A sliding mode controller design for a missile autopilot system

Abstract

A description is given of an application of the sliding mode control (SMC) for stabilizing the static and dynamic characteristics of an anti-aircraft missile. The solution provides effective separation of the control process from the dynamics of the missile airframe. In the equivalent part of the stabilization system, a linear-quadratic regulator (LQR) is considered, and an analytical method of selecting the weighting elements of the gain matrix is proposed. This eliminates the need for an iterative solution of the Riccati equation. A nonlinear switching component is introduced into the control signal to provide smoothness of the system response. In simulation tests, the proposed solution was evaluated against selected quantity indices. The paper ends with observations and conclusions.

Tuning of a Linear-Quadratic Stabilization System for an Anti-Aircraft Missile

“…namely, the angular rate ω of the airframe should be equal to the angular rateθ of the missile's velocity vector, and not depend on the dynamics of the missile itself [6][7][8]. This requirement, impossible to fulfill in practice however, leads to the conclusion that the absolute rotation angle of the airframe should be approximately equal to the absolute rotation angle of the missile velocity vector; i.e.…”

“…In extremely unfavorable tactical conditions-despite the use of an adequate seeker stabilization loop-the target tracking process may break. It therefore becomes necessary to identify solutions enabling stabilization of the operating conditions of the on-board seeker [6][7][8]. They are often designed using adaptive linear control, which has certain benefits.…”

“…In this case, a state feedback linear quadratic regulator was proposed to stabilize the plant and a forward path H ∞ optimal controller was used to achieve the required performance and robustness. Several papers describe the use of an LQR as a part of the missile stabilization system; e.g., [25] discusses a cascaded LQR controller for effective roll stabilization of the missile autopilot in a realistic model; robust missile roll autopilot design with an LQR application for solving the flexible airframe dynamics is also discussed in [23]; and in [7] LQR was chosen as an equivalent part of the sliding mode control (SMC) airframe stabilization system. These selected examples show the multitude of possible LQR applications in aerospace and missile technology.…”

“…The fundamental difficulty with this approach is the necessity for the computations to be carried out in real time [19,27]. There are also certain technical hitches related to the software implementation, e.g., the weak conditioning of the matrices [7,8]. It is therefore valuable to find an analytical solution of the controller, which ensures adaptability according to the state of the system.…”

“…In the author's previous work, an initial concept of achieving an analytical solution of a time-varying linear-quadratic stabilization system was proposed and tested. A basic formula of feedback loop gain matrix equations (without a tuning parameter) was introduced and used as a part of the SMC stabilization system in [7].…”