Robust H ∞ control of single input-delay systems based on sequential sub-predictors
- Author(s): Majdeddin Najafi 1 ; Farid Sheikholeslam 2 ; Qing-Guo Wang 2 ; Saeed Hosseinnia 3
-
-
View affiliations
-
Affiliations:
1:
Avionics Research Institute, Isfahan University of Technology, Isfahan, Iran;
2: Department of Electrical and Computer Engineering, Isfahan University of Technology, Isfahan, Iran;
3: Department of Electrical Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
-
Affiliations:
1:
Avionics Research Institute, Isfahan University of Technology, Isfahan, Iran;
- Source:
Volume 8, Issue 13,
04 September 2014,
p.
1175 – 1184
DOI: 10.1049/iet-cta.2012.1004 , Print ISSN 1751-8644, Online ISSN 1751-8652
This study presents an approach to the H ∞ control of linear input-delay systems. First, an H ∞ state predictor is introduced for dead-time systems with disturbance input and measurable outputs. The author's proposed method focuses on optimisation of the disturbance propagation in sequential sub-predictors (SSP). Each of the predictors is employed to forecast the state for one portion of the delay. The H ∞ performance of the prediction error can be improved by increasing the number of predictors. Consequently, an H ∞ controller is designed for the standard H ∞ problem of dead-time systems using SSP. More importantly, the SSP method is extended to the robust H ∞ control in presence of uncertainties. Some examples are given to illustrate the effectiveness of proposed method.
Inspec keywords: robust control; H∞ control; linear systems; control system synthesis; delay systems
Other keywords: single input-delay systems; disturbance propagation; prediction error; SSP method; linear input-delay systems; H∞ state predictor; robust H∞ control; sequential sub-predictors; dead-time systems
Subjects: Stability in control theory; Control system analysis and synthesis methods; Distributed parameter control systems; Optimal control
References
-
-
1)
- M.-T. Ho . Synthesis of H∞ PID controllers: a parametric approach. Automatica , 6 , 1069 - 1075
-
2)
- C.J. Doyle , K. Glover . State space solution to standard H2 and H∞ control problems. IEEE Trans. Autom. Control , 8 , 831 - 847
-
3)
-
20. Santos, T.L.M., Limon, D., Normey-Rico, J.E., Raffo, G.V.: ‘Dead-time compensation of constrained linear systems with bounded disturbances: output feedback case’, IET Control Theory Appl., 2013, 7, (1), pp. 52–59 (doi: 10.1049/iet-cta.2012.0684).
-
-
4)
-
14. Kirtania, K., Choudhury, M.A.A.S.: ‘A novel dead-time compensator for stable processes with long dead times’, J. Process Control, 2012, 22, pp. 612–625 (doi: 10.1016/j.jprocont.2012.01.003).
-
-
5)
-
11. Chien, I.L., Peng, S.C., Liu, G.H.: ‘Simple control method for integrating processes with long dead time’, J. Process Control, 2002, 12, pp. 391–404 (doi: 10.1016/S0959-1524(01)00040-3).
-
-
6)
-
3. Normey-Rico, J.E., Camacho, E.F.: ‘Unified approach for robust dead-time compensator design’, J. Process Control, 2009, 19, pp. 38–47 (doi: 10.1016/j.jprocont.2008.02.003).
-
-
7)
-
38. Du, B., Lam, J., Shu, Z.: ‘Strong stabilisation by output feedback controller for linear systems with delayed input’, IET Control Theory Appl., 2012, 6, (10), pp. 1329–1340 (doi: 10.1049/iet-cta.2011.0312).
-
-
8)
-
17. Artstien, Z.: ‘Linear systems with delayed controls: a reduction’, IEEE Trans. Autom. Control, 1989, 27, (5), pp. 869–879.
-
-
9)
- W.H. Kwon , A.E. Pearson . Feedback stabilization of linear systems with delayed control. IEEE Trans. Autom. Control , 2 , 266 - 269
-
10)
-
32. Mirkin, L., Raskin, N.: ‘State-space parameterization of all stabilizing dead-time controllers’. Proc. 38th Conf. on Decision & Control, Phoenix, Arizona, USA, 1999, pp. 221–226.
-
-
11)
- I.R. Petersen . A stabilization algorithm for a class of uncertain linear systems. Syst. Control Lett , 4 , 351 - 357
-
12)
-
7. Wang, D., Zhou, D., Jin, Y., Qin, S.J.: ‘A strong tracking predictor for nonlinear processes with input time delay’, Comput. Chem. Eng., 2004, 28, pp. 2523–2540 (doi: 10.1016/j.compchemeng.2004.06.013).
-
-
13)
- L.E. Ghaoui , F. Oustry , M. AitRami . A cone complementarity linearization algorithm for static output-feedback and related problems. IEEE Trans. Autom. Control , 8 , 1171 - 1176
-
14)
-
28. Zames, G., Mitter, S.K.: ‘A note on essential spectra and norms of mixed Hankel–Toeplitz operators’, Syst. Control Lett., 1988, 10, pp. 159–165 (doi: 10.1016/0167-6911(88)90047-3).
-
-
15)
-
30. Albertos, P., García, P.: ‘Robust control design for long time-delay systems’, J. Process Control, 2009, 19, pp. 1640–1648 (doi: 10.1016/j.jprocont.2009.05.006).
-
-
16)
-
25. Zhou, K., Khargonekar, P.P.: ‘On the weighted sensitivity minimization problem for delay systems’, Syst. Control Lett., 1987, 8, pp. 307–312 (doi: 10.1016/0167-6911(87)90096-X).
-
-
17)
-
34. Zhong, Q.C.: ‘On standard H∞ control of processes with a single delay’, IEEE Trans. Autom. Control, 2003, 48, (6), pp. 1097–1103 (doi: 10.1109/TAC.2003.812818).
-
-
18)
-
16. Najafi, M., Hosseinnia, S., Sheikholeslam, F., Karimadini, M.: ‘Closed-loop control of dead time systems via sequential sub-predictors’, Int. J. Control, 2013, 86, (4), pp. 599–609 (doi: 10.1080/00207179.2012.751627).
-
-
19)
-
2. Sheng, J., Ding, Z.: ‘Optimal consensus control of linear multi-agent systems with communication time delay’, IET Control Theory Appl., 2013, 7, (15), pp. 1899–1905 (doi: 10.1049/iet-cta.2013.0478).
-
-
20)
-
9. Wang, Q.G., Lee, T.H., Tan, K.K.: ‘Finite spectrum assignment for time delay systems’ (Springer-Verlag, London, 1999).
-
-
21)
-
44. Xu, S., Lam, J.: ‘Improved delay-dependent stability criteria for time delay systems’, IEEE Trans. Autom. Control, 2005, 50, (4), pp. 384–387.
-
-
22)
-
26. Zwart, H.J., Curtain, R.F., Partington, J.R., Glover, K.: ‘Partial fractions expansions for delay systems’, SIAM J. Control Optim., 1988, 32, pp. 808–830.
-
-
23)
-
24. Tadmor, G.: ‘H∞ interpolation in systems with commensurate input lags’, SIAM J. Control Optim., 1989, 27, pp. 511–526 (doi: 10.1137/0327027).
-
-
24)
-
31. Meinsma, G., Zwart, H.: ‘On H∞ control for dead-time systems’, IEEE Trans. Autom. Control, 2000, AC-45, (3), pp. 272–285 (doi: 10.1109/9.839949).
-
-
25)
- G. Tadmor . The standard H∞ problem in systems with a single input delay. IEEE Trans. Autom. Control. , 3 , 382 - 397
-
26)
-
18. Mirkin, L., Raskin, N.: ‘Every stabilizing dead-time controller has an observer-predictor-based structure’, Automatica, 2003, 39, (10), pp. 1747–1754 (doi: 10.1016/S0005-1098(03)00182-1).
-
-
27)
-
21. Nikolaos, B.L., Miroslav, K.: ‘Robustness of nonlinear predictor feedback laws to time-and state-dependent delay perturbations’, Automatica, 2013, 49, (6), pp. 1576–1590 (doi: 10.1016/j.automatica.2013.02.050).
-
-
28)
- K. Watanabe , M. Ito . A process-model control for linear systems with delay. IEEE Trans. Autom. Contr. , 6 , 1261 - 1269
-
29)
-
10. Zhong, Q., Weiss, G.: ‘A unified smith predictor based on the spectral decomposition of the plant’, Int. J. Control, 2004, 77, pp. 1362–1371 (doi: 10.1080/0020717042000297171).
-
-
30)
-
33. Zhong, Q.C.: ‘Frequency domain solution to delay-type Nehari problem’, Automatica, 2003, 39, pp. 499–508 (doi: 10.1016/S0005-1098(02)00246-7).
-
-
31)
-
5. Smith, O.J.M.: ‘Closer control of loops with dead-time’, Chem. Eng. Progr., 1957, 53, pp. 217–219.
-
-
32)
-
27. Glover, K., Partington, J.R.: ‘Robust stabilization of delay systems by approximation of co-prime factors’, Syst.Control Lett., 1990, 14, pp. 325–331.
-
-
33)
-
22. Foias, C., Tannenbaum, A., Zames, G.: ‘Weighted sensitivity minimization for delay systems’, IEEE Trans. Autom. Control, 1986, AC-31, pp. 763–766 (doi: 10.1109/TAC.1986.1104398).
-
-
34)
-
4. Huaicheng, Y., Zhenzhen, S., Hao, Z., Fuwen, Y.: ‘Observer-based H∞ control for discrete-time stochastic systems with quantisation and random communication delays’, IET Control Theory Appl., 2013, 7, (3), pp. 372–379 (doi: 10.1049/iet-cta.2012.0600).
-
-
35)
-
40. Dugard, L., Verriest, E.I.: ‘Stability and control of time-delay systems’ (Springer, 1997).
-
-
36)
-
43. Lee, S.C., Wang, Q.G., Nguyen, L.B.: ‘Stabilizing control for a class of delay unstable processes’, ISA Trans., 2010, 49, (3), pp. 318–325 (doi: 10.1016/j.isatra.2010.03.006).
-
-
37)
-
23. Flamm, D., Mitter, S.: ‘H∞ sensitivity minimization for delay systems’, Syst. Control Lett., 1987, 9, pp. 17–24 (doi: 10.1016/0167-6911(87)90004-1).
-
-
38)
-
12. Matausek, M.R., Ribic, A.I.: ‘Control of stable, integrating and unstable processes by the modified Smith predictor’, J. Process Control, 2012, 22, pp. 338–343 (doi: 10.1016/j.jprocont.2011.08.006).
-
-
39)
-
36. Nagpal, K.M., Ravi, R.: ‘H∞ control and estimation problems with delayed measurements: state-space solutions’, SIAM J. Control Optim., 1997, 35, (4), pp. 1217–1243 (doi: 10.1137/S0363012994277499).
-
-
40)
- W. Chen , S. Chang , W. Zhang . Linear matrix inequality-based repetitive controller design for linear systems with time-varying input delay. IET Control Theory Appl. , 6 , 1071 - 1078
-
41)
-
1. Bolea, Y., Puig, V., Blesa, J.: ‘Gain-scheduled Smith proportional–integral derivative controllers for linear parameter varying first-order plus time-varying delay systems’, IET Control Theory Appl., 2011, 5, (15), pp. 2142–2155 (doi: 10.1049/iet-cta.2010.0088).
-
-
42)
-
15. Garcia, P., Albertos, P.: ‘Dead-time-compensator for unstable MIMO systems with multiple time delays’, J. Process Control, 2010, 20, pp. 877–884 (doi: 10.1016/j.jprocont.2010.05.009).
-
-
43)
-
19. Karafyllis, , I., , Krstic, , M., : ‘Delay-robustness of linear predictor feedback without restriction on delay rate’, Automatica, 2013, 49, (6), pp. 1767–1767 (doi: 10.1016/j.automatica.2013.02.019).
-
-
44)
-
13. Flesch, R.C.C., Torrico, B.C., Normey-Rico, J.E., Cavalcante, M.U.: ‘Unified approach for minimal output dead time compensation in MIMO processes’, J. Process Control, 2011, 21, pp. 1080–1091 (doi: 10.1016/j.jprocont.2011.05.005).
-
-
45)
-
35. Zhong, Q.C.: ‘H∞ control of dead-time systems based on a transformation’, Automatica, 2003, 39, pp. 361–366 (doi: 10.1016/S0005-1098(02)00225-X).
-
-
46)
- M. Sun , Y. Jia . Delay dependent robust H∞ control of time-delay systems. IET Control Theory Appl. , 1122 - 1130
-
1)