Oded M. Golan

Sliding-Mode Control for Integrated Missile Autopilot Guidance

A sliding-mode controller is derived for an integrated missile autopilot and guidance loop. Motivated by a differential game formulation of the guidance problem, a single sliding surface, defined using the zero-effort miss distance, is used. The performance of the integrated controller is compared with that of two different two-loop designs. The latter use a sliding-mode controller for the inner autopilot loop and different guidance laws in the outer loop: one uses a standard differential game guidance law, and the other employs guidance logic based on the sliding-mode approach. To evaluate the performance of the various guidance and control solutions, a two-dimensional nonlinear simulation of the missile lateral dynamics and relative kinematics is used, while assuming first-order dynamics for the target evasive maneuvers. The benefits of the integrated design are studied in several endgame interception engagements. Its superiority is demonstrated especially in severe scenarios where spectral separation between guidance and flight control, implicitly assumed in any two-loop design, is less justified. The results validate the design approach of using the zero-effort miss distance to define the sliding surface.

Integrated Sliding Mode Autopilot-Guidance for Dual-Control Missiles

An integrated autopilot and guidance algorithm is developed, using the sliding mode control approach, for a missile with forward and aft control surfaces. Based on guidance considerations, the zero efiort miss (ZEM), encountered in difierential games guidance solutions, is used as one of the sliding variables in the proposed control scheme. The dual control conflguration provides an additional degree of freedom in the integrated design. This degree of freedom is exploited by introducing a second sliding surface, selected based on autopilot design considerations. Restraining the system to the ZEM surface guarantees zero miss distance, while remaining on the second surface provides a damped response. The performance of the integrated dual controller is evaluated using a two-dimensional nonlinear simulation of the missile lateral dynamics and relative kinematics, assuming flrst order dynamics for the target evasive maneuvers. The simulation results validate the design approach of using ZEM and the ∞ight-control based sliding surfaces to attain high accuracy interceptions.

Integrated Sliding Mode Guidance and Control for a Missile with On-Off Actuators

A sliding mode controller was recently introduced for integrated guidancecontrol loops of agile missiles. The sliding surface was chosen to be the zeroeffort miss-distance. The current work extends this result to address nonlinear on-off actuators commonly used in such interceptors. The performance of the integrated design is compared with a two-loop design, i.e., separate guidance and autopilot loops. The simulation includes a detailed pneumatic model of the aerodynamic surface actuators. Compared to the results obtained with a linear first order actuation system, it is shown that the advantages of the integrated design are more significant when tested with the on-off actuator. The proposed integrated algorithm is effective especially for the endgame phase of the interception. However, its high interception accuracy can be attained only if engaged from a limited range of initial conditions within the so called region of attraction, thus posing performance requirements to the midcourse guidance system. The paper presents the regions of attraction for a sample interception setup.

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.

Bounded differential games guidance law for dual-controlled missiles

A new guidance law tailored for an interceptor missile having forward and aft controls is proposed. The guidance law is derived using a differential games formulation with bounded controls. For the derivation, the interceptor closed-loop dynamics is represented by two first-order bi-proper transfer functions. Possible game-space structures are investigated, including a new one with two closed singular regions. The effect of the direct lift associated with the canard and tail controls is investigated, and it is proved that zero miss distance can always be guaranteed for some initial conditions. It is also shown that for the tail control a switching surface at some constant time before interception exists in the game-space, resulting from its nonminimum-phase nature.

Linear Quadratic Differential Games Guidance Law for Dual Controlled Missiles

A novel guidance law designed specifically for a missile having forward and aft control systems is presented. For the derivation a linear quadratic differential games formulation of the end-game interception scenario is used. Conditions for achieving perfect intercept are given and new game spaces are presented. It is also shown that increasing the direct lift associated with the canard control allows intercepting targets with higher maneuvering capability, while for the tail control the effect is opposite.

Head Pursuit Guidance

DOI: 10.2514/1.27737 Aguidancelawforintercepting high-speedtargetsinanovelheadpursuitengagementispresented.Theguidance law imposes a geometric relation in which the interceptor missile is positioned ahead of the target so that both fl yi n the same direction. The missile speed is planned to be lower than that of the target, and therefore the target closes in on the interceptor missile and it is intercepted from its front end. The guidance law also enables enforcing a predeterminedinterceptionanglerelativetothetarget’s flightdirection.Analyticconditionsenablinginterceptionin this novel engagement are provided. The guidance law is implemented using the sliding mode approach, and simulation results confirm its viability in several representative engagements against maneuvering high-speed targets. NTERCEPTION of high-speed targets, such as reentering ballistic missiles, is a formidable challenge. The interception in these scenarios is typically head-on, with a very high closing speed. This imposes severe requirements on the interceptor systems such as precise detection of the target from a large distance by the onboard seekers, and very fast response time of the missile subsystems. To overcome these difficulties, a different approach was suggested in [1],inwhichtheinterceptorvelocityismatchedwiththatofthetarget by a preliminary maneuver. If the target path is predictable, as in the case of ballistic missiles, the maneuver can be designed such that the interceptor missile is positioned ahead of the target on its predicted flight path, flying in the same direction but at a slightly lower speed. This way the target closes in on the interceptor that is conducting the necessary lateral maneuvers to achieve interception. The interceptor speed along the target’s predicted path can be selected to achieve a desired closingrate. Asimilar lowclosingspeedcanbe obtainedina tail-chase scenario. However, tail chase requires that the interceptor will be faster than the target, and therefore more energy is needed during the preliminary maneuver to reach the desired closing speed. Various guidance methods have been examined for implementation in the different stages of high-speed exo- or endo-atmospheric interception scenarios of ballistic missiles. Some of these methods are described next. In [2] a modified version of proportional navigation (PN) guidance law [3] was proposed for implementation in the coast phase. A variable bias was applied to the actual line of sight (LOS) to account for engine burn. The terminal guidance in a hyper-velocity exo-atmospheric orbital interception was studied in [4]. The control energy expenditure is reduced by constraining the expected final state to a function of the estimation error. An optimal guidance algorithm was proposed in [5] for the interception of a nonmaneuvering target decelerated by atmospheric drag. Its implementation requires knowledge on many scenario states, obtained from a nonlinear state estimator. In a recent paper [6] a differential game guidance law was proposed against targets having knownspeedandlateralaccelerationlimitprofiles.Itwasshownthat in a ballistic missile interception scenario such a guidance law provides a significant improvement in the homing accuracy

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). >

Exo-Atmospheric Guidance of an Accelerating Interceptor Missile

Abstract An exo-atmospheric interception scenario between an accelerating missile and its target is investigated. It is assumed that the maneuvering acceleration is obtained by instantaneous rotation of the missiles body to the required attitude. Two different guidance laws are derived for such an interceptor using the sliding mode control methodology. The difference is in the definition of the sliding surface enforcing different trajectories for the interceptor. It is shown that if this surface is chosen as the zero-effort-miss of the well-known proportional navigation guidance law, then the missile is commanded to point its acceleration vector along the line-of-sight and consequently fly along a curved trajectory. For the second guidance law, a unique sliding surface is chosen enforcing the missile to fly on a straight line towards collision, after the initial heading error is nulled. The performance of the guidance laws is analyzed and compared using a nonlinear two dimensional simulation. It is shown that on top of enforcing a different flight geometry for the interceptor, the use of the new guidance to collision sliding mode guidance law can enhance the capture zone of the interceptor.

Head Pursuit Guidance for Hypervelocity Interception

*† A new guidance law for intercepting targets in a novel head-pursuit engagement is presented. The guidance law positions the interceptor missile ahead of the target, on its flight trajectory, so that both fly in the same direction. The missile speed is planned to be lower than that of the target, and therefore the target closes in on the interceptor missile. Using this approach the closing speed is significantly reduced relative to a head-on engagement; compared to a tail-chase engagement, the low closing speed is achieved with reduced energy requirements. The guidance law is similar to deviated pure pursuit but with a time varying lead angle. Analytic solutions of the relative trajectories and interception envelopes are given for the case of a non-maneuvering target. The performance of the new guidance law is studied through simulation for the case of a maneuvering target and interceptor employing a continuous or bang-bang maneuver device. The implementation of the new guidance scheme may dramatically reduce the requirements from missile subsystems for the interception of high speed targets, such as ballistic missiles.