Ciann-Dong Yang

NONLINEAR H ROBUST GUIDANCE LAW FOR HOMING MISSILES

This paper proposes an H1 robust guidance law for homing missiles with nonlinear kinematics in the homing phase. Unlike conventional approaches where target’ s acceleration is often assumed to be known or needs to be estimated in real time, the proposed robust guidance law can achieve performance robustness in the absence of target’ s acceleration information and under variations of the initial conditions of engagement. The most dife cult and challenging task involved in applying nonlinear H1 control theory is the solution of theassociated Hamilton ‐ Jacobipartial differentialinequality.In thispaperweshowthattheHamilton ‐Jacobipartialdifferential inequality of the missile guidance problem can be solved analytically with simple manipulations. The numerical simulations show that the H1 robust guidance law exhibits strong robustness properties against disturbances from target’ s maneuvers and variations in initial engagement conditions.

Generalized guidance law for homing missiles

The concept of a generalized guidance law is presented, and the closed-form solution for a homing missile pursuing a maneuvering target according to generalized guidance laws is given. It is shown that the guidance laws appearing in the literature are merely special cases of the one proposed by the authors. The derived generalized forms of capture area, missile acceleration, and homing time duration that are derived provide insight into the performance of the guidance laws being considered and lead to the discovery of new ones. The problem of finding a nonlinear optimal guidance law for a homing missile with controlled acceleration, applied so as to capture a maneuvering target with a predetermined trajectory while minimizing a weighted linear combination of time of capture and energy expenditures, is solved in closed form. The derived optimal control law is equal to the LOS (line of sight) rate multiplied by a trigonometric function of the aspect angle. Numerical simulation shows that the resulting guidance law appears to yield a significant advantage over true proportional navigation. >

Mixed H2/H cruise controller design for high speed train

A cruise controller for two typical traction types of high speed train (HST), the push-pull driving (PPD) type and the distributed driving (DD) type, are designed using a mixed H2

A unified approach to proportional navigation

In this paper, the two major classes of proportional navigation (PN), namely, true proportional navigation (TPN) and pure proportional navigation (PPN) are analyzed and solved by a unified approach. The analytical tools used in the line-of-sight (LOS) referenced systems such as TPN, realistic true proportional navigation (RTPN), generalized true proportional navigation (GTPN) and ideal proportional navigation (IPN), are extended here to handle the interceptor velocity referenced systems such as PPN and its variants. It is found that the above two branches of guidance systems belong to a more general PN scheme which defines the acceleration of the interceptor as being proportional to the LOS rate with direction normal to an arbitrarily assigned vector L/spl I.oarr/. For example, L/spl I.oarr/ of TPN is LOS, and L/spl I.oarr/ of PPN is the interceptors velocity. Every PN scheme associates with a specific form of L/spl I.oarr/. The optimal PN (OPN) problem which concerns the determination of the optimal direction L/spl I.oarr/ is also addressed. Under the proposed general PN scheme, its six special cases, i.e., TPN, RTPN, GTPN, IPN, PPN, and OPN are solved in a unified way from which many new relations among them can be revealed, and their performances can be compared on a common basis.

Analytical Solution of Three-Dimensional Realistic True Proportional Navigation

True proportional navigation with varying closing speed is called realistic true proportional navigation, which is implemented in practice. Our main goal is to derive the complete solutions of three-dimensional realistic true proportional navigation for nonmaneuvering and maneuvering targets. Three coupled nonlinear second-order state equations describing the relative motion are solved analytically without any linearization for performance and trajectory analysis. Properties of three-dimensional realistic true proportional navigation such as capture region, range-to-go, time-to-go, and two aspect angles within spherical coordinates are all obtained in closed form. Furthermore, the two-player game between three-dimensional realistic true proportional navigation and threedimensional ideal proportional navigation is investigated analytically in the pursuit-evasion scenario, where a realistic true proportional navigation guided missile is designed to pursue an ideal proportional navigation guided target. It is found that an ideal proportional navigation guided target is much harder to intercept than a realistic true proportional navigation guided target. I. Introduction ROPORTIONAL navigation (PN) for short-range tactical misP siles is the optimal interceptive law in the sense of producing zero miss distance with the least integral square control effort. PN has been studied since the 1940s. During the four decades that followed, proportional navigation has been explored in many different ways, such as true proportional navigation, pure proportional navigation (PPN), generalized proportional navigation, realistic true proportional navigation (RTPN), and ideal proportional navigation It has long been recognized that there exists a significant difference in the way in which PN guidance law is analyzed and in the way in which it is implemented. Most analytical studies of PN assume that the closing velocity in the PN guidance law is constant, whereas in realistic situations, the instantaneous closing speed may be continuously estimated or measured using devices such as homing seekers with Doppler radar. To remove this difference, RTPN, which adapts to varying closing speed, has recently been proposed. Performance and trajectory analysis of two-dimensional RTPN was studied by

Helicopter H∞ control design with robust flying quality

Abstract The purpose of this paper is to design helicopter H∞ flight control system to improve its stability, maneuverability, and agility. Firstly, the linear mathematical model of a helicopter is established from the nonlinear six degree-of-freedom dynamic equations. Then, linear H∞ control theory is applied to the linearized model to design the H∞ controller, which, in turn, is integrated in the nonlinear model of a helicopter to simulate nonlinear dynamic response, and to evaluate flying quality. Two helicopter flying quality indices, quickness index and phase delay margin, are adopted to test the robustness of H∞ controller, and the results show that while the forward velocity of helicopter changes, the H∞ controller can maintain the specifications in level-1 standard.

Nonlinear H~ ¿ Flight Control of General Six-Degree-of-Freedom Motions

This paper investigates the application of nonlinear H,~) control theory to flight vehicles whose complete six degree-of-freedom lioiilinear equations of motion are considered directly without linearization. Nonlinear flight control modes such as velocity control, body-rate control, attitude control, and hovering control are designed in a unified framework such that the derived nonlinear H,.,, control law is valid for arbitrary flight vehicles. The most difficult and challenging task involved in applying the nonlinear H,,, control theory is to solve the associated HamiltonJacobi partial differential inequality (HPDI). In this paper we show that the H.PD1 of flight control problems can be solved analytically with simple manipulations. A closed-form expression for the nonlinear H,n flight controller is derived from the solution ofH.PDI and shown to be in the simple structure of proportional feedback. The numerical simulations show that the derived nonlinear H,,, control law can ensure global and asymptotical stability of the closed loop system and have strong robustness against wind gusts with varying statistical characteristics.

Analytical solution of 3D true proportional navigation

The commanded acceleration applying in the direction normal to the line of sight (LOS) between the interceptor and its target is called true proportional navigation (TPN). The main goal of this work is to derive the complete analytical solutions of three-dimensional (3D) TPN for nonmaneuvering and maneuvering targets. Three coupled nonlinear second-order state equations describing the relative motion are solved analytically without any linearization for performance and trajectory analysis. Properties of 3D TPN such as capture region, range-to-go, time-to-go, and two aspect angles within spherical coordinates are all obtained in closed form. Furthermore, the comparison between 3D TPN and 3D realistic true proportional navigation (RTPN) is investigated analytically in the two-player game where a TPN-guided missile is commanded to pursue a RTPN-guided target, and vice versa.

Robust cruise control of high speed train with hardening/softening nonlinear coupler

Addresses the dynamics and optimal cruise control of concentrated-driven high speed train. The dynamical model is completed by a multi-body system, in which couplers connecting adjacent vehicles are characterized by nonlinear hardening/softening springs. The design specification is a mix of command tracking and disturbance rejection. The authors apply a linear matrix inequalities approach to synthesize a multi-model multi-objective (H/sub 2//H/sub /spl infin// performance) state-feedback controller. Numerical simulations show the validity of the resulting controller.

Vibration and Control of a Flexible Rotor in Magnetic Bearings Using Hybrid Method and H∞ Control Theory

The vibration and active control of a flexible rotor system with magnetic bearings are investigated using Hybrid Method (HM) and H{sup {infinity}} control theory with consideration of gyroscopic effect. The hybrid method, which combines the merits of the finite element method (FEM) and generalized polynomial expansion method (GPEM) is employed to model the flexible rotor system with small order of plant. The mixed sensitivity problem of H{sup {infinity}} control theory is applied to design the control of system vibration with spillover phenomena for the reduced order plant. The H{sub 2} control design is also employed for comparison with the H{sup {infinity}} design. The experimental simulation is used to illustrate the effects of control design. It is shown that the H{sup {infinity}} controller design can be very effective to suppress spillover phenomena. In addition, the H{sup {infinity}} control design has robustness to the variation of the model parameters. The application of the hybrid method (HM) together with H{sup {infinity}} control design is highly recommended for vibration control of flexible rotor systems with magnetic bearings.