|M.Sc Student||Grinfeld Natan|
|Subject||An Optimal Missile Guidance Law with a Jerk Constraint|
|Department||Department of Aerospace Engineering||Supervisor||Professor Yoseph Ben-Asher|
|Full Thesis text|
Many tactical and strategic missiles have been using Proportional Navigation guidance law for decades (PN). Its simple implementation along with its relatively high accuracy has made PN the most popular guidance law in many applications. Some specific applications, however, may face problems when trying to implement the PN law. One such application is the case of a design constraint on the jerk (first derivative of the acceleration) for the intercepting missile. This case may occur in maneuvering missiles using Thrust Vector Control (TVC), in which the rate of body turn may be limited due to design considerations, producing a limit on the rate of acceleration, denoted as jerk. Examples of such considerations are structural constraints or sensors limitations. The main purpose of this work is to develop an optimal guidance law which minimizes the cost on the jerk. This work shows first that the motivation is justified. By introducing a jerk limit to the common PN and APN (Augmented Proportional Navigation) laws it is shown that a miss is produced, under a certain limit. The new jerk-limited guidance law (JLG) is developed by means of Cauchy-Schwartz inequality, ensuring its optimality. JLG is then compared to the common PN and APN guidance laws through many case studies run in Simulink to find it has an advantage over both of them in tight interception cases (low maneuverability ratio, limited jerk, short game time, complicated target maneuver). An implementation form for JLG is developed (one that uses commonly measured properties) and discovers a similarity to PN with a navigation ratio of 5 (PN5). JLG is then compared to PN5 and the common PN and to APN and APN5 and found to perform well, yet slightly inferior to PN in the case of an heading error and to perform better than all other guidance laws for the case of an extreme target maneuver. The results of this comparison also demonstrate the capability to tune the performance of JLG by the right choice of a jerk limit value (within the design limit of the missile) to achieve better results in terms of miss distance. Next, JLG is re-developed, this time with a first order dynamics assumed about the jerk. The new guidance law derived, called FOJG (First Order Jerk Guidance), is again compared to other guidance laws to find it is effective especially in the target maneuver case, achieving zero-miss distance in most cases.