Abstract
To tackle systems with both uncertainties and time delays, several modified active disturbance rejection control (ADRC) methods, including delayed designed ADRC (DD-ADRC), polynomial based predictive ADRC (PP-ADRC), Smith predictor based ADRC (SP-ADRC) and predictor observer based ADRC (PO-ADRC), have been proposed in the past years. This paper is aimed at rigorously investigating the performance of these modified ADRCs, such that the improvements of each method can be demonstrated. The capability to tackle time delay, the necessity of stable open loop and the performance of rejecting uncertainties for these methods are fully studied and compared. It is proven that large time delay cannot be tolerated for the stability of the closed-loop systems based on DD-ADRC and PP-ADRC. Moreover, stable open loop is shown to be necessary for stabilizing the closed-loop systems based on SP-ADRC. Furthermore, the performance of rejecting the “total disturbance” at low frequency for these modified ADRCs is evaluated and quantitatively discussed. Finally, the simulations of a boiler turbine system illustrate the theoretical results.
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References
Moore R L. The Dynamic Analysis of Automatic Process Control. Durham: Instrument Society of America, 1985
Wu X, Shen J, Li Y G, et al. Steam power plant configuration, design, and control. Wiley Interdisciplinary Rev Energy Environ, 2015, 4: 537–563
Niculescu S I. Delay Effects on Stability: a Robust Control Approach. London: Springer, 2001
Kolmanovskii V, Myshkis A. Introduction to the Theory and Applications of Functional Differential Equations. Dordrecht: Kluwer Academic Publishers, 1999
Smith O J M. Close control of loops with dead time. Chem Eng Prog, 1957, 53: 217–219
Krstic M. Delay Compensation for Nonlinear, Adaptive, and PDE Systems. Boston: Birkh¨auser, 2009
Xi Y G, Li D W, Lin S. Model predictive control — status and challenges. Acta Automatica Sin, 2013, 39: 222–236
Richard J P. Time-delay systems: an overview of some recent advances and open problems. Automatica, 2003, 39: 1667–1694
Normey-Rico J E, Camacho E F. Dead-time compensators: a survey. Control Eng Practice, 2008, 16: 407–428
Palmor Z J, Halevi Y. On the design and properties of multivariable dead time compensators. Automatica, 1983, 19: 255–264
Mayne D Q, Rawlings J B, Rao C V, et al. Constrained model predictive control: stability and optimality. Automatica, 2000, 36: 789–814
Zhong Q C, Normey-Rico J E. Control of integral processes with dead-time. Part 1: disturbance observer-based 2DOF control scheme. IEE Proc Control Theor Appl, 2002, 149: 285–290
Kim S Y, Lee W, Rho M S, et al. Effective dead-time compensation using a simple vectorial disturbance estimator in PMSM drives. IEEE Trans Ind Electron, 2010, 57: 1609–1614
Shimmyo S, Ohnishi K. Disturbance observer for dead-time compensation with variable gain and its stability analysis based on Popov criterion. In: Proceedings of the 41st Annual Conference of the IEEE Industrial Electronics Society, Yokohama, 2015. 2550–2555
Yang J, Li S, Chen X, et al. Disturbance rejection of dead-time processes using disturbance observer and model predictive control. Chem Eng Res Des, 2011, 89: 125–135
Wang C, Yang J, Zuo Z, et al. Output feedback disturbance rejection for a class of linear systems with input delay via DOBC approach. In: Proceedings of the 35th Chinese Control Conference, Chengdu, 2016. 136–141
Han J. Active disturbance rejection control for time delay systems (in Chinese). Control Eng China, 2008, 15: 7–18
Tan W, Fu C F. Analysis of active disturbance rejection control for processes with time delay. In: Proceedings of American Control Conference (ACC), Chicago, 2015. 3962–3967
Zheng Q, Gao Z. Predictive active disturbance rejection control for processes with time delay. ISA Trans, 2014, 53: 873–881
Zhao S, Gao Z. Modified active disturbance rejection control for time-delay systems. ISA Trans, 2014, 53: 882–888
Chen S, Xue W, Huang Y, et al. On comparison between smith predictor and predictor observer based adrcs for nonlinear uncertain systems with output delay. In: Proceedings of American Control Conference (ACC), Seattle, 2017. 5083–5088
Xue W C, Liu P, Chen S, et al. On extended state predictor observer based active disturbance rejection control for uncertain systems with sensor delay. In: Proceedings of the 16th International Conference on Control, Automation and Systems, Gyeongju, 2016. 1267–1271
Han J. From PID to active disturbance rejection control. IEEE Trans Ind Electron, 2009, 56: 900–906
Xue W, Huang Y. Performance analysis of active disturbance rejection tracking control for a class of uncertain LTI systems. ISA Trans, 2015, 58: 133–154
Xue W, Huang Y. Performance analysis of 2-DOF tracking control for a class of nonlinear uncertain systems with discontinuous disturbances. Int J Robust NOnlinear Control, 2018, 28: 1456–1473
Zhao Z L, Guo B Z. A novel extended state observer for output tracking of mimo systems with mismatched uncertainty. IEEE Trans Autom Control, 2018, 63: 211–218
Tan W, Fang F, Tian L, et al. Linear control of a boiler-turbine unit: analysis and design. ISA Trans, 2008, 47: 189–197
Sbarciog M, de Keyser R, Cristea S, et al. Nonlinear predictive control of processes with variable time delay. A temperature control case study. In: Proceedings of IEEE International Conference on Control Applications (CCA), San Antonio, 2008. 1001–1006
Normey-Rico J E, Camacho E F. Unified approach for robust dead-time compensator design. J Process Control, 2009, 19: 38–47
Normey-Rico J E. Control of Dead-Time Processes. London: Springer, 2007
Wood R K, Berry M W. Terminal composition control of a binary distillation column. Chem Eng Sci, 1973, 28: 1707–1717
Chen S, Bai W, Huang Y. ADRC for systems with unobservable and unmatched uncertainty. In: Proceedings of the 35th Chinese Control Conference (CCC), Chengdu, 2016. 337–342
Hang C C, Chin D. Reduced order process modelling in self-tuning control. Automatica, 1991, 27: 529–534
Halevi Y. Optimal reduced order models with delay. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton, 1991. 602–607
Gao Z Q. Scaling and bandwidth-parameterization based controller tuning. In: Proceedings of American Control Conference (ACC), Denver, 2003. 4989–4996
Acknowledgements
This work was supported in part by National Natural Science Foundation of China (Grant Nos. 61633003-3, 61603380), and National Basic Research Program of China (973 Program) (Grant No. 2014CB845301).
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Chen, S., Xue, W., Zhong, S. et al. On comparison of modified ADRCs for nonlinear uncertain systems with time delay. Sci. China Inf. Sci. 61, 70223 (2018). https://doi.org/10.1007/s11432-017-9403-x
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DOI: https://doi.org/10.1007/s11432-017-9403-x