Jae-Hyuk Oh

Capturability of the 3-dimensional pure PNG law

Although a lot of effort has been recently devoted to the capturability analysis of the pure proportional navigation guidance (PPNG) law, there are still significant discrepancies between the analysis results and the actual capturability of the PPNG law. In this paper, a Lyapunov-like approach along with a vector analysis method based on the so-called LOS (line of sight) plane is introduced to analyze the capturability of the 3-dimensional PPNG law against a target maneuvering arbitrarily with time-varying normal acceleration. Thereby, our analysis result can explain the high capturability of the PPNG law theoretically much better than those presented in the prior literature. In our capturability analysis, the nonlinear dynamics of 3-dimensional pursuit situations have been taken into full account. Our approach is also expected to be useful for the design and analysis of other PPNG-like missile guidance laws.

Solving a nonlinear output regulation problem: zero miss distance of pure PNG

Presents a solution to the output regulation problem of a nonlinear system with time-varying disturbance: the system represents the well-known missile-target pursuit situation where the missile is guided by the pure proportional navigation guidance (PPNG) law while the target maneuvers with time-varying normal acceleration, and the problem is to prove the zero miss distance property of PPNG, which has been studied for decades without satisfactory success. To solve this problem, we construct a function by which a time sequence of the missile-to-target range is upper-bounded, and prove that the function is strictly decreasing, which is also proven to guarantee that there is always a sub-sequence that asymptotically converges to zero. The solution is given in the form of a necessary and sufficient condition guaranteeing the zero miss distance of PPNG.

Axiomatic Design of Machine Control System

Abstract Machine control system development typically relies on the developers experience and trial-and-error. This ad hoc approach can undermine the very success of the system development, with a lengthy and costly development period and, possibly, an endless cycle of upgrade and maintenance. The resulting system also lacks the interchangeability and reusability. This paper presents the framework based on Axiomatic Design for the systematic design and implementation of machine control systems. It structures a complex control system and guides the design and development of its subcomponents. Various levels of system design issues are addressed in this structural approach. Based on the methodology presented in this paper, a control system for an industrial scale Chemical-Mechanical Polishing (CMP) machine has been developed.

Linear matrix inequalities for free flight conflict problems

Under the concept of free flight, aircraft will be allowed much greater flexibility in trajectory planning than ever before. The ability to anticipate and resolve conflicts provides one of the greatest challenges to this proposed environment. In this paper, the following problem is addressed: given two aircraft, their intended trajectories and uncertainty about their behavior, what is their worst-case miss distance over a given time horizon? This question is answered using linear matrix inequalities and positive semi-definite programming. The proposed approach provides guaranteed lower bounds on minimum miss distances in polynomial time. Several increasingly complex examples are given that illustrate the efficiency of the proposed method.

Primal-dual quadratic programming approach to multiple conflict resolution

This paper considers a multiple conflict resolution problem for air traffic control systems. The time required to optimally solve aircraft conflicts is known to grow exponentially with the number of aircraft involved and may become prohibitive when large numbers of aircraft are involved. As an attempt to circumvent this issue, a heuristic polynomial-time conflict resolution algorithm is proposed on the basis of analysis results on the relationship between primal and dual quadratic programs.

Design and analysis of conflict resolution algorithms via positive semidefinite programming [aircraft conflict resolution]

Considers the problem of resolving conflicts involving multiple aircraft. First a framework is formulated where conflicts may be solved efficiently. Within this framework, the conflict resolution problem is shown to be a non-convex, quadratically constrained quadratic program. Cheap lower bounds to this problem are developed based on positive semidefinite relaxations of the dual of this program. A unique method is proposed to systematically determine the regions of the state-space where the conflict resolution algorithm is guaranteed to perform well within the proposed framework.

Safety certification of air traffic conflict resolution algorithms involving more than two aircraft

Many future air traffic control tasks will require online safety-critical optimization algorithms. Among these tasks, real-time air traffic conflict resolution involving more than two aircraft is one of the most challenging. Air traffic control systems based on online optimization algorithms must face safety-certification issues such as guaranteed feasibility and guaranteed time of computation. This paper deals with the question of guaranteed feasibility and presents an initial effort at developing an off-line procedure to prove the safety of such an algorithm. The procedure is based on convex optimization technology combined with the so-called S-procedure.

Synthesis and Analysis of a Digital Droplet-Size Control System

Abstract Iaminar jet break-up caused by Rayleighs instability. First, the control plant is represented as an algebraic affine nonlinear system with disturbances. To obtain an on-line droplet diameter measurement, an imaging system was employed and an image processing algorithm was developed. Then, a digital integral controller was synthesized, and explicit stability conditions were derived and incorporated in the design of the controller. The proposed control system is shown to provide uniformly sized droplets of molten metals with the melting temperatures of up to 1200°C., with less than 3% variation over the diameter range of 100μm -800μm, despite the existence of disturbances.