Research On Finite-time Convergent Sliding-mode Guidance Law

In order to improve the efficiency or cope with some special tactical purposes, the problem of terminal impact angle and rapid convergence for homing missiles must be considered to enhance the precision and speed of attack. For example, the strapdown passive imaging homing system has a very narrow detection field due to the lacking of servo mechanism. Thus we need to design the guidance law to straighten the ballistic trajectory quickly in the forepart of the guidance process in order to create convenient conditions for the homing terminal guidance. As another example, we hope that penetrating bomb missiles could be stable as early as possible and the flight path angle can converge to the vertical direction, so that the missile can get sufficient vertical impact velocity to penetrate multi-storey buildings or underground hideout. Therefore, it is natural and important to design the finite time guidance law with impact angle constraint for engineering application. In this thesis, we study the guidance law problem with impact angle constraint and accounting for autopilot lag. The main result of this thesis can be summarized as follows:(1) Finite-time convergent guidance law with impact angle constraint based on sliding-mode control.Based on the sliding-mode variable structure control, a finite-time convergent sliding-mode guidance law is presented for the finite-time convergence problem of guidance systems with terminal impact angle constraint. The guidance law makes sure that the line-of-sight(LOS) angular rate can convergence to zero quickly, while the missile angular meets the impact angle constraint. By employing the finite time convergence stability theory of nonlinear control systems to analyze the guidance law, the math formula of convergence time is given, which proves that the guidance system is finite-time convergent.(2) Finite-time convergent sliding-mode guidance law with impact angle constraint accounting for autopilot lag.The dynamics of missile’s autopilot is considered as a first-order lag, then a finite-time convergent sliding-mode guidance law with terminal impact angle constraint is presented by sliding-mode variable structure control theory. Based on the finite-time stability of homogeneous system theorem and Barbalat theorem, the finite-time convergence of the guidance system is proved. The designed variable structure guidance law can guarantee that the LOS rate can converge to zero before impact and the terminal flight path angle can meet the specified impact requirement in a finite time. The guidance law has good robustness and can effectively compensate the delay characteristics of missile’s autopilot lag.(3) Discrete finite-time convergent sliding-mode guidance law accounting for autopilot lag.The discrete guidance control model is constructed, due to the composite control missile guidance commands with the discrete characteristics in the cycle response. By employing the variable structure control theory of discrete sliding-mode, the finite-time convergent discrete sliding-mode guidance law is designed. We deal with the uncertainty of the guidance system by two different methods. The first method is to estimate the upper bound of the uncertainty. The second one is to calculate the variation of the uncertainty in guidance control sampling period. The two designed guidance law can also make the LOS angular rate convergence to the boundary layer of zero in finite time and effectively compensate the delay characteristics of missile’s autopilot lag.The main innovative points of this thesis are as follows:1) A finite time convergent sliding-mode guidance law is presented for the finite time convergence problem of guidance systems with terminal impact angle constraint. By employing the finite time convergence stability theory of nonlinear control systems, the finite-time convergence of guidance system is proved and the math formula of convergence time is given.2) For the guidance law with impact angle constraint accounting for autopilot lag, a variable structure guidance law is designed. By using the finite-time stability of homogeneous system theorem and Barbalat theorem, the finite-time convergence of the guidance system is proved, which ensure that the LOS angular rate and the terminal flight path angle can converge to zero. This guidance law can effectively compensate the delay characteristics of missile’s autopilot lag.3) Based on discrete guidance system control model, using of the theory of discrete sliding-mode variable structure control, the finite-time discrete sliding-mode guidance laws are designed. The guidance laws ensure the LOS angular rate convergence to the boundary layer of zero in finite time and can effectively compensate the delay characteristics of missile’s autopilot lag.