Modified linear-quadratic regulator used for controlling anti-tank guided missile in vertical plane

Abstract

The paper concerns the issue of optimum control of the strongly non-linear dynamic system, i.e. Anti-Tank Guided Missile (ATGM). The linear-quadratic regulator (LQR) was used to provide control capabilities. In order to use the classic LQR, the dynamics of the object must be presented in the form of a linear-stationary model. This is not possible in the case of the considered missile, mostly due to mass changing in time (intensive consumption of fuel) and varying aerodynamic conditions depending on the Mach number Ma. Thus, we are dealing with a non-stationary system. Moreover, state variables are frequently involved in complex functions, which do not allow one to separate coefficients related to state variables very easily. In order to linearize such a complex system, the paper uses Jacobian, as the matrix of state, calculated at each time instant. The automatic pilot of the ATGM, using the LQR method, determines the signals controlling the angles of flight control surfaces and the thrust vector using continuously calculated Jacobians. The paper presents the algorithm for the ATGM control.

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

“…where Q ∈ R n×n and R ∈ R k×k are symmetric, positive (semi-positive) definite matrices of weighting parameters for the state vector x ∈ R n×1 and the control vector u ∈ R k×1 , respectively. In general, there are no unified methods of selecting the Q and R entries; however, several approaches can be found in the literature [21,[27][28][29][30][31][32][33][34][35][36], usually based on modified (e.g., time-varying) Bryson principle or "trial and error" methods. The main problem connecting all of these is the need to define the values of Q and R to find the solution of the feedback gain matrix K. In this study, determining the entry values of matrix Q is not necessary.…”

“…The field of linear systems has been declared many times to be exploited and obsolete from a research point of view, but interest has repeatedly been renewed due to new viewpoints and the introduction of new theories [9,10]. Recently, an interest in linear adaptive control in missile and space technology can be observed, where adaptive-tuned PID [11][12][13][14], FPID [11,[15][16][17] and linear-quadratic regulator (LQR) [18][19][20][21][22][23][24][25] controllers are widely proposed.…”

“…As opposed to classical approaches, the actual states of the flight system were employed to calculate the parameters in weighting matrices. The LQR method is also applied in [21] as a solution for the anti-tank missile guiding process and determines the commands controlling the fin deflections and the thrust vector via continuously calculating Jacobians. In turn, in [18], the LQR formulation is the same, but it was extended to describe the full-state feedback robust integral servo controller equations.…”

Balancing Control of an Absolute Pressure Piston Manometer Based on Fuzzy Linear Active Disturbance Rejection Control

“…Relatively few scholars at home and abroad have studied piston manometer balancing control methods, but for quadrotors [4,5], inverted pendulums [6][7][8], balancing vehicles [9,10], permanent-magnet synchronous motors [11,12], and other such similar balancing systems, there are many modern control algorithms currently applied, such as proportional-integralderivative (PID) control [13][14][15], linear quadratic regulator control (LQR) [16,17], robust control [18,19], fuzzy control [20][21][22][23], adaptive control [24,25], sliding mode control [26][27][28], etc. Theoretically, the control methods applied to these equilibrium systems can also be applied to piston manometers.…”

Research on Angular Motion Characteristics and Stability of Trajectory‐Corrected Rocket Projectile with Isolated Rotating Tail Rudder

“…Te efective range of an unguided, man-portable, antiarmor weapon such as rocket-propelled grenades is generally within 500 m. Although these devices are inexpensive to build, they have a small efective range with accuracies that decrease signifcantly over distance. In comparison, manportable antitank missiles, such as the "Javelin" missile of the United States, can strike fxed or moving targets within 2000 m with high precision using infrared imaging guides and four movable rudder blades [1]. However, because of its high cost, this type of weapon is only suitable to attack highvalue targets.…”