Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

doi:10.23919/JSEE.2024.000017

Journal of Systems Engineering and Electronics ›› 2024, Vol. 35 ›› Issue (1): 242-258.doi: 10.23919/JSEE.2024.000017

• CONTROL THEORY AND APPLICATION • Previous Articles

Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

Muhammad WASIM¹^,*(), Ahsan ALI²(), Mohammad Ahmad CHOUDHRY²(), Inam Ul Hasan SHAIKH¹(), Faisal SALEEM³^,⁴()

¹ Department of Aeronautics and Astronautics Engineering, Institute of Space Technology, Islamabad 44000, Pakistan
² Department of Electrical Engineering, University of Engineering and Technology, Taxila 47080, Pakistan
³ Department of Measurements and Control Systems, Silesian University of Technology, Gliwice 44-101, Poland
⁴ The Joint Doctoral School, Silesian University of Technology, Gliwice 44-100, Poland

Received:2021-12-28 Online:2024-02-18 Published:2024-03-05
Contact: Muhammad WASIM E-mail:muhammad077wasim@gmail.com;ahsan.ali@uettaxila.edu.pk;dr.ahmad@uettaxila.edu.pk;inam.hassan@uettaxila.edu.pk;faisal.saleem@polsl.pl
About author:
WASIM Muhammad was born in 1990. He received his M.S. degree in electrical engineering from Electrical and Mechanical Engineering College, National University of Sciences & Technology (NUST), Islamabad, Pakistan. He received his Ph.D. degree in electrical engineering with specialization of control system from University of Engineering and Technology Taxila, Taxila, Pakistan. He is currently working as an assistant professor at the Department of Aeronautics and Astronautics Engineering, Institute of Space Technology, Islamabad, Pakistan. His research interests include modelling and control of aerial vehicles, model uncertainty estimation using Kalman filter theory, nonlinear state observer, fault tolerant control, nonlinear control theory, construction of Lyapunov function for nonlinear systems, linear parameter-varying (LPV) modelling, and LPV control of airship.E-mail: muhammad.077wasim@gmail.com

ALI Ahsan was born in 1977. He received his Ph.D. degree in control systems from TU Hamburg-Harburg, Germany. Currently, he is working as an associate professor with the Department of Electrical Engineering at University of Engineering and Technology Taxila, Pakistan. His research interests include machine learning, model identification, linear parameter-varying (LPV) modeling, and control design. E-mail: ahsan.ali@uettaxila.edu.pk

CHOUDHRY Mohammad Ahmad was born in 1957. He received his B.S. degree in electrical engineering from University of Engineering and Technology Lahore, in 1982, M.S. from the George Washington University, USA in 1992 and Ph.D. degree from Virginia Tech, USA in 1995. He is a professor emeritus from the Department of Electrical Engineering, University of Engineering and Technology Taxila, Pakistan, where he worked as a full professor and the dean of the department. His research interests include renewable energy systems, power electronics, control system, and smart grids. E-mail: dr.ahmad@uettaxila.edu.pk

SHAIKH Inam Ul Hasan was born in 1971. He received his Ph.D. degree in electrical engineering from University of Manchester, UK. Currently, he is working as an assistant professor with the Department of Electrical Engineering at University of Engineering and Technology Taxila, Pakistan. His research interests lie in iterative learning control, H_∞, nonlinear, and linear parameter-varying (LPV) control of the complex systems. E-mail: inam.hassan@uettaxila.edu.pk

SALEEM Faisal was born in 1994. He is currently enrolled as a Ph.D. student at the Department of Measurements and Control Systems, the Joint Doctoral School, Silesian University of Technology, Gliwice, Poland. He received his B.S. degree in electrical engineering (EE) from University of Engineering and Technology (UET) Lahore in 2016 and M.S. degree in EE (control systems) from UET Taxila, Pakistan in 2018. From September 2019, he is also working as a lecturer in the department of EE at Riphah International University Islamabad, Pakistan. His research interests include evaluation of uncertainty of measurements, fractional-order (FO) modeling, and control design. E-mail: faisal.saleem@polsl.pl

Abstract

Abstract:

The robotic airship can provide a promising aerostatic platform for many potential applications. These applications require a precise autonomous trajectory tracking control for airship. Airship has a nonlinear and uncertain dynamics. It is prone to wind disturbances that offer a challenge for a trajectory tracking control design. This paper addresses the airship trajectory tracking problem having time varying reference path. A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters. It uses extended Kalman filter (EKF) for uncertainty and disturbance estimation. The estimated parameters are used by sliding mode controller (SMC) for ultimate control of airship trajectory tracking. This comprehensive algorithm, EKF based SMC (ESMC), is used as a robust solution to track airship trajectory. The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies. The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis. The simulation results show that the proposed method efficiently tracks the desired trajectory. The method solves the stability, convergence, and chattering problem of SMC under model uncertainties and wind disturbances.

Key words: airship, chattering, extended Kalman filter (EKF), model uncertainties estimation, sliding mode controller (SMC)

Muhammad WASIM, Ahsan ALI, Mohammad Ahmad CHOUDHRY, Inam Ul Hasan SHAIKH, Faisal SALEEM. Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation[J]. Journal of Systems Engineering and Electronics, 2024, 35(1): 242-258.

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References 35

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State	Symbol	Value
Position/m	$ {\boldsymbol{X}}_{0} $	$ \left[-20,400,80\right] $
Attitude/rad	$ {\boldsymbol{\varTheta }}_{0} $	$ [0,0,0.484] $
Linear velocity/ms⁻¹	$ {\boldsymbol{\upsilon }}_{0} $	$ [5,0,0] $
Angular velocity/rads⁻¹	$ {\boldsymbol{\varOmega }}_{0} $	$ \left[0,0,0\right] $

State	Symbol	Value
Position/m	$ {\boldsymbol{X}}_{0} $	$ \left[-10,200,70\right] $
Attitude/rad	$ {\boldsymbol{\varTheta }}_{0} $	$ \left[0,0,0\right] $
Linear velocity/ms⁻¹	$ {\boldsymbol{\upsilon }}_{0} $	$ \left[2,1,1\right] $
Angular velocity/rads⁻¹	$ {\boldsymbol{\varOmega }}_{0} $	$ [0.2,0.3, $$ 0.1] $
Uncertainty vector	$ \Delta {\boldsymbol{F}}_{\rm{Mu}0} $	$ \left[\begin{array}{cccccc}0& 0& 0& 0& 0& 0\end{array}\right] $

EKF parameter	Symbol	Value
Process noise covariance	Q	$ \mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}(0.1,0.1,0.1,0.1,0.1,\mathrm{0.1,10}, $ $ 10,10,10,10,10,100,100, $ $ 100,100,100,100) $
Measurement noise covariance	R	$ \mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\left(2,2,2,2,2,2\right) $
State error covariance	$ {\boldsymbol{P}}_{0} $	$ \mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}(1,1,1,1,1,1,1,1,1, $ $ 1,1,1,\mathrm{1,100},100,100, $ $ 100,100,100) $

Controller parameter	Value
$ \boldsymbol{a} $	$ \mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\left(6,6,6,6,6,6\right) $
$ \boldsymbol{K} $	$ \mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}(10,10,10,10,10,10) $

Controller parameter	Value
$ \boldsymbol{a} $	$ \mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\left(2,2,2,2,2,2\right) $
$ \boldsymbol{K} $	$ \mathrm{d}\mathrm{i}\mathrm{a}\mathrm{g}\left(6,6,6,6,6,6\right) $

Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

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Technique	Reference	NSS	RSS	DAAS	MMV	AMV	WD
PID	[3]	Yes	No	Yes	Not considered	Not considered	Not considered
PID and dynamic inversion	[4,5]	Yes	No	Yes	Not considered	Not considered	Not considered
MPC	[6]	Yes	No	Yes	Not considered	Not considered	Considered
NMPC	[10]	Yes	No	Yes	Not considered	Not considered	Considered
Gain scheduling	[11]	Yes	Yes	Yes	Not considered	Not considered	Considered
BSC	[12]	Yes	No	Yes	Not considered	Not considered	Considered
Adaptive BSC	[13,14,15]	Yes	Yes	Yes	Not considered	Considered	Considered
NN-BSC	[16]	Mixed	Yes	Yes	Considered	Considered	Not considered
Adaptive SMC	[17,18]	Yes	Yes	Yes	Considered	Considered	Considered
Adaptive integral SMC	[19]	Yes	Yes	Yes	Considered	Considered	Considered
Fuzzy SMC	[20,21]	Mixed	Yes	Yes	Considered	Considered	Considered
Adaptive fuzzy SMC	[22]	Mixed	Yes	Yes	Considered	Considered	Considered
NN-SMC	[23]	Mixed	Yes	Yes	Considered	Considered	Considered
NN-NTSMC	[24,25]	Mixed	Yes	Yes	Considered	Considered	Considered
NN-Fuzzy-SMC	[26]	Mixed	Yes	Yes	Considered	Considered	Considered
ESMC	−	Yes	Yes	No	Considered	Considered	Considered

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