Missile longitudinal autopilot design using backstepping approach

Abstract

The tactical missile autopilot design process is detailed from a backstepping control perspective. Wherein, two autopilot topologies are proposed, i.e. the angle of attack (AOA) autopilot and acceleration autopilot. The nonlinear missile longitudinal dynamics is dealt with firstly to meet the strict feedback form. Control parameters of AOA autopilot are introduced in turn and required to be positive real numbers during the recursive process, however, act with some combination form in the final law. Thus a set of new parameters is presented to simplify the expression and disclose the conservatism of the aforementioned autopilot design. The results show that the positive real requirement on AOA autopilot parameters during step by step design has an unfavorable effect on closed loop system performance. An acceleration autopilot as a tracking problem is then set up and developed. On the one hand, the derivative of measured acceleration containing much noise is included in the law, which is thus not benefit to practical implementation. On the other hand, it's hard to transform the design parameters in the control formula into a compact form similar to the case of AOA autopilot. Two control gains, i.e. k 1 and k 2 , are determined on the basis of step and sine command tracking. The results show that k 1 affects mainly system steady state error, and k 2 affects mainly response speed. Moreover, k 1 is bounded and its upper bound has less relevance with k 2 . Compared with the traditional linear three-loop acceleration topology, the nonlinear acceleration autopilot based on a backstepping approach exhibits excellent tracking performance and robustness. In spite of good performance, the application of nonlinear autopilot is limited owing to a lack of physical meaning and complex engineering implementation. Actually, the exact mathematical model including aerodynamics and unconventional control strategy of an advanced missile could hardly be obtained from wind tunnel testing data or software simulation. Both linear and nonlinear autopilots could stabilize a static unstable missile. Through the control usage analysis, it can be concluded that actuator resource is the crucial factor in controlling a static unstable missile 12 .

Robust Missile Autopilots With Finite‐Time Convergence

“…1(d), 2(d), and 3(d), it can be seen that the estimation accuracy of the presented NDOB is quite satisfactory in spite of the time-varying sinusoidal disturbances as in Case 3, and its sharp nature as in Case 2. Next, in order to demonstrate the superiority of finitetime stability, another autopilot, which incorporates standard backstepping [12] and NDOB (14), is used for comparison. Following the same line as shown in [12] and Theorem 1, it can be proved that this autopilot guarantees asymptotical stability, i.e.…”

“…For comparison, the predictive control-based autopilot [10] and backstepping autopilot [12] are also applied to simulations (for convenience, the details of these two autopilots are presented in Appendices B and C, respectively). The details of the missile model presented in Section II, taken from [2], are listed in Table I.…”

“…Value Symbol Value Next, in order to demonstrate the superiority of finitetime stability, another autopilot, which incorporates standard backstepping [12] and NDOB (14), is used for comparison. Following the same line as shown in [12] and Theorem 1, it can be proved that this autopilot guarantees asymptotical stability, i.e. the angle-of-attack tracking error will converge to zero asymptotically.…”

“…As for progress in modern control theory, many advanced nonlinear control approaches have been applied to design a robust high-performance missile autopilot, for instance, H infinity control [9], predictive control [10,11], backstepping technique [12], dynamic inversion [13], sliding mode control [14][15][16], optimal control [17,18] and references therein. As for these methods, most of them require the exact missile model to design the autopilot except for H infinity control and sliding mode control.…”

Missile Longitudinal Dynamics Control Design Using Pole Placement and LQR Methods

“…The step response showed the adequacy of all the three control methods but LQR method performed better than PID and pole placement in terms of faster response and minimising system overshoots. Longitudinal control of missile has been carried out by various researchers using different modern control techniques [8][9][10] such as H∞ 11 , back stepping [12][13][14] , sliding model control 15 . An application of LQR technique for UAV was presented in 16,17 .…”