Moshe Guelman

Finite Time Stability Approach to Proportional Navigation Systems Analysis

The e nite time stability of proportional navigation guidance systems is considered. Assuming planar geometry and linear missile dynamics, a proportional navigation missile ‐target guidance model is e rst formulated. The model exhibitsa feedback cone guration consisting of a lineartime-invariant element and a time-varying gain. The dee nition of e nite timeglobal absolutestability isthen presented. Itisshown that by employing thecirclecriterion, the e nite time stability of the guidance dynamics can be analyzed. An analytic bound for the time of e ight up to which stability can be assured is established. The bound depends on the system parameters and the time of e ight. Less conservative results, as compared to previous works, are obtained. This approach enables not only analysis of the system behavior for given missile dynamics, but more importantly, enables generation of a tool for system design. Illustrative examples are presented showing the effect of the system parameters on the bound. In addition, some design implications, such as the relation to miss distance, are outlined.

Optimal planar interception with terminal constraints

In this paper, planar interception laws for maneuvering targets with known trajectories are presented. Optimal interception problems are defined, which include constraints on the initial and final flight-path angles of the interceptor. For cases where the initial flight-path angle can be freely assigned, it is included in the optimization problem. Analytical solutions for the planar interception problems are derived. Numerical examples that demonstrate the optimal trajectories are presented showing also the effect of the interceptor initial flight-path angle on the interception characteristics. It is shown that when the interceptor initial conditions can be optimized superior performance is obtained.

Neoclassical Guidance for Homing Missiles

A new approach to guidance of homing missiles is considered. Like classical proportional navigation (PN), the new guidance law utilizes line-of-sight (LOS) rate measurement only. However, its performance is superior to PN, in the sense that zero-miss-distance (ZMD) is obtained against highly maneuvering targets. This merit is achieved withneithertheestimationoftargetmaneuvernortimetogo.Inthederivationofthenewguidancelaw,alinearized formulation of the PN interception kinemtics is used. Based on themethod ofadjoints, it is proved analytically that whentheoveralltransferfunctionofthemissileisbiproper,thatis, thedegreeofthenumeratorequalsthedegreeof thedenominator,ZMDisobtained.TheZMDpropertyholdsinthefollowingcases:deterministictargetmaneuvers, random target maneuvers, deterministic target maneuvers with random starting times, fading noise, and passiveand active-receiver noise. The realization of the new guidance law requires lead compensation. When LOS rate measurement is corrupted by noise, lead ‐lag compensation can be used instead. These design considerations are illustrated in simulations, which verify that negligiblemissdistanceagainst highly maneuvering targetsis obtained even when the LOS rate measurement is noisy.

Three-dimensional minimum energy guidance

Using the exact nonlinear equations of motion, an optimal guidance law (OGL) for a vehicle intercepting a maneuvering target in the three dimensional space is derived. It is assumed that a complete knowledge of the motion of the target is available to the interceptor. The guidance law minimizes a weighted linear combination of the time of capture and the expended maneuvering energy. It is proven that the optimal interceptor trajectory is confined to one plane. The planar case solution, in terms of elliptic integrals, is extended to the three dimensional case. Numerical results are presented to compare the OGL with the pure proportional navigation guidance (PPNG). >

Autonomous navigation and guidance system for low thrust driven deep space missions

Abstract Presented herein is a concept of an Autonomous Navigation & Guidance System for electrically propelled deep space missions, including hardware configuration, algorithms for autonomous navigation and guidance, and estimates of potential guidance precision and mass consumption. This concept is actually a unified Navigation, Guidance and Attitude Control system. The unification is imposed by strong coupling between the orbital motion and the spacecraft attitude characteristic of low thrust space flights. The sensor set of the system consists of an optical instrument (Coupled Sun Star Tracker), and a block of four vector accelerometers. The propulsion subsystem is a set of nearly parallel Hall thrusters rigidly attached to the spacecraft body. The final stage of data processing is combining the thrust and torque programs and generating power and mass rate shares for every thruster. An end-to-end computer simulation provides guidance accuracy estimates versus the navigation data precision, flight time and available maximum thrust. Terminal guidance errors of a few tens of km in position and a few tens of cm/s in velocities are predicted under plausible assumptions on system parameters. Mass expenditures for the control are typically below one percent of total fuel mass budget.

Investigation of physical processes in CAMILA Hall thruster using electrical probes

The CAMILA (co-axial magneto-isolated longitudinal anode) concept was developed to improve the anode efficiency in low-power Hall thrusters. Previous measurements, performed in Asher Space Research Institute, have shown that the thruster has the highest efficiency for its class. This paper presents an analysis of the discharge structure in an effort to improve understanding of the physical processes in CAMILA type thrusters. Internal measurements of the discharge parameters were performed using an emissive probe, a biased probe and a Faraday cup. The probes were mounted on a positioning system capable of mapping the channel in two dimensions. Maps for the plasma potential, the ion current density and the electron temperature were obtained. In addition, a one-dimensional fluid model was developed in order to compute the distribution of the plasma density and the ion velocity. The experimental investigations confirmed the basic assumptions used in the physical model of the CAMILA concept and revealed phenomena related to the radial non-uniformity of the discharge. In particular, focusing equipotentials were discovered in the area of intense ionization, reducing ion loss to the walls of the channel. This mechanism is principal in obtaining the high efficiency of the thruster. When operated with strengthened longitudinal magnetic field, the plasma density inside the anode cavity was significantly higher in the middle than near the anodes. The fraction of ion current generated inside the anode cavity was greater than in the simplified case, 19% compared with 13% respectively. In addition, it was shown that electrons in the cusp region, the region between predominately radial to predominately axial magnetic fields, were not well confined, however, no potential hump is created and ions are able to cross this region to the acceleration channel.

Integrated adaptive control for space manipulators

Abstract The paper focuses on indirect adaptive control of space robot manipulators when maneuvering payloads with imperfectly known mechanical parameters. The objective is to estimate system mechanical parameters during the maneuver itself. The system bodies are rigid, and are concatenated by ideal, rotational joints. Existing adaptive control laws are investigated in an application to a rotating, single-degree-of-freedom body. Even in this simple case, and more so in general multibody cases, improvements in adaptive control laws are found to be needed. A new adaptive control law is developed which is applicable to general, rigid, multibody systems. It is based on the reinterpretation of the system dynamic equations as a measurement equation. The adaptive control law is of the “integrated” type, i.e. the estimator part is used to estimate the integrated influence of the system mechanical parameters, rather than the parameters themselves. The controller part (the control law proper) is of the “certainty equivalence” type. For the single-degree-of-freedom case, the system formal solution is presented. Then the parameter estimation process and the control law are separately analyzed to show that the control system output error is globally asymptotically stable, as well as the parameter error, provided the external command input satisfies a persistent excitation condition. In one numerical example it is shown how a two-armed, nine-degree-of-freedom space robot can be controlled almost as if the mechanical parameters were perfectly known.

The Israeli microsatellite TECHSAT for scientific and technological research: Development and in-orbit testing

Abstract A description of the TECHSAT microsatellite, as well as its on-board housekeeping systems and scientific equipment is presented. The satellite is a universal three-axis platform carrying devices for space research and technological experiments. Preliminary results of testing the microsatellite itself and the different on-board systems during the first 6 months of its in-orbit operation are set out. In-flight parameters of satellite equipment are compared with those at the stage of development; this comparison confirmed the effectiveness of adopted scientific approaches and technical solutions. Some results obtained from the on-board measurements processing relevant to space radiation and to Earths images are presented.

Asymptotic optimization of very long, low thrust propelled inter-orbital maneuvers

Abstract Electric propulsion is capable of providing control accelerations of 1 mm/s 2 or less, four or more decimal orders below orbital gravity accelerations. This implies very long inter-orbital maneuvers counting many hundreds of revolutions. Any straightforward numerical method of thrust optimization, quite successful in deep space trajectory design, is doomed to fail when applied to trajectories this long. A practical approach is use of thrust-to-gravity ratio as a small parameter When dealing with quadratic quality criteria such as fuel consumption, this approach leads to splitting the problem into a sequence of two Optimal Control problems, corresponding to “fast” and “slow” time. The strategy has much in common with the averaging methods widely used in Celestial Mechanics. Its implementation is based on the use of the two sets of osculating elements, which describe the orbit and the thrust program, respectively. The latter one is considered as a control vector. Both sets obey the differential equations derived from the Maximum Principle Their structure is well adapted to averaging over an orbital period. The procedure eliminates the fast time, i.e. filters out the oscillatory terms with this period from the osculating elements and leaves the slow secular changes untouched. Averaging simplifies the problem so much as to make it solvable numerically. Efficient quadrature formulae were developed supplying exact numerical values as well as convenient semi-analytical representation to the integrals that appear in the averaging process. The averaged (secular, slow time) problem actually constructs an optimal end-to-end trajectory as an optimal concatenation of a set of locally optimal arcs built at the previous phase. Pontryagins principle reduces the optimization problem to a two-point boundary value problem. An algorithm designed to solve this TPBVP was developed. A representative sample transfer trajectory is presented as an illustration of the proposed technique.

Investigation of two discharge configurations in the CAMILA Hall thruster by the particle-in-cell method

The CAMILA (co-axial magneto-isolated longitudinal anode) concept was introduced to improve the ionization efficiency in low-power Hall thrusters. With relatively large coaxial anode surfaces and longitudinal magnetic strength, the CAMILA represents a significant departure from conventional Hall thrusters. In order to investigate the physical processes inside the CAMILA thruster, a two-dimensional particle-in-cell simulation of the thruster channel is used. The discharge parameters are analysed in two magnetic configurations: simplified CAMILA with a conventional magnetic field and full CAMILA with strengthened longitudinal component of the magnetic field. The simulation is fully kinetic with electrons, ions and gas atoms (xenon) represented as particles. Electron–neutral interactions are included together with particle–boundary interactions such as recombination and secondary emission. In addition, dielectric boundaries float and the cathode is represented as a free-space boundary, emitting electrons to satisfy quasi-neutrality on its surface. The high anode efficiency, observed in experiments, can be explained by several mechanisms found in this work. In the simplified case (magnetic configuration similar to the experiments) a focusing potential is created near the anode–dielectric boundary that directs ions away from the walls. It is created due to a combination of anode placement, in parallel with the channel, penetration of the plasma inside the anode cavity and the shape of magnetic force lines. Simulated steady-state results show good agreement with experimental measurements. In the full CAMILA case we demonstrate that the ionization region is found in the anode cavity. The electric field inside the anode cavity is substantial and it is directed towards the anode cavity centreline. Electrons are heated sufficiently to reach a high degree of ionization inside the anode cavity while ion currents to the anode surfaces are reduced significantly.