Abstract
The huge developments in computational capabilities facilitate the design and implementation of adaptive and robust control. Furthermore, the great developments in nanotechnology and its availability in civilian level with less cost, weight, and size attract the researchers all over the world towards embedded systems especially the embedded flight control. One of the real applications are the guided missiles especially the anti-tank guided missile systems which are launched against the ground and short-range targets and is called command line of sight. The present work is concerned with improving the performance of an anti-tank guided missile system belonging to the first generation via adaptive synthesis of guidance systems. The online system identification is required to complete the cycle of adaptive autopilot design. This paper is devoted to designing an adaptive autopilot for the intended system using model reference and self-tuning regulator with justification against previous work and reference flight data concerning the performance requirements of time responses and flight path characteristics. The new design is implemented within the 6-DOF simulation from which the obtained results clarify its capability to stabilize the system in presence of unmodeled dynamics and satisfy the performance requirements with disturbance rejection and measurement noise attenuation. Also, the flight path is evaluated considering the HIL environment.
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Abbreviations
- \(\hbox {X}_{1}, \hbox {Y}_{1}\), and \(\hbox {Z}_{1}\) :
-
Vectors components along the board reference axes
- \(\hbox {X}_{\mathrm{g}}, \hbox {Yg}\), and \(\hbox {Z}_{\mathrm{g}}\) :
-
Vectors components along the ground reference axes
- \(\hbox {X}, \hbox {Y}\), and \(\hbox {Z}\) :
-
Vectors components along the velocity reference axes
- \(\hbox {T}_{\mathrm{bg}}\) :
-
Transformation matrix from board to ground reference axes
- \(\hbox {T}_{\mathrm{vg}}\) :
-
Transformation matrix from velocity to ground reference axes
- \(\hbox {T}_{\mathrm{bg}}\) :
-
Transformation matrix from board to ground reference axes
- \({\updelta }_{\mathrm{jp}}\) and \({\updelta }_{\mathrm{jy}}\) :
-
Thrust jetivator angles in pitch and yaw planes
- \(F_{{ TX}_1}, F_{{ TY}1} \hbox { and }F_{{ TZ}_1}\) :
-
Thrust forces along the board reference axes
- \(F_{{ AX}}, F_{{ AY}}\) and \(F_{{ AZ}}\) :
-
Drag, lateral, and lift forces along the velocity axes
- S:
-
Characteristic area
- q:
-
Dynamic pressure given by \(\hbox {q} = 0.5\uprho \,(\hbox {V}_{\mathrm{m}})^{2}\,(\hbox {Kg/m/s}^{2}]\)
- \(\uprho \) :
-
Air density (\(\hbox {kg/m}^{3}\))
- \(\hbox {V}_{\mathrm{M}}\) :
-
Missile velocity
- \(\hbox {C}_{\mathrm{x}}, \hbox {C}_{\mathrm{y}}\), and \(\hbox {C}_{\mathrm{z}}\) :
-
Dimension-less aerodynamic coefficients
- \(\hbox {m}_{\mathrm{s}}\) :
-
Instantaneous total missile mass
- \({\overline{g}}\) :
-
Vector of gravity acceleration
- \(\hbox {m}_{\mathrm{o}}\) :
-
Initial missile mass
- \(\hbox {m}_{\mathrm{sec}}\) :
-
Burnt quantity of fuel or propellant per second
- M:
-
Mach number and given by \(\hbox {M}=\hbox {V}_{\mathrm{m}}/\hbox {V}_{\mathrm{a}}\)
- \(\hbox {V}_{\mathrm{a}}\) :
-
Sound velocity at missile position
- \(l_T\) :
-
Perpendicular distance between the missile C.G. and the point of lateral thrust forces action
- \(l_{{ TX}}\) :
-
Perpendicular distance between longitudinal axis and thrust force line
- \(l_x, l_y, l_z\) :
-
Characteristic linear dimensions of missile
- \(m_{x_1}, m_{y_1}\) and \(m_{z_1}\) :
-
Dimensionless aerodynamic coefficients
- \({\upomega }_{x_1 }, {\upomega }_{y_1} \hbox { and } {\upomega }_{z_1}\) :
-
Airframe-turn rates along board coordinate axes
- \({\overline{J}}\) :
-
Acceleration of missile
- \(\Omega \) :
-
Angular velocity of VCS w.r.t GCS
- \(\hbox {I}_{\mathrm{XX}}, \hbox {I}_{\mathrm{YY}}\), and \(\hbox {I}_{\mathrm{ZZ}}\) :
-
Moments of inertia components along the BCS
- \(\upalpha \) :
-
Angle of attack [angle of incidence] [Degree]
- \(\upbeta \) :
-
Sideslip angle [angle of drift] [Degree]
- \(\hbox {U, V}\), and \(\hbox {W}\) :
-
Velocities Along board coordinate axis
- \(\hbox {U}_{\mathrm{d}}, \hbox {V}_{\mathrm{d}}\), and \(\hbox {W}_{\mathrm{d}}\) :
-
Derivative of velocities along board coordinate axis
- \(\hbox {g}_{\mathrm{x}}, \hbox {g}_{\mathrm{y}}\), and \(\hbox {g}_{\mathrm{z}}\) :
-
Gravity acceleration along board coordinate axis
- \(\upvarepsilon _{\mathrm{T}}\) and \({\updelta }_{\mathrm{T}}\) :
-
Elevation and azimuth angles of target
- \(\upvarepsilon _{\mathrm{M}}\) and \(\upvarepsilon _{\mathrm{M}}\) :
-
Elevation and azimuth angles of missile
- \(\Delta {\upvarepsilon }\) and \(\Delta _{{\updelta }}\) :
-
LOS angular error
- \(\hbox {R}_{\mathrm{m}}\) and \(\hbox {R}_{\mathrm{t}}\) :
-
Missile and target range
- \({\uptheta }_{\mathrm{p}}\) :
-
Pitch demand
- \({\uppsi }_{\mathrm{s}}\) :
-
Angle between missile and LOS in yaw plane
- \(\upvarepsilon _{1}, {\upsigma }_{1}\) :
-
LOS angular errors for the two planes expressed in meters
- \(\hbox {e}\) :
-
Tracking error
- \(\hbox {J}\,({\uptheta })\) :
-
Cost function of theta
- \(\hbox {I}_{\mathrm{WP}}\) and \(\hbox {V}_{\mathrm{WP}}\) :
-
Pitch wire current and voltage
- \(\hbox {V}_{\mathrm{ep}}\) :
-
Pitch error signal
- \(\hbox {V}_{\mathrm{sp}}\) :
-
Pitch autopilot output
- \(\hbox {V}_{\mathrm{gp}}\) :
-
Pitch gyro output
- ADC:
-
Aero dynamic coefficients
- AP:
-
Autopilot
- BCS:
-
Board coordinate system
- CLOS:
-
Commanded to line of sight
- MRARC:
-
Model reference adaptive robust controller
- LOS:
-
Line of sight
- 6-DOF :
-
Six degrees of freedom
- Adaptive STR:
-
Adaptive self tuning regulator
- TVC:
-
Thrust vector control
- VCS:
-
Velocity coordinate system
- c.g.:
-
Centre of gravity
- HIL:
-
Hardware in loop
References
Oda AN, El-Sheikh GA, El-Halwagy YZ, Al-Ashry M (2010) Robust CLOS guidance and control part-1: system modelling and uncertainty evaluation. In: 14th International conference on aerospace sciences and aviation technology
Oda AN, El-Sheikh GA, Al-Ashry M, El-Halwagy YZ (2010) Robust CLOS guidance and control part-2: scalar \(\text{H}\infty \) autopilot synthesis. In: 14th International conference on aerospace sciences and aviation technology
Oda AN, El-Sheikh GA, El-Halwagy YZ, Al-Ashry M (2010) Robust CLOS guidance and control part-3: HIL system simulation. In: 14th International conference on aerospace sciences and aviation technology
Ouda AN, Cairo MTC (2012) Performance investigation of adaptive guidance algorithms and its effectiveness
Zhou D, Xu B (2016) Adaptive dynamic surface guidance law with input saturation constraint and autopilot dynamics. J Guid Control Dyn 39(5):1155–1162
Yang PF, Fang YW, Chai D, Wu YL (2016) Fuzzy control strategy for hypersonic missile autopilot with blended aero-fin and lateral thrust. Proc Inst Mech Eng I J Syst Control Eng 230(1):72–81
He S, Wang J, Lin D (2016) Robust missile autopilots with finite-time convergence. Asian J Control 18(3):1010–1019
Fan YH, Yan PP, Wang F, Xu HY (2016) Discrete sliding mode control for a hypersonic cruise missile. Discrete Dyn Nat Soc (2016). doi:10.1155/2016/2402794
Yan H, Wang X, Yu B, Ji H (2014) Adaptive integrated guidance and control based on back stepping and input-to-state stability. Asian J Control 16(2):602–608
Liang X, Hou M, Duan G (2014) Adaptive dynamic surface control for integrated missile guidance and autopilot in the presence of input saturation. J Aerosp Eng 28(5):401–412
Hou M, Liang X, Duan G (2013) Adaptive block dynamic surface control for integrated missile guidance and autopilot. Chin J Aeronaut 26(3):741–750
Aseltine JA, Mancini AR, Sartune CW (1958) A survey of adaptive control. IRE Trans Autom Control 3:102–108
Zhang J (2006) Practical adaptive control: theory and application. University of Southern California
Astrom KJ, Wittenmark B (1995) Adaptive control. Addison-Wesley, Reading
Filatov NM, Unbehauen H (2000) Survey of adaptive dual control methods. IEEE Proc Control Theory Appl 147(1):118–128
Kreisselmeier G (1989) An indirect adaptive controller with a self-excitation capability. IEEE Trans Autom Control 34:524–528
Anderson BDO, Brinsmead T, Liberzon D, Morse AS (2001) Multiple model adaptive control with safe switching. Int J Adapt Control Signal Process 15:445–470
Fujii S, Hespanha JP, Morse AS (1998) Supervisory control of families of noise suppressing controllers. In: 37th IEEE conference on decision and control, vol 2, pp 1641–1646
Morse AS (1996) Supervisory control of families of linear set-point controller part 1. IEEE Trans Autom Control 41:1413–1431
Morse AS (1997) Supervisory control of families of linear set-point controller part 2. IEEE Trans Autom Control 42:1500–1515
Rodriguez TM, Banks SP (2010) Linear time-varying approximation to nonlinear dynamical system: with application in control and optimization. Springer, Berlin
Blackelock JH (1991) Automatic control of aircraft and missile. Wiley-IEEE, New York
Fu M, Barmish B (1986) Adaptive stabilization of linear system via switching control. IEEE Trans Autom Control 31:1097–1103
Matensson B (1985) The order of any stabilizing regulator is sufficient a priori information for adaptive stabilization. Syst Control Lett 6:87–91
Miller DE, Davison EJ (1991) An adaptive controller which provides an arbitrarily good transient and steady-state response. IEEE Trans Autom Control 36:68–81
Wang R, Paul A, Stevanovic M, Safanov MG (2005) Cost-detectability and stability of adaptive control system. In: 44th IEEE conference on decision and control
Wang R, Safonov MG (2005) Stability of unfalsified adaptive control using multiple controllers. In: American control conference, vol 5, pp 3162–3167
Fidan B, Kosmatopoulos EB, Ioannou PA (2002) A switching controller for multivariable LTI systems with known and unknown parameters. In: 41st IEEE conference on decision and control, vol 4, pp 4688–4693
Morse AS, Mayne DQ, Goodwin GC (1992) Application of hysteries switching in parameter adaptive control. IEEE Trans Autom Control 37:1343–1354
Hespanha JP, Liberzon D, Morse AS (2003) Hysteresis-based switching algorithm for supervisory control of uncertain system. Automatica 39:263–272
Kosmatopoulos EB, Ioannou PA (1999) A switching adaptive controller for feedback linearizable systems. IEEE Trans Autom Control 44:742–750
Kosmatopoulos EB, Ioannou PA (2002) Robust switching adaptive control of multi-input nonlinear system. IEEE Trans Autom Control 47:610–624
Narendra KS, Balakrishnan J (1994) Improving transient-response of adaptive control system using multiple models and switching. IEEE Trans Autom Control 39:1861–1866
Narendra KS, Balakrishnan J (1997) Adaptive control system using multiple models. IEEE Trans Autom Control 42:171–187
Narendra KS, Balakrishnan J, Ciliz MK (1995) Adaptation and learning using multiple models, switching and tuning. IEEE Control Syst Mag 15:37–51
Safonov MG, Tsao TC (1997) The unfalsified control concept and learning. IEEE Trans Autom Control 42:843–847
Yan L, Wenhan D (2004) Model reference robust controller design for flight control. A back stepping. In: 5th world congress on intelligent control and automation
Mahdianfar H, Prempain E (2016) Adaptive augmenting control design for a generic longitudinal missile autopilot. In: American control conference (ACC), 2016, pp 3138–3143. IEEE
Marzbanrad J, Tahbaz-zadeh Moghaddam I (2016) Self-tuning control algorithm design for vehicle adaptive cruise control system through real-time estimation of vehicle parameters and road grade. Veh Syst Dyn 54(9):1291–1316
Sarhadi P, Noei AR, Khosravi A (2017) Model reference adaptive autopilot with an anti-windup compensator for an autonomous underwater vehicle: design and hardware in the loop implementation results. Appl Ocean Res 62:27–36
Rusnak I, Weiss H, Barkana I (2014) Improving the performance of existing missile autopilot using simple adaptive control. Int J Adapt Control Signal Process 28(7–8):732–749
Xu B, Shi Z (2015) An overview of flight dynamics and control approaches for hypersonic vehicles. Sci China Inf Sci 58(7):3–21
Jianping C (2011) Adaptive autopilot design for missile systems with aerodynamics uncertainties. Comput Meas Control 5:032
Rong HJ, Yang ZX, Wong PK, Vong CM (2017) Adaptive self-learning fuzzy autopilot design for uncertain bank-to-turn missiles. J Dyn Syst Meas Control 139(4). doi:10.1115/1.4035091
Cai J, Xing L, Zhang M, Shen L (2017) Adaptive neural network control for missile systems with unknown hysteresis input. In: IEEE Access, vol 99
Astrom KJ, Hagglund T, Hang CC, Ho WK (1993) Automatic tuning and adaptation for PID controller. Control Eng Pract 1(4):699–714
Astrom KJ, Hagglund T (1984) Automatic tuning of simple regulators with specifications on phase and amplitude margins. Automatica 20:645–651
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Ouda, A.N. A robust adaptive control approach to missile autopilot design. Int. J. Dynam. Control 6, 1239–1271 (2018). https://doi.org/10.1007/s40435-017-0352-4
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DOI: https://doi.org/10.1007/s40435-017-0352-4