Abstract
This paper is concerned with the types of stochastic disturbances affecting the potential of the aerial system. The satellite system for continuous and discrete time domain is discussed. A phase lead compensator completes the orientation successfully. Astrom’s single-input single-output (SISO) model is implemented with using the minimum variance control strategy. The separation principle then provides the optimal control law which curtails the cost function to a value as small as possible. The satellite system is positioned for one quarter revolution with the co-ordination of generalized minimum variance controller (GMVC) and standard generalized dual controller (GDC) based on certainty equivalence assumption. The revolutions in radians are tracked as output of the system for the input specified in degrees to the system. The controller proved useful in reducing the overshoot and atmospheric disturbances which allows a stable motion even for larger time delays.
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Abbreviations
- e:
-
Independent vector
- k′ :
-
Gain factor
- u(t) :
-
Control signal
- x :
-
Radial perturbation
- y(t) :
-
System output
- ω d :
-
Damping frequency
- ξ:
-
Damping ratio
- ξ t :
-
Gaussian white noise
- G LA :
-
Longitudinal disturbance
- G P :
-
Pressure disturbance
- G T :
-
Temperature disturbance
- I q :
-
Covariance matrix
- T s :
-
Time delay
- V :
-
Loss function
- W x :
-
Weiner process
- Y r :
-
Desired signal
References
Hunek, W.P., Latawiec, K.J.: Minimum variance control of discrete time and continuous-time LTI MIMO systems a new unified framework. J. Control Cybern. 38(3), 609624 (2009)
Soroka, E., Shaked, U.: The properties of reduced-order minimum-variance filters for systems with partially perfect measurements. IEEE Trans. Autom. Control 330(11), 1022–1034 (1988)
Shiino, T., Kawada, K., Yamamoto, T., Komichi, M., Nishioka, T.: Gimbals control with the camera for aerial photography in RC helicopter. In: International Conference on Control, Automation and Systems, vol. 120, no. 5, pp. 1135–1139, 14–17 Oct 2008
Grimble, M.J., Naz, S.A.: Nonlinear minimum variance estimation for discrete-time multi-channel systems. IEEE Trans. Signal Process. 57(7), 2437–2444 (2009)
Silveira, A.S., Coelho, A.A.R.: Generalised minimum variance control state-space design. IET Control Theor. Appl. 5(15), 1709–1715 (2016)
Yokoyama, R., Masuda, S.: Convergence property for iterative data driven PID gain tuning based on generalized minimum variance regulatory control. In: 6th International Symposium on Advanced Control of Industrial Processes (AdCONIP), Taipei, Taiwan, pp. 511–516, 28–31 May 2017
Kopasakis, G.: Atmospheric turbulence modeling for aero vehicles: fractional order fits. NASA Center for Aerospace Information, Glenn Research Center Cleveland, Ohio, pp. 1–12, Dec 2010
Sagirow, P.: Stochastic Methods in the Dynamics of Satellite. Int. Centre for Mechanical Sciences, Springer, Berlin (1970)
Kloeden, P., Platen, E.: Numerical Solution of Stochastic Differential Equation. Springer, Berlin (2013)
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Dube, D.Y., Patel, H.G. (2020). Discrete Time Minimum Variance Control of Satellite System. In: Manna, S., Datta, B., Ahmad, S. (eds) Mathematical Modelling and Scientific Computing with Applications. ICMMSC 2018. Springer Proceedings in Mathematics & Statistics, vol 308. Springer, Singapore. https://doi.org/10.1007/978-981-15-1338-1_25
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DOI: https://doi.org/10.1007/978-981-15-1338-1_25
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