This article approaches the issue of the optimal control of a hypothetical anti-tank guided missile (ATGM) with an innovative rocket engine thrust vectorization system. This is a highly non-linear dynamic system; therefore, the linearization of such a mathematical model requires numerous simplifications. For this reason, the application of a classic linear-quadratic regulator (LQR) for controlling such a flying object introduces significant errors, and such a model would diverge significantly from the actual object. This research paper proposes a modified linear-quadratic regulator, which analyzes state and control matrices in flight. The state matrix is replaced by a Jacobian determinant. The ATGM autopilot, through the LQR method, determines the signals that control the control surface deflection angles and the thrust vector via calculated Jacobians. This article supplements and develops the topics addressed in the authors’ previous work. Its added value includes the introduction of control in the flight direction channel and the decimation of the integration step, aimed at speeding up the computational processes of the second control loop, which is the LQR based on a linearized model.
The control of a homing flying object, which a guided aerial bomb (GAB) is, takes place in the earth’s atmosphere, which may feature various atmospheric phenomena that are disturbances to the GAB control. The atmospheric disturbances include air turbulences, wind pockets, and wind gusts. For the purpose of the research discussed in this paper, the atmospheric disturbances were qualified as a stochastic process of power spectral density according to the Dryden model. This paper presents a method of controlling a GAB in motion through a turbulent atmosphere of the earth. The GAB was homed to a moving ground target by the most universal method of proportional navigation. The research discussed in this paper included an analysis of the effect of atmospheric disturbances on the target striking accuracy of a GAB moving along a vertical plane, the GAB flight trajectory, the values of force inputs which controlled the GAB flight, the values of actual attack angles, the values of kinematic transverse overloads, and the control errors input to the guidance controller. The numerical simulations were completed during the research in Matlab/Simulink, and certain results thereof are represented in a graphical format.
This article presents a mathematical model and an algorithm for controlling a guided bomb to a moving and a stationary ground target. The target path was determined from the kinematic relationships of the reciprocal movement of the bomb and the ground target, based on the proportional approximation method. The analysed control system used sliding control, with the PID algorithm to determine the sliding plane. Three types of sliding planes were considered. In addition, a comparative analysis was carried out for three types of controllers: classic PID, sliding and hybrid. Selected results of the computer simulation are listed.
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