The closed-form solution of generalized proportional navigation

Yang, Ciann-Dong; Yeh, Fang-Bo; Chen, Jen-Heng

doi:10.2514/3.20205

Cited by 75 publications

(22 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The corresponding commanded acceleration can be described as a c = Xv0 = Xv 0 0 0 (7) Since the actual responsed acceleration is finite, X is normally chosen to be >2 to avoid a c going to infinity.…”

Section: Solution For a Nonmaneuvering Targetmentioning

confidence: 99%

Ideal proportional navigation

Yuan

Chern

1992

Journal of Guidance, Control, and Dynamics

134

View full text Add to dashboard Cite

Proportional navigation has been proved to be a useful guidance technique in several surface-to-air and air-to-air homing systems for interception of airborne targets. Besides the familiar pure, true, and generalized proportional navigation guidance laws, a new guidance scheme, called ideal proportional navigation, with commanded acceleration applied in the direction normal to the relative velocity between interceptor and target, is presented. In this study the closed-form solutions of ideal proportional navigation are completely derived for maneuvering and nonmaneuvering targets, and some important characteristics related to the system performance are introduced. Under this scheme the capture criterion is related to the effective proportional navigation constant only, no matter where the initial condition and target maneuver are. With some more energy consumption, this new guidance scheme has a larger capture area and is much more effective than the other schemes. Nomenclature a = acceleration r = distance between interceptor and target T = total time of flight t = time of flight V = velocity v = relative velocity between interceptor and target F = gamma function 6 = angle between line of sight and inertial reference line X = effective proportional navigation constant (/) = angle between relative velocity and line of sight Subscripts c = commanded value / = final value M = missile, interceptor r = parallel to line of sight T = target z = normal to the intercept plane 0 = normal to line of sight 0 = initial value 1 = state at maximum r Superscript ' = time derivative

show abstract

Section: Solution For a Nonmaneuvering Targetmentioning

confidence: 99%

Ideal proportional navigation

Yuan

Chern

1992

Journal of Guidance, Control, and Dynamics

134

View full text Add to dashboard Cite

show abstract

“…However, it is much easier to gain closed-form solution of TPN rather than PPN. For the purpose of enlarging the capture region of TPN, generalized TPN was proposed [13,14]. Ghose [15] studied the efficiency of these guidance laws carefully and still found PPN to be the most efficient.…”

Section: Introductionmentioning

confidence: 99%

Differential geometric modeling of guidance problem for interceptors

Chen

Bai

2011

Sci. China Technol. Sci.

View full text Add to dashboard Cite

It is a comparatively convenient technique to investigate the motion of a particle with the help of the differential geometry theory, rather than directly decomposing the motion in the Cartesian coordinates. The new model of three-dimensional (3D) guidance problem for interceptors is presented in this paper, based on the classical differential geometry curve theory. Firstly, the kinematical equations of the line of sight (LOS) are gained by carefully investigating the rotation principle of LOS, the kinematic equations of LOS are established, and the concepts of curvature and torsion of LOS are proposed. Simultaneously, the new relative dynamic equations between interceptor and target are constructed. Secondly, it is found that there is an instantaneous rotation plane of LOS (IRPL) in the space, in which two-dimensional (2D) guidance laws could be constructed to solve 3D interception guidance problems. The spatial 3D true proportional navigation (TPN) guidance law could be directly introduced in IRPL without approximation and linearization for dimension-reduced 2D TPN. In addition, the new series of augmented TPN (APN) and LOS angular acceleration guidance laws (AAG) could also be gained in IRPL. After that, the differential geometric guidance commands (DGGC) of guidance laws in IRPL are advanced, and we prove that the guidance commands in arc-length system proposed by Chiou and Kuo are just a special case of DGGC. Moreover, the performance of the original guidance laws will be reduced after the differential geometric transformation. At last, an exoatmospheric interception is taken for simulation to demonstrate the differential geometric modeling proposed in this paper. kinematic equations of LOS, instantaneous rotation plane of LOS, proportional navigation, augmented true proportional navigation, LOS angular acceleration guidance law, differential geometric guidance commands Citation:

show abstract

“…Optimal guidance leads to a nonlinear two-point boundary-value problem whose solution has been obtained analytically in closed form by Lin and Tsai, 4 Rao, 5 and Hough. 6 Yang et al 8 have extended the results of TPN to any angle between the missile acceleration and the LOS GTPN. Their GTPN closed-form results are restricted to cases where the theoretical acceleration gain constant K r is zero.…”

mentioning

confidence: 95%