Di Zhou

Guidance Laws with Finite Time Convergence

Conventional guidance laws are designed based on Lyapunov theorems on asymptotic stability or exponential stability. They will guide the line-of-sight angular rate to converge to zero or its small neighborhood, however, only as time approaches infinity. In this paper, new guidance laws with finite convergent time are proposed. The guidance laws are obtained based on new sufficient conditions derived in this paper for the finite time convergence of the line-of-sight angular rate. It is proved that, with the guidance laws, the line-of-sight angular rate will converge to zero or a small neighborhood of zero before the final time of the guidance process. Furthermore, such guidance laws will ensure finite time convergence and finite time stability in both the planar and three-dimensional environments. Simulation results show that the guidance laws are highly effective.

A Guidance Law With Terminal Impact Angle Constraint Accounting for Missile Autopilot

A sliding-mode guidance (SMG) law is designed to intercept maneuvering targets with impact angle constrained flight trajectories under the assumption of ideal missile autopilot. Furthermore, accounting for the autopilot as second-order dynamics, a new guidance law with terminal impact angle constraint is designed using the dynamic surface control method. Some first-order low-pass filters are introduced into the designing process to avoid the occurrence of high-order derivatives of the line of sight (LOS) angle in the expression of the guidance law such that the guidance law can be implemented in practical applications. The proposed guidance law is effective in compensating for the second-order autopilot lag. Simulation results show that it is able to guide a missile to impact a maneuvering target with a desired angle and a small miss distance.

Nonlinear optimal feedback control for lunar module soft landing

In this paper, the task of achieving the soft landing of a lunar module such that the fuel consumption and the flight time are minimized is formulated as an optimal control problem. The motion of the lunar module is described in a three dimensional coordinate system. We obtain the form of the optimal closed loop control law, where a feedback gain matrix is involved. It is then shown that this feedback gain matrix satisfies a Riccati-like matrix differential equation. The optimal control problem is first solved as an open loop optimal control problem by using a time scaling transform and the control parameterization method. Then, by virtue of the relationship between the optimal open loop control and the optimal closed loop control along the optimal trajectory, we present a practical method to calculate an approximate optimal feedback gain matrix, without having to solve an optimal control problem involving the complex Riccati-like matrix differential equation coupled with the original system dynamics. Simulation results show that the proposed approach is highly effective.

Synchronization control for a class of underactuated mechanical systems via energy shaping

A synchronization control strategy for a class of underactuated mechanical systems is proposed by using the energy shaping technique, aiming to achieve the required performance of the synchronization motion. A synchronization controller is designed based on the interconnection and damping assignment passivity-based control methodology. It will guarantee that the position tracking errors and the synchronization errors of the underactuated mechanical systems are to converge to zero asymptotically. Experiments on a synchronization control system with two single-inverted pendulums as well as simulations of a synchronization control system consisting of four ball-beam devices are presented to demonstrate the effectiveness of the proposed method.

Synchronization control of parallel dual inverted pendulums

A partially linearized model for the underactuated Euler-Lagrangian system composed of two single linear inverted pendulums is obtained based on the feedback linearization method. Then, the small deviation linearization technique is applied to the partially linearized model to obtain the linear model. For the linear model which is completely controllable, we propose a method to construct a synchronization error signal between the two inverted pendulum systems to guarantee that an augmented system, which contains the original state variables of the two subsystems and the synchronization error, is still completely controllable. For the augmented system an optimal synchronization controller is designed. Experimental results show that the optimal synchronization control system has realized a stable balance of the two inverted pendulums and a precise location of the two cars while they move synchronously. The effect of the optimal synchronization control scheme is better than the usual master-slave synchronization scheme.

Robust Dual Stage Control for Inertially Stabilized Platform

A dual stage control system for inertially stabilized platform can be represented by a multi-input multi-output (MIMO) system which often consists of a gyro-stabilized platforms as the coarse stage and an additional servo mechanism in the imaging optical path as the fine stage. This paper presents a robust MIMO controller, which focused on the systematic design method not only for the fine stage but also for the coarse stage. And by considering the obvious difference of the model uncertainties and bandwidths between the two stages, the frequency separation design can be obtained by the well-defined weighting functions. The proposed controller can achieve both good tracking performance and overall system stability. Simulations indicate that the proposed controller can effectively improve the steady state tracking performance and overall system stability.