Missile Guidance and Pursuit

Kinematics, Dynamics and Control

N A Shneydor

• Publisher: Woodhead Publishing
• Year: 1998
• ISBN:
  9781782420590
• Topic: Technology & Engineering
• Subtopic: Aeronautic & Astronautic Engineering
• Index: Technology & Engineering

The continuing evolving capability of guided weapons demands ever more knowledge of their development. This modern and comprehensive book covers the control aspect of guidance of missiles, torpedoes, robots, and even animal predators, from the viewpoint of the pursuer. The text studies trajectories, zones of interception, the required manoeuvre effort, time of flight, launch envelopes, and stability of the guidance process. Mathematics at first-year university level is the only prerequisite. Acquaintance with feedback control theory would be helpful to the reader.

• Covers the control aspect of guidance of missiles, torpedoes, robots, and even animal predators, from the viewpoint of the pursuer
• Studies trajectories, zones of interception, the required manoeuvre effort, time of flight, launch envelopes, and stability of the guidance process

Chapter 1

Terminology and Definitions

This chapter is dedicated to definitions of several concepts and terms used in the study of guidance. Some of these definitions are not universal, there being differences between British and American usage as well as between individual authors. We shall use the terminology that seems most accepted, giving alternatives where relevant.

1.1 The Three Levels of the Guidance Process

‘Guidance’ is the process for guiding the path of an object towards a given point, which in general may be moving. If the given point is fixed and the guided object is ‘manned’ (or is, for example, a migrating bird), then the process is simply navigation.¹ Thus, although navigation can be said to be a subclass of guidance, in this book we give the term ‘guidance’ a narrower meaning, which excludes navigation. This specific meaning will now be explained.

1.1.1 Definitions

Guidance is a hierarchical process which may be said to consist of three levels.

(a) In the highest one, a geometrical rule is stated in terms of a line-of-sight that passes through the objective of the guidance. We shall henceforth refer to this objective as the target T, and to the guided object as M. This definition serves to distinguish between guidance in the meaning given to it in this book and marine navigation, for example, or inertial guidance.

The kinematics of the engagement is dealt with in this level, and problems of shape of trajectories, curvature, and required lateral accelerations are examined. Time t, of course, is usually a parameter; very often, the total time of the guidance process, from t = 0 when it started till intercept at t = t_f, is of importance. We call it the time-of-flight although M may not necessarily be an aircraft or a spacecraft.

(b) In the second level of the process, a guidance law appears. A guidance law is the algorithm by which the desired geometrical rule is implemented; this is done by closing a guidance loop (Fig. 1.1). The ‘error’ e in this feedback loop is a direct function of the measured deviation of M’s state in space from the state required by the geometrical rule. It is used to produce a steering command given to M according to the guidance law.

Figure 1.1 The guidance loop

In most cases, the command is for lateral acceleration, which will be denoted here by $a_{M_c}$

, ‘c’ signifying ‘command’. The lateral acceleration (sometimes called latax) actually performed by M is a_M · Similarly, a_T denotes the lateral acceleration of T. The resulting motion of M is such that e is reduced by the feedback, eventually driven to zero.

(c) We now come to the third level of the process, that of control. Here M is no more just a point. Rather, it is a body, say rigid, with mass and moments of inertia, whose attitude in space is defined by three angles. Clearly, it is in this level that we study the stability and performance of the body control loop, which is an inner loop whithin...