Sep 2, 2011 - of the overall missile homing loop and its design depends on several factors such ... Longitudinal or pitch-axis autopilot is one of the common.
Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011
Outer-Loop Sliding Mode Control Approach to Longitudinal Autopilot Missile Design B. Kada* *Aeronautical Engineering Department, King Abdulaziz University, P O Box 80204, Jeddah, 21589 KSA (Tel: 966-2-640-2000 ext. 68729; e-mail: bkada@ kau.edu.sa). Abstract: This paper presents a new feedback control methodology to design robust Outer-Loop Sliding Mode (OLSM) controllers for systems with nonlinear rapidly time varying and highly uncertain dynamics such as tactical missiles. Within Sliding Mode Control (SMC) framework and based on relative degree and local diffeomorphic coordinate transformation concepts, OLSM controllers that feature short finite time convergence, heavy modeling uncertainties robustness, and chattering extinction and suppression are designed. Two OLSM pitch-axis autopilots for tail-controlled missile are designed and implemented in computer-simulation environment. Simulation results demonstrate the capabilities of OLSM approach in providing high performance levels while maintaining robustness against heavy uncertainties. 1.
INTRODUCTION
Due to large uncertainties of aerodynamics and modeling errors appearing in the modeling of missile’s dynamics, robust integrated Flight Control System (FCS) is necessary to orchestrate the various missile subsystems to successfully track the desired guidance commands and to ensure that all performance requirements are met. The FCS is one element of the overall missile homing loop and its design depends on several factors such as system mission, performance requirements, operating range, control constraint, and cost. Longitudinal or pitch-axis autopilot is one of the common FCSs designed to track desired Angle-Of-Attack (AOA), pitching rate, and commanded normal acceleration using tailfin deflection control. As the overall performance of a guided missile system depends on the performance of its Guidance and Control Algorithms (GCA), during the few past decades considerable attention has been paid to the design and implementation of such algorithms. Using different control methodologies, researchers have sought to alleviate the problem of classical controllers by augmenting these controllers with modern robust algorithms. A standard method in designing missile autopilots has been to apply linear design techniques within gain scheduling framework (Robert et al. 1993). As this method is a tedious procedure, and leads to a sub-optimal controllers whose actual performance and robustness properties are unknown, various approaches have been developed to minimize the required gain scheduling. These approaches have focused on involving nonlinear control techniques and seeking to minimize the effect of system nonlinearities on performance. In (Nicholas 1993) a nonlinear pitch-axis autopilot was designed by scheduling linear ∞ controller designs at constant operating conditions bounding the operating range of the scheduling variables. Linear Parameter Varying (LPV) Copyright by the International Federation of Automatic Control (IFAC)
was also used to design quasi-LPV robust missile autopilots using H∞ optimal control and µ-synthesis (Pellanda et al. 2002; Devant et al., 1999; Misgeld et al., 2011). Feedback linearization is also one of the most popular nonlinear control design methods that have been used for flight control applications (Zhou 2009), but the method shows instability when applied to minimum phase. For their online learning and functional approximation capabilities, neural networks have been also emerged as a means of explicitly accounting for uncertainties in the nonlinear plant dynamics (Lin and Hwang 2003). Recently, backstepping approach was used to design certain missile autopilots (Lin and Fan 2009; Fan and Su 2010), but the complexity of the designed autopilots and the lack of physical meaning restrict their application and integration within real time FCS. Due to its impressive performances and exceptional robustness, sliding mode control approach is becoming very popular in the field of design of GCA. Standard Sliding Modes (SSM) so-called 1-sliding modes provide the best achievable tracking performances in terms of asymptotic stability, finite time convergence, precise keeping of the desired constraints, and robustness against internal and external disturbances. Based upon this approach, certain longitudinal missile autopilot topologies have been recently designed (Fu-Kuang et al., 2004; Shima et al., 2006; Lee et al., 2009; Bahrami et al., 2010). Although their impressive features, 1-sliding modes suffer from certain drawbacks and restrictions regarding the design of sliding manifolds, convergence rate, and chattering effect. Also, it is found that 1-sliding modes only exist on the zero level set of the output function which means that they may be implemented only if the relative degree of the controlled system is one (Utkin 1992; Zinober 1994; Levant 1993, 2005). Due to these limitations, it appears that there is not much enthusiasm to use 1-sliding modes or inner-loop sliding modes for the design of high-performance FCS.
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Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011
Higher relative degree based-design approach provides an alternate to overcome the aforementioned restrictions of 1sliding mode controllers and yields feedback controllers that feature high-performance levels such as fast time convergence, heavy modeling uncertainties robustness, and chattering extinction and suppression. The relative degree appears as important knowledge about dynamical systems in many control issues such as local stabilization, disturbance decoupling, interaction decoupling, nonlinear adaptive control and Higher Order Sliding Mode (HOSM) control (Isidori 1989; Sira-Ramirez 1990, 1993; Levant 2001, 2003, 2005). Recently a certain missile autopilots have been designed based on HOSM strategy (Shang et al., 2004; Foreman et al., 2010). In this paper and within SMC framework, an outer loop control strategy is presented to design sliding regimes for a class of nonlinear smooth affine systems. Our primary concerns are to induce sliding regimes on systems with relative degree higher than one, and to examine the relevance of higher relative degree and local diffeomorphic coordinate transformation concepts to design enhanced sliding mode controllers that feature high-tracking performances. Within this strategy, two pitch-axis missile autopilot topologies are design and implemented in MATLAB environment. The agility and robustness of the controllers are analyzed via different computer-simulation scenarios.
where
The aerodynamic coefficients and ! are estimated from wind-tunnel measurements as 0 1 2 || 4 * 5 + 6 9 0 1 2 || 4 % 7* 5 8 + 6 !
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Actuator dynamics describing the tail-fin deflections are governed by the following second-order differential equation 6: ;
