Abstract
This paper derives some necessary conditions for output redefinition. It is shown that for defining a new output it should contain at least one linear term to have a well-defined relative degree. In addition, it is presented that by a static transformation on system output, relative degree and the zero dynamics of the system are not changed. Therefore, output signal is not enough for output redefinition to convert a non-minimum phase system to a minimum phase system and availability of required state variables or at least observability of the states is necessary.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Khalil HK (1996) Nonlinear systems. Prentice-Hall, New Jersey
Kokotovic PV, Arcak M (2001) Constructive nonlinear control: a historical perspective. Automatica 37(5):637–662
Massera JL (1956) Contributions to stability theory. Ann Math 64:182–206
DeCarlo RA, Zak SH, Matthews GP (1988) Variable stucture control of nonlinear mulivariable systems: a tutorial. In: IEEE, pp 212–232
Isidori A (1995) Nonlinear control systems, 3rd edn. Springer, London
Qui L, Davison EJ (1993) Performance limitations of nonminimum phase systems in the servomechanism problem. Automatica 29:337–349
Utkin VI (1992) Sliding modes in control and optimization. Springer, Berlin
Chang J-L (2011) Dynamic output feedback sliding mode control for nonminimum phase linear systems with disturbance attenuation. Asian J Control 13(4):562–569
Al-Hiddabi SA, McClamroch NH (2002) Aggressive longitudinal aircraft trajectory tracking using nonlinear control. J Guid Control Dyn 25(1):26–32
Hauser J, Sastry S, Meyer G (1992) Nonlinear control design for slightly nonminimum phase systems: application to V/STOL aircraft. Automatica 28(4):665–679
Kwon D, Book WJ (1994) A time-domain inverse dynamic tracking control of a single-link flexible manipulator. ASME J Dyn Syst Meas Control 116(2):193–200
Lin F, Zhang W, Brandt R (1999) Robust hovering control of a PVTOL aircraft. IEEE Trans Control Syst Technol 7(3):343–351
Zhang Y, Zhu Q, Xiong R (2018) Precise tracking for continuous-time non-minimum phase systems. Asian J Control 21(5):2395–2406
Devasia S, Chen D, Paden B (1996) Nonlinear inversion-based output tracking. IEEE Trans Autom Control 41:930–943
Kinosita K, Sogo T, Adachi N (2002) Iterative learning control using adjoint systems and stable inversion. Asian J Control 4(1):60–67
Zhu Q, Zhang Y, Xiong R (2018) Stable inversion based precise tracking for periodic systems. Asian J Control 22:217
Moallem M, Khorasani K, Patel RV (1996) Tip position tracking of flexible multi-link manipulators: an integral manifold approach. In: Paper presented at the IEEE international conference on robotics and automation, Minneapolis, Minnesota
Moallem M, Patel RV, Khorasani K (1996) An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators. In: Paper presented at the international federation of automatic control (IFAC) World Congress, San Francisco
Wu W (1999) Adaptive nonlinear control of non-minimum phase processes. Chem Eng Sci 54:3815–3829
Cheng D (2000) Stabilization of a class of nonlinear non-minimum phase systems. Asian J Control 2(2):132–139
Gopalswamy S, Hedrick JK (1993) Tracking nonloinear non-minimum phase systems using sliding control. Int J Control 57(5):1141–1158
Slotine JE, Li W (1991) Applied nonlinear control. Prentice-Hall, Englewood Cliffs
Wang D, Vidyasagar M (1989) Transfer functions for a single flexible link. In: Proceedings of IEEE international conference on robotics and automation, pp 1042–1047
Benvenuti L, Benedetto DIMD, Grizzle JW (1994) Approximate output tracking for nonlinear non-minimum phase systems with an application to flight control. Int J Robust Nonlinear Control 4(3):397–414
Ho D, Hedrick JK (2015) Control of nonlinear non-minimum phase systems with input-output linearization. In: Paper presented at the American Control Conference, Chicago
Hu A, Sadegh N (2001) Nonlinear non-minimum phase output tracking via output redefinition and learning control. In: Proceedings of the American control conference, Arlington, VA, pp 4264–4269
Talebi HA, Patel RV, Khorasani K (2001) Control of flexible-link manipulators using neural networks. Springer, London
Yang H, Krishnon H, Angi MH (2000) Tip-trajectory tracking control of single-link flexible robots by output redefinition. In: IEE proceedings -control theory and applications, pp 580–587
Jahangiri F, Talebi HA, Menhaj MB, Ebenbauer C (2018) A novel scheme for output redefinition in feedback passivation of nonlinear systems. Int J Syst Sci 49:1
Enns D, Bugajski DJ, Hendrick RC, Stein G (1994) dynamic inversion: an evolving methodology for flight control design. Int J Control 59(1):71–91
Necsulescu D, Jiang Y-W, Kim B (2007) Neural network based feedback linearization control of an unmanned aerial vehicle. Int J Autom Comput 4(1):71–79
Shao-lei Z, Yu-ting X, Zuo-e F, Peng-cheng H (2010) Design of an adaptive fuzzy sliding mode controller for uncertain anti-ship missiles. In: Paper presented at the 2010 international conference on computer design and applications
Jahangiri F, Talebi HA, Menhaj MB, Ebenbauer C, Allgoewer F (2014) A new method for finding minimum phase outputs. In: Paper presented at the 53rd IEEE conference on decision and control, California, December 2014
Jahangiri F, Talebi HA, Menhaj MB, Ebenbauer C (2016) A new approach for minimum phase output definition. Int J Syst Sci 48(2):264–271
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jahangiri, F., Talebi, H.A. & Menhaj, M.B. Some necessary conditions on output redefinition in non-minimum phase systems. Int. J. Dynam. Control 9, 173–178 (2021). https://doi.org/10.1007/s40435-020-00630-1
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40435-020-00630-1