H∞ Control Oriented LFT Modelling of Linear Dynamical System

H∞ Control Oriented LFT Modelling of Linear Dynamical System

Tamal Roy* Ranjit Kumar Barai Rajeeb Dey

Electrical Engineering Department, MCKV Institute of Engineering Liluah, Howrah 711204, India

Electrical engineering Department, Jadavpur University, Kolkata 700032, India

Electrical Engineering Department NIT, Silchar, Assam 788010, India

Corresponding Author Email: 
tamalroy77@gmail.com
Page: 
189-196
|
DOI: 
https://doi.org/10.18280/ama_c.730408
Received: 
29 June 2018
| |
Accepted: 
15 October 2018
| | Citation

OPEN ACCESS

Abstract: 

This paper presents a systematic formulation of control-oriented linear fractional transformation (LFT) modelling of the linear dynamical system, truly integrates the objective of control theory. A novel methodology has been introduced for modeling quality improvement to achieve certain performance specification considering the modeling uncertainties arising due to the difference between the mathematical model and the actual system and the presence of disturbance signal during the formulation of LFT framework. For the convenience of compact modelling, the generalized transfer function of the linear dynamical system has been represented into the LFT framework by incorporating the real parametric uncertainties enter rationally into the system modelling. The generalized LFT modeling algorithm is convenient to address the issues like identifiability and persistence of excitation for a huge class of system model structures can be accommodated because of its general nature. The proposed modelling algorithm has been applied to a benchmarked industrial mechatronics system, to verify the effectiveness of control theory.

Keywords: 

generalized LFT modeling, parametric uncertainty, linear dynamical system,

 control
1. Introduction
2. H∞ Control Oriented Modelling of NTH Order Linear Dynamical System
3. Real Time Implementation of the Proposed Modelling Algorithm
4. Frequency Domain Validation of LFT Modelling
5. Conclusions
  References

[1] Mary AD, Mathew AT, Jacob J. (2013). A robust H-infinity control approach of uncertain tractor trailer system. IETE Journal of Research 59(1): 38-47. https://doi.org/10.4103/0377-2063.110626

[2] Giarre L, Milanese M. (1997). H∞ identification and model quality evaluation. IEEE Transaction on Automation Control 42(2): 188-199. https://doi.org/10.1109/9.554399

[3] Casella F, Lovera M. (2008). LPV/LFT modeling and identification: Overview, synergies and a case stud. Symposium on Computer-Aided Control System Design, 852-857. https://doi.org/10.1109/CACSD.2008.4627358

[4] Marcos A, Bates DG, Postlethwaite I. (2005). Exact nonlinear modelling using symbolic linear fractional transformation. 16th IFAC World Congress 16(1): 31-36. https://doi.org/10.3182/20050703-6-CZ-1902.00032

[5] Zhou K, Doyle JC. (1998). Essentials of Robust Control. New Jersey: Prentice-Hall.

[6] Conway R, Felix S, Horowitz R. (2007). Parametric uncertainty identification and reduction for robust H2 synthesis for track- following in dual-stage hard disk drives. American Control Conf., 68-75. https://doi.org/10.1109/ACC.2007.4282569

[7] Cheng Y, Moor BD. (1993). A multidimensional realization algorithm for parametric uncertainty modeling problems. 32rd IEEE Conf. on Decision and Control, 3022-3023. https://doi.org/10.1109/CDC.1993.325755

[8] Hecker S, Varga A. (2004). Generalized LFT- based representation of parametric uncertain models. European Journal of Control 10(4): 326-337. https://doi.org/10.3166/ejc.10.326-337

[9] Gu WD, Petkov PH, Konstantinov MM. (2005). Robust Control Design with MATLAB. 1st ed., Springer, Germany.

[10] Oguntoyinbo OJ. (2009). PID control of Brushless DC moor and robot trajectory planning simulation with MATLAB/SIMULINK’, M. Tech. diss. Vaasan Ammatikorkeakoulu University of Applied Sciences.

[11] Paw YC, Balas GJ. (2008). Parametric uncertainty modeling for LFT model realization. IEEE International Conference on Computer-Aided Control System Design, San Antonio, 834-839. https://doi.org/10.1109/CACSD.2008.4627338