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A Matlab program for control of time-delay systems using modified Smith predictors.


Presence of time-delay always means serious complications in process control and therefore this phenomenon has been widely studied (Richard, 2003). The relatively effective tool for compensation of time-delay term represents the classical Smith predictor which has been known to automation community since 1959 (Smith). On the other hand, this control structure has also its disadvantages and limitations.

Naturally, some of drawbacks have been eliminated by improving the idea and creating many modifications of Smith predictor (Watanabe & Ito, 1981); (Astrom et al., 1994); (Matausek & Micic, 1996); (Majhi & Atherton, 1998); (Kaya & Atherton, 1999); (Hamamci et al., 2001). Furthermore, several of them have been applied also to other problems, e.g. to control of systems with time-varying delay (Matusu & Prokop, 2010a); (Matusu & Prokop, 2011).

This contribution describes facilities of a Matlab environment for control of time-delay systems using three selected modifications of Smith Predictor (Matusu & Prokop, 2010b). The program is a translated version of the one created under the scope of the Master's Theses (Matusu, 2002).


As it has been outlined above, three modifications of classical Smith predictor have been studied and implemented into the software support. More specifically it covers:

* Modified Smith predictor for unstable and integrating processes (Majhi & Atherton, 1998).

* Modified PI-PD Smith predictor for systems with long dead time (Kaya & Atherton, 1999).

* Modified Smith predictor design by CDM (Hamamci et al., 2001).

All three incorporated methods have improved the Smith predictor loop using more sophisticated and complicated structure with additional controllers. An example of such embellishment is depicted in fig. 1, which shows the modified Smith predictor structure for CDM with trio of controllers [G.sub.c1](s), [G.sub.c2](s) and [G.sub.c3](s) (Hamamci et al., 2001). Due to the limited space, other structures can be found in respective literature or in the program itself (Matusu & Prokop, 2010b).

Anyway, all the methods use mathematical model of really controlled plant including time-delay term in the inner loop.

Moreover, this model is assumed also during design of controllers as a nominal system.


The controller synthesis itself is based on various approaches and techniques according to the applied modification. For example the standard forms for obtaining the optimal closed-loop transfer function parameters in the meaning of integral squared time error (ISTE) criterion; a simple algebraic approach to control system design; coefficient diagram; modification of Kessler standard form; or Lipatov stability analysis have been utilized (Matausek & Micic, 1996); (Majhi & Atherton, 1998); (Manabe, 1998); (Kaya & Atherton, 1999); (Hamamci et al., 2001); (Hamamci & Ucar, 2002); etc. The final relations for controller design have been usually pre-derived for first and second order time-delay plants.


The software package with basic instructions can be freely downloaded from the web page (Matusu & Prokop, 2010b). The main window of the program GUI (fig. 2) allows selecting the modification which should be used for a whole control experiment.


Subsequently, sort of controlled system (e.g. first order, second order or integrating plant as a special type) can be chosen together with fundamental properties of the experiment (simulation time, reference signal, disturbances)--see fig. 3.

In the next step, coefficients of the controlled system of specific type and possibly some other additional parameters depending on the used method can be set as illustrated in fig. 4. However, the program permits not only adjustment of nominal system (considered as a model for control design and in control loop--fig. 1), but also of the perturbed system (used as a really controlled plant) with potentially different coefficients.




Finally, the program computes the controllers and opens the Simulink scheme where control behaviour with the preset values can be simulated. An example is shown in fig. 5.


The paper has been focused on description of the program for control of time-delay systems using modified Smith predictor for unstable and integrating processes, modified PIPD Smith predictor for systems with long dead time, and modified Smith predictor design by CDM. The software has been created in Matlab R13 but tested also under several newer versions.


The work was supported by the Ministry of Education, Youth and Sports of the Czech Republic under Research Plan No. MSM 7088352102. This aid is gratefully acknowledged.


Astrom, K. J.; Hang, C. C. & Lim, B. C. (1994). A new Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control, Vol. 39, No. 2, pp. 343-345

Hamamci, S. E. & Ucar, A. (2002). A robust model-based control for uncertain systems. Transactions of the Institute of Measurement and Control, Vol. 24, No. 5, pp. 431-445

Hamamci, S. E.; Kaya, I. & Atherton, D. P. (2001). Smith predictor design by CDM. In: Proceedings of the European Control Conference, Porto, Portugal

Kaya, I. & Atherton, D. P. (1999). A new PI-PD Smith predictor for control of processes with long dead time. In: Proceedings of the 14th IFAC World Congress, Beijing, China

Majhi, S. & Atherton, D. P. (1998). A new Smith predictor and controller for unstable and integrating processes with time delay. In: Proceedings of the 37th IEEE Conference on Decision & Control, Tampa, Florida, USA

Manabe, S. (1998). Coefficient diagram method. In: Proceedings of the 14th IFAC Symposium on Automatic Control in Aerospace, Seoul, Korea

Matausek, M. R. & Micic, A. D. (1996). A modified Smith predictor for controlling a process with an integrator and long dead-time. IEEE Transactions on Automatic Control, Vol. 41, No. 8, pp. 1199-1203

Matusu, R. & Prokop, R. (2010a). Control of Systems with Time-Varying Delay: A Comparison Study. In: Proceedings of the 12th WSEAS International Conference on Automatic Control, Modelling and Simulation, Catania, Italy

Matusu, R. & Prokop, R. (2010b). Control of Time-Delay Systems Using Modified Smith Predictors, Available from:, Accessed: 2010-07-07

Matusu, R. & Prokop, R. (2011). Various approaches to control of systems with time-varying delay. International Journal of Modelling, Identification and Control, Manuscript accepted for publication

Matusu, R. (2002). Control of time-delay systems. (Rizeni systemu s dopravnlm zpozdenim). Master's Theses, Faculty of Technology, Tomas Bata University in Zlin. (In Czech).

Richard, J.-P. (2003). Time-delay system: an overview of some recent advances and open problems. Automatica, Vol. 39, No. 10, pp. 1667-1694

Smith, O. J. M. (1959). A controller to overcome dead time. ISA Journal, Vol. 6, No. 2, pp. 28-33.

Watanabe, K. & Ito, M. (1981). A process-model control for linear systems with delay. IEEE Transactions on Automatic Control, Vol. 26, No. 6, pp. 1261-1269
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Author:Matusu, Radek; Prokop, Roman
Publication:Annals of DAAAM & Proceedings
Article Type:Report
Geographic Code:1USA
Date:Jan 1, 2010
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