10.1016/j.jprocont.2019.11.001
12.
Zhang
,
L.
,
Liu
,
S.
, and
Hua
,
C.
,
2022
, “
Truncated Predictor Stabilization Control for Interconnected Nonlinear Systems With Time-Varying Input Delay
,”
Nonlinear Dyn.
,
107
(
3
), pp.
2421
2428
.10.1007/s11071-021-07126-3
13.
Sheng
,
Z.
,
Lin
,
C.
,
Chen
,
B.
, and
Wang
,
Q. G.
,
2021
, “
Asymmetric Lyapunov–Krasovskii Functional Method on Stability of Time-Delay Systems
,”
Int. J. Robust Nonlinear Control
,
31
(
7
), pp.
2847
2854
.10.1002/rnc.5417
14.
Zhang
,
L.
,
Wu
,
B.
, and
Liu
,
L.
,
2021
, “
Finite-Time H Dynamic Quantization Inputs Control for Uncertain Switched Systems
,”
Trans. Inst. Meas. Control
,
43
(
4
), pp.
771
781
.10.1177/0142331220933424
15.
Priyanka
,
S.
,
Sakthivel
,
R.
,
Tharanidharan
,
V.
, and
Nithya
,
V.
,
2021
, “
Quantized Output-Feedback Guaranteed Cost Control for Discrete-Time Large-Scale Interconnected Systems With Actuator Faults
,”
Int. J. Robust Nonlinear Control
,
31
(
12
), pp.
5890
5909
.10.1002/rnc.5574
16.
Nithya
,
V.
,
Sakthivel
,
R.
,
Alzahrani
,
F.
, and
Ma
,
Y. K.
,
2020
, “
Fault-Tolerant H Filtering for Fuzzy Networked Control Systems With Quantisation Effects
,”
Int. J. Syst. Sci.
,
51
(
7
), pp.
1149
1161
.10.1080/00207721.2020.1752416
17.
Li
,
L.
, and
Liu
,
J.
,
2023
, “
Consensus Tracking and Vibration Control for Multiple Single-Link Flexible Manipulators With Input Signal Quantization
,”
ISA Trans.
,
142
, pp.
228
241
.10.1016/j.isatra.2023.08.017
18.
Yu
,
X.
, and
Lin
,
Y.
,
2023
, “
Adaptive Quantized Tracking Control for a Class of Nonlinear Systems
,”
IEEE Trans. Syst., Man, Cybern.: Syst.
,
53
(
4
), pp.
2554
2559
.10.1109/TSMC.2022.3213003
19.
Zhao
,
Y.
,
Li
,
X.
, and
Song
,
S.
,
2021
, “
Observer-Based Sliding Mode Control for Stabilization of Mismatched Disturbance Systems With or Without Time-Delays
,”
IEEE Trans. Syst., Man, Cybern. Syst.
,
51
(
12
), pp.
7337
7345
.10.1109/TSMC.2020.2967032
20.
Defeng
,
H.
,
Tianxiang
,
Q.
, and
Liangye
,
L.
,
2019
, “
Input-to-State Stability of Contractive EMPC of Non-Linear Systems With Bounded Disturbances
,”
IET Control Theory Appl.
,
13
(
5
), pp.
651
658
.10.1049/iet-cta.2018.5708
21.
Chen
,
S.
,
Xue
,
W.
, and
Huang
,
Y.
,
2019
, “
Analytical Design of Active Disturbance Rejection Control for Nonlinear Uncertain Systems With Delay
,”
Control Eng. Pract.
,
84
, pp.
323
336
.10.1016/j.conengprac.2018.12.007
22.
Gao
,
F.
,
Wu
,
M.
,
She
,
J.
, and
Cao
,
W.
,
2016
, “
Disturbance Rejection in Nonlinear Systems Based on Equivalent-Input-Disturbance Approach
,”
Appl. Math. Comput.
,
282
, pp.
244
253
.10.1016/j.amc.2016.02.014
23.
Yu
,
P.
,
Wu
,
M.
,
She
,
J.
,
Liu
,
K. Z.
, and
Nakanishi
,
Y.
,
2018
, “
Robust Tracking and Disturbance Rejection for Linear Uncertain System With Unknown State Delay and Disturbance
,”
IEEE/ASME Trans. Mechatron.
,
23
(
3
), pp.
1445
1455
.10.1109/TMECH.2018.2816005
24.
Li
,
M.
,
She
,
J.
,
Zhang
,
C. K.
,
Liu
,
Z. T.
,
Wu
,
M.
, and
Ohyama
,
Y.
,
2021
, “
Active Disturbance Rejection for Time-Varying State-Delay Systems Based on Equivalent-Input-Disturbance Approach
,”
ISA Trans.
,
108
, pp.
69
77
.10.1016/j.isatra.2020.09.001
25.
Du
,
Y.
,
Cao
,
W.
,
She
,
J.
,
Wu
,
M.
,
Fang
,
M.
, and
Kawata
,
S.
,
2022
, “
Disturbance Rejection and Robustness of Improved Equivalent-Input-Disturbance-Based System
,”
IEEE Trans. Cybern.
,
52
(
8
), pp.
8537
8546
.10.1109/TCYB.2021.3053597
26.
Wu
,
Y.
,
Du
,
D.
, and
Mao
,
Z.
,
2022
, “
Actuator Fault Detection for a Two-Stage Chemical Reactor Based on the Functional Observer Approach
,”
Can. J. Chem. Eng.
,
100
(
4
), pp.
800
810
.10.1002/cjce.24198
27.
Selvaraj
,
P.
,
Sakthivel
,
R.
, and
Karimi
,
H. R.
,
2016
, “
Equivalent-Input-Disturbance-Based Repetitive Tracking Control for Takagi-Sugeno Fuzzy Systems With Saturating Actuator
,”
IET Control Theory Appl.
,
10
(
15
), pp.
1916
1927
.10.1049/iet-cta.2016.0036
28.
Fu
,
L.
, and
Ma
,
Y.
,
2016
, “
Passive Control for Singular Time-Delay System With Actuator Saturation
,”
Appl. Math. Comput.
,
289
, pp.
181
193
.10.1016/j.amc.2016.05.001
29.
Jia
,
X.
,
Xu
,
S.
,
Shi
,
X.
,
Du
,
B.
, and
Zhang
,
Z.
,
2021
, “
Adaptive Output Feedback Tracking for Time-Delay Nonlinear Systems With Unknown Control Coefficient and Application to Chemical Reactors
,”
Inf. Sci.
,
581
, pp.
755
772
.10.1016/j.ins.2021.10.015
30.
Zhang
,
L.
,
Sui
,
S.
,
Li
,
Y.
, and
Tong
,
S.
,
2015
, “
Adaptive Fuzzy Output Feedback Tracking Control With Prescribed Performance for Chemical Reactor of MIMO Nonlinear Systems
,”
Nonlinear Dyn.
,
80
(
1–2
), pp.
945
957
.10.1007/s11071-015-1919-2
You do not currently have access to this content.