In this paper, a decentralized proportional–integral proportional–retarded (PI-PR) controller design method is proposed for two-input two-output (TITO) systems in discrete-time domain. The well-known dominant pole assignment (DPA) approach is used as the basis of the proposed approach. The controller design starts with the decoupling of a given TITO system into two sub-systems and continues with the design of proportional–integral–retarded (PIR) controllers for each sub-system, respectively. The feasible discrete PIR controller parameter set is obtained through the Nyquist stability criterion by considering the desired closed-loop performance specifications. The obtained PIR controllers are then implemented using a PI-PR control structure to avoid poor performance of the closed-loop system (CLS) transient response, which can be caused by the controller zeros. Moreover, a case study is presented to show the performance of the PI-PR controller in a simulation environment. It is shown that the proposed control structure provides a satisfactory performance when compared with the other proportional–integral–derivative (PID) control methods from the literature.
AckermannJ (2012) Robust Control: Systems with Uncertain Physical Parameters. Berlin: Springer Science & Business Media.
2.
ÅströmHägglundT (2001) The future of PID control. Control Engineering Practice9(11): 1163–1175.
3.
ÅströmMurrayRM (2010) Feedback Systems: An Introduction for Scientists and Engineers. Princeton, NJ: Princeton University Press.
4.
ChenYH (1987) New type of controller: The proportional integral minus delay controller. International Journal of Systems Science18(11): 2033–2041.
5.
ChienILHuangHPYangJC (1999) A simple multiloop tuning method for PID controllers with no proportional kick. Industrial & Engineering Chemistry Research38(4): 1456–1468.
6.
DasSHalderKGuptaA (2018) Performance analysis of robust stable PID controllers using dominant pole placement for SOPTD process models. Knowledge-Based Systems146: 12–43.
7.
DasSHalderKGuptaA (2019) Delay handling method in dominant pole placement based PID controller design. IEEE Transactions on Industrial Informatics16(2): 980–991.
8.
De KeyserRMuresanCIIonescuCM (2016) A novel auto-tuning method for fractional order PI/PD controllers. ISA Transactions62: 268–275.
9.
DincelESöylemezMT (2014) Guaranteed dominant pole placement with discrete-PID controllers: A modified Nyquist plot approach. IFAC Proceedings Volumes47(3): 3122–3127.
10.
DincelESöylemezMT (2018) Digital PI-PD controller design for arbitrary order systems: Dominant pole placement approach. ISA Transactions79: 189–201.
11.
DincelEMutluİSchrödelF, et al. (2018) Further results on dominant pole placement via stability mapping approach. IFAC-Papersonline51(4): 918–923.
12.
FišerJZítekP (2019) PID controller tuning via dominant pole placement in comparison with Ziegler-Nichols tuning. IFAC-Papersonline52(18): 43–48.
13.
Galip UlsoyA (2015) Time-delayed control of SISO systems for improved stability margins. Journal of Dynamic Systems, Measurement, and Control137: 041014.
14.
HajareVPatreB (2015) Decentralized PID controller for TITO systems using characteristic ratio assignment with an experimental application. ISA Transactions59: 385–397.
15.
HajareVPatreBKhandekarA, et al. (2017) Decentralized PID controller design for TITO processes with experimental validation. International Journal of Dynamics and Control5(3): 583–595.
16.
HalderKDasSGuptaA (2020) Time delay handling in dominant pole placement with PID controllers to obtain stability regions using random sampling. International Journal of Control94: 3384–3405.
17.
HuZLiDWangJ, et al. (2011) Analytical design of PID decoupling control for TITO processes with time delays. JCP6(6): 1064–1070.
18.
HuangHPLinFY (2006) Decoupling multivariable control with two degrees of freedom. Industrial & Engineering Chemistry Research45(9): 3161–3173.
19.
JinQLiuQ (2014) Decoupling proportional–integral–derivative controller design for multivariable processes with time delays. Industrial & Engineering Chemistry Research53(2): 765–777.
20.
KhandelwalSAldhandiSDetrojaKP (2019) Decoupling control with ETF based GPM tuning for multivariable processes. In: 2019 fifth Indian control conference (ICC), New Delhi, India, 9–11 January, pp. 63–67. New York: IEEE.
21.
KharitonovVLNiculescuSIMorenoJ, et al. (2005) Static output feedback stabilization: Necessary conditions for multiple delay controllers. IEEE Transactions on Automatic Control50(1): 82–86.
22.
KohMRamírezASipahiR (2018) Single-delay proportional-retarded (PR) protocols for fast consensus in a multi-agent system. IFAC-Papersonline51(14): 31–36.
23.
LakshmanaprabuSElhosenyMShankarK (2019) Optimal tuning of decentralized fractional order PID controllers for TITO process using equivalent transfer function. Cognitive Systems Research58: 292–303.
24.
LengareMChileRWaghmareLM (2012) Design of decentralized controllers for MIMO processes. Computers & Electrical Engineering38(1): 140–147.
25.
LiuTZhangWGuD (2005) Analytical multiloop PI/PID controller design for two-by-two processes with time delays. Industrial & Engineering Chemistry Research44(6): 1832–1841.
26.
LópezKGarridoRMondiéS (2017) Position control of servodrives using a cascade proportional integral retarded controller. In: 2017 4th international conference on control, decision and information technologies (CoDIT), Barcelona, 5–7 April, Pp, 120–125. New York: IEEE.
27.
LópezKMondiéSGarridoR (2018) A tuning procedure for the cascade proportional integral retarded controller. IFAC-Papersonline51(14): 61–65.
28.
MaghadeDPatreB (2012) Decentralized PI/PID controllers based on gain and phase margin specifications for TITO processes. ISA Transactions51(4): 550–558.
29.
MaghadeDPatreB (2014) Pole placement by PID controllers to achieve time domain specifications for TITO systems. Transactions of the Institute of Measurement and Control36(4): 506–522.
30.
MokadamHRPatreBMMaghadeDK (2013) Tuning of multivariable PI/PID controllers for TITO processes using dominant pole placement approach. International Journal of Automation and Control7(1–2): 21–41.
31.
NiculescuSIMichielsW (2004) Stabilizing a chain of integrators using multiple delays. IEEE Transactions on Automatic Control49(5): 802–807.
32.
NoedingMMartensenJLemkeN, et al. (2018) Selection of decoupling control methods suited for automated design for uncertain TITO processes. In: 2018 IEEE 14th international conference on control and automation (ICCA), Anchorage, AK, 12–15 June, pp. 498–505. New York: IEEE.
33.
OnatC (2019) A new design method for PI–PD control of unstable processes with dead time. ISA Transactions84: 69–81.
34.
ParkBESungSWLeeIB (2017) Design of centralized PID controllers for TITO processes. In: 2017 6th international symposium on advanced control of industrial processes (AdCONIP), Taipei, Taiwan, 28–31 May, pp. 523–528. New York: IEEE.
35.
PekerFKayaI (2017) Identification and real time control of an inverted pendulum using PI-PD controller. In: 2017 21st international conference on system theory, control and computing (ICSTCC), Sinaia, 19–21 October, pp. 771–776. New York: IEEE.
36.
PeramMMishraSVemulapatyM, et al. (2018) Optimal PI-PD and I-PD controller design using Cuckoo search algorithm. In: 2018 5th international conference on signal processing and integrated networks (SPIN), Noida, India, 22–23 February, pp. 643–646. New York: IEEE.
37.
RajapandiyanCChidambaramM (2012) Controller design for MIMO processes based on simple decoupled equivalent transfer functions and simplified decoupler. Industrial & Engineering Chemistry Research51(38): 12398–12410.
38.
RamírezASipahiR (2018) Fast consensus against noise in a large-scale multi-agent system with distributed proportional-retarded (PR) controllers. In: 2018 annual American control conference (ACC), Milwaukee, WI, 27–29 June, pp. 3666–3671. New York: IEEE.
39.
RamírezAGarridoRMondiéS (2015) Velocity control of servo systems using an integral retarded algorithm. ISA Transactions58: 357–366.
40.
RamírezAMondiéSGarridoR (2013) Proportional integral retarded control of second order linear systems. In: 52nd IEEE conference on decision and control, Firenze, 10–13 December, pp. 2239–2244. New York: IEEE.
41.
RamirezAMondiéSGarridoR, et al. (2015) Design of proportional-integral-retarded (PIR) controllers for second-order LTI systems. IEEE Transactions on Automatic Control61(6): 1688–1693.
42.
ReddyMLPadhyPKAnsariIA (2019) Auto-tuning method for decentralized PID controller of TITO systems using firefly algorithm. In: 2019 international conference on intelligent computing and control systems (ICCS), Madurai, India, 15–17May, pp. 683–688. New York: IEEE.
43.
SeborgDEMellichampDAEdgarTF, et al. (2010) Process Dynamics and Control. London: John Wiley & Sons.
44.
SinghVKPadhyP (2018) A new approach to PI-PD controller design using modified relay feedback. In: 2018 international conference on power energy, environment and intelligent control (PEEIC), Greater Noida, India, 13–14 April, pp. 349–353. New York: IEEE.
45.
SöylemezMTMunroNBakiH (2003) Fast calculation of stabilizing PID controllers. Automatica39(1): 121–126.
46.
SrivastavaSMisraASarkarA (2019) Analysis & design of robust PID controller with dominant pole placement approach. In: 2019 6th international conference on signal processing and integrated networks (SPIN), Noida, India, 7–8 March, pp. 908–914. New York: IEEE.
47.
SuhHBienZ (1980) Use of time-delay actions in the controller design. IEEE Transactions on Automatic Control25(3): 600–603.
48.
SuhIBienZ (1979) Proportional minus delay controller. IEEE Transactions on Automatic Control24(2): 370–372.
49.
SwisherGMTenqchenS (1988) Design of proportional-minus-delay action feedback controllers for second-and third-order systems. In: 1988 American control conference, Atlanta, GA, 15–17 June, pp. 254–260. New York: IEEE.
50.
VillafuerteRMondiéSGarridoR (2012) Tuning of proportional retarded controllers: Theory and experiments. IEEE Transactions on Control Systems Technology21(3): 983–990.
51.
WangHHanQLLiuJ, et al. (2020) Discrete-time filter proportional–integral–derivative controller design for linear time-invariant systems. Automatica116: 108918.
52.
WangQGZhangZAstromKJ, et al. (2009) Guaranteed dominant pole placement with PID controllers. Journal of Process Control19(2): 349–352.
53.
WutthithanyawatCWangnippamtoS (2018) Design of decentralized PID controller with coefficient diagram method based on inverted decoupling for TITO system. In: 2018 international electrical engineering congress (iEECON), Krabi, Thailand, 7–9 March, pp. 1–4. New York: IEEE.
54.
XiongQCaiWJ (2006) Effective transfer function method for decentralized control system design of multi-input multi-output processes. Journal of Process Control16(8): 773–784.
55.
XiongQCaiWJHeMJ (2007) Equivalent transfer function method for PI/PID controller design of MIMO processes. Journal of Process Control17(8): 665–673.
