Characteristic Functions Assignment by Adding Perturbation

Document Type : Technical Paper

Authors

‎Electrical Engineering Department, ‎Imam Khomeini International University, ‎Qazvin‎, ‎I‎. ‎R‎. ‎Iran

Abstract

‎This paper presents a method for characteristic function assignment on rational functions by adding perturbation in systems with irrational characteristic functions‎. ‎Generally‎, ‎in systems with irrational characteristic loci‎, ‎commutative compensator designs are not possible‎. ‎Irrational characteristic functions have different forms‎. ‎In our previous work‎, ‎mentioned in the introduction section‎, ‎a form of these characteristic functions was presented‎. ‎Another form of irrational characteristic functions is considered in this paper‎. ‎This approach is not based on the transfer function inverting‎, ‎and characteristic loci are not used directly in the design process‎. ‎The efficacy of the proposed approach is investigated through two numerical examples‎.

Keywords

Main Subjects


[1] J. P. Corriou, Process Control, Springer, London, 2004.
[2] J. M. Maclejowski, Multivariable Feedback Design, Electronic Systems Engineering Series, 1989.
[3] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, John Wiley and Sons, 2005.
[4] D. J. Cloudt and B. Kouvaritakis, Commutative controllers revisited: parallel computation, a new lease of life, Int. J. Control 45 (1987) 1335 - 1370, https://doi.org/10.1080/00207178708933812.
[5] M. V. Moreira and J. C. Basilio, Characteristic locus method robustness improvement through optimal static normalizing precompensation, Int. J. Robust Nonlinear Control 20 (2010) 371 - 386, https://doi.org/10.1002/rnc.1429.
[6] M. V. Moreira and J. C. Basilio, Static normalizing pre-compensator: the first step for addressing robustness in the design of multivariable controllers using the characteristic locus method, In 2007 European Control Conference (ECC),
IEEE, (2007) 1142 - 1148, https://doi.org/10.23919/ECC.2007.7068932.
[7] J. Doyle and G. Stein, Multivariable feedback design: concepts for a classical/ modern synthesis, IEEE Trans. Autom. Control 26 (1981) 4 - 16, https://doi.org/10.1109/TAC.1981.1102555.
[8] I. Postlethwaite, Sensitivity of the characteristic gain loci, Automatica 18 (6) (1982) 709 - 712, https://doi.org/10.1016/0005-1098(82)90059-0.
[9] J. C. Basilio and B. Kouvaritakis, The use of rational eigenvector approximations in commutative controllers, Int. J. Control 61 (1995) 333- 356, https://doi.org/10.1080/00207179508921906.
[10] J. C. Basilio and J. A. Sahate, A normalizing precompensator for the design of effective and reliable commutative controllers, Int. J. Control 73 (2000) 1280- 1297, https://doi.org/10.1080/002071700421673.
[11] M. V. Moreira, J. C. Basilio and B. Kouvaritakis, Rational stabilising commutative controllers: parameterisation and characterisation of degrees of freedom, Int. J. Control 79 (2006) 1601 - 1612, https://doi.org/10.1080/00207170600867073.
[12] Y. K. Foo, Design of robust decentralised large-scale inter-connected control systems via characteristic locus method, Int. J. Syst. Sci. 44 (2013) 641-651, https://doi.org/10.1080/00207721.2011.617897.
[13] M. V. Moreira and J. C. Basilio, Design of normalizing precompensators via alignment of output-input principal directions, Proceedings of the 44th IEEE Conference on Decision and Control, (2005) 2170 - 2175,
https://doi.org/10.1109/CDC.2005.1582483.
[14] A. Shahmansoorian and P. Ahmadi, Assignment of characteristic functions and a new method for stabilizing multivariable systems, Circuits, Syst. Signal Process. 40 (2021) 5983-5996, https://doi.org/10.1007/s00034-021-01762-1.