Analytical solution of generalized three-dimensional proportional navigation

Yang, Ciann-Dong; Yang, Chi Ching

doi:10.2514/3.21685

Cited by 39 publications

(14 citation statements)

References 7 publications

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“…Although many three-dimensional PN guidance laws for control systems described by equations of three-dimensional relative motion have been proposed and analyzed (see, for example, [32][33][34][35][36][37]), some major deficiencies remain. For example, such three-dimensional PN guidance laws are ineffective to overcome unfavorable influences of target maneuvers.…”

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confidence: 99%

Guidance Laws with Finite Time Convergence

Zhou

Sun

Teo

2009

Journal of Guidance, Control, and Dynamics

240

235

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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. Nomenclature a Mr , a M , a M = missile acceleration along the line-of-sight axes a r , a , a = relative acceleration along line-of-sight axes a Tr , a T , a T = target acceleration along line-of-sight axes N = navigation ratio q = line-of-sight angle _ q = derivative of q with respect to time q = second-order derivative of q with respect to time r = relative range _ r = derivative of r with respect to time r = second-order derivative of r with respect to time t = time u = missile acceleration normal to line of sight u r = missile acceleration along line of sight V M = missile velocity V T = target velocity w = target acceleration normal to line of sight w r = target acceleration along line of sight x M , y M , z M = position coordinates of missile in inertial frame x T , y T , z T = position coordinates of target in inertial frame = azimuth = elevation ' M = flight-path angle of missile ' T = flight-path angle of target M = heading angle of missile T = heading angle of target

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confidence: 99%

Guidance Laws with Finite Time Convergence

Zhou

Sun

Teo

2009

Journal of Guidance, Control, and Dynamics

240

235

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“…During the derivation of [x lb ] l in the three dimension guidance law 14,15 and in Ref. 13 , the rotation around centroid is usually ignored based on the ''instantaneous equilibrium hypothesis''.…”

Section: Relative Angular Velocity Between S B and S Lmentioning

confidence: 99%

Three-dimensional analysis of relationship between relative orientation and motion modes

Fan

Xiao

et al. 2014

Chinese Journal of Aeronautics

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Target motion modes have a close relationship with the relative orientation of missile-totarget in three-dimensional highly maneuvering target interception. From the perspective of relationship between the sensor coordinate system and the target body coordinate system, a basic model of sensor is stated and the definition of relative angular velocity between the two coordinate systems is introduced firstly. Then, the three-dimensional analytic expressions of relative angular velocity for different motion modes are derived and simplified by analyzing the influences of target centroid motion, rotation around centroid and relative motion. Finally, the relationships of the relative angular velocity directions and values with motion modes are discussed. Simulation results validate the rationality of the theoretical analysis. It is demonstrated that there are significant differences of the relative orientation in different motion modes which include luxuriant information about motion modes. The conclusions are significant for the research of motion mode identification, maneuver detection, maneuvering target tracking and interception using target signatures.

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“…The PNG law seeks to null the line-of-sight (LOS) rate by making the missile turn rate directly proportional to the LOS rate, and its characteristics against various targets have been broadly studied for a long time [1][2][3][4][5][6][7][8]. Guelman [9] proved that an ideal missile guided by the conventional PNG law can always intercept the target maneuvering with constant acceleration.…”

Section: Introductionmentioning

confidence: 99%