Abstract
As shown in the previous chapters, several different control schemes for integral processes with dead time resulted in the same disturbance response. Moreover, it has already been shown that such a response is sub-ideal (Mirkin and Zhong, IEEE Trans. Autom. Control 48(11), 1999–2004, 2003; Zhong, Robust Control of Time-delay Systems, Springer, Berlin, 2006). In this chapter, the achievable specifications of this disturbance response and the robust stability regions of the system are quantitatively analysed. The control parameter is quantitatively determined with compromise between the disturbance response and the robustness. Four specifications—(normalised) maximal dynamic error, maximal decay rate, (normalised) control action bound, and approximate recovery time—are given to characterise the step-disturbance response. It shows that any attempt to obtain a (normalised) dynamic error less than L m is impossible, and a sufficient condition on the (relative) gain-uncertainty bound is \(\frac{\sqrt{3}}{2}\).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
e without a subscript stands, as usual, for the exponential constant.
References
Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: On the Lambert W function. Adv. Comput. Math. 5, 329–359 (1996). Available at http://www.apmaths.uwo.ca/~rcorless/frames/papers.htm, accessed on 3/9/2005
Mirkin, L., Zhong, Q.-C.: Coprime parametrization of 2DOF controller to obtain sub-ideal disturbance response for processes with dead time. In: Proceedings IEEE International Conference on Decision and Control, pp. 2253–2258, Orlando, USA, December 2001
Mirkin, L., Zhong, Q.-C.: 2DOF controller parametrization for systems with a single I/O delay. IEEE Trans. Autom. Control 48(11), 1999–2004 (2003)
Normey-Rico, J.E., Camacho, E.F.: Robust tuning of dead-time compensators for process with an integrator and long dead-time. IEEE Trans. Autom. Control 44(8), 1597–1603 (1999)
Smith, O.J.M.: Feedback Control Systems. McGraw-Hill, New York (1958)
Zhang, W., Sun, Y.X.: Modified Smith predictor for controlling integrator/time delay process. Ind. Eng. Chem. Res. 35, 2769–2772 (1996)
Zhong, Q.-C.: Robust stability analysis of simple systems controlled over communication networks. Automatica 39(7), 1309–1312 (2003)
Zhong, Q.-C.: Robust Control of Time-delay Systems. Springer, Berlin (2006)
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 Theory Appl. 149(4), 285–290 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2011 Springer-Verlag London Limited
About this chapter
Cite this chapter
Visioli, A., Zhong, QC. (2011). Quantitative Analysis. In: Control of Integral Processes with Dead Time. Advances in Industrial Control. Springer, London. https://doi.org/10.1007/978-0-85729-070-0_11
Download citation
DOI: https://doi.org/10.1007/978-0-85729-070-0_11
Publisher Name: Springer, London
Print ISBN: 978-0-85729-069-4
Online ISBN: 978-0-85729-070-0
eBook Packages: EngineeringEngineering (R0)