Guided Missiles

Guided Missile:

• ·       Unmanned Explosive device.
• ·       Combination of electrical, digital and mechanical parts.
• ·       Internal control monitors every function to assure the success of mission otherwise aborted.

    Mainly of two types

• ·       Strategic Missile: Like ICBM (Internal Continental Ballistic Missile), attacks target at long distances – thousands of miles.
• ·       Tactical Missile: Shorter distances like few to hundred miles.

               5 to 20 ft long

               Weigh - 20 to 2000 pounds

               Construction – Titanium Alloy

               Speed – Average 700 mph

               Cost – Tens to hundreds of thousands of Dollars

   Missiles Classification:

·       Ground to Ground – Tow

·       Ship to Ground – Cruise

·       Ground to Air – Stinger

·       Air to Ground – Apache

·       Ship to Air – Standard Missile

Parts and Functionality of Tactical Missile:

•        Radome

•        Housing made of ceramic material and located at the   front nose of the missile.

•        Non Metallic.

•        Guidance

•        A system that receives radio information from its launch controller -  a computer.

•        The Guidance system also transmits all missile functions back to its launch controller.

•        Warhead

•        A system containing missile internal homing radar.

•        explosive surrounded by thousands of serrated iron pieces or other destroying material.

•        Autopilot

•        A system that provides missile location, direction, velocity and "attitude".

•        Autopilot contains an antenna to receive and transmit information to its home controller.   It also contains a battery.

•        Dorsal Fins

•        The fins, along with the missile body, provide surfaces against which air exerts pressure.

•        change the direction and attitude of the missile.

•        Rocket Motor

•        A mixture of solid chemical fuels.   When ignited, the chemicals propel the missile from its launcher into space.

•        Steering Control

•        A system that electrically changes the Control Surfaces that change the missile motion.

•        It reacts to information sent to it by the Autopilot.

•        Control Surface

•        These are four "fins" that act against air resistance to change the direction of the missile.

Missile Control and Guidance

Missile Guidance and Controls

Introduction

The term missile in the post- World War II era has generally been used synonymously with "guided missile," due to the wide impact of guided missile technology upon the weapons field.

        FUNDAMENTALS OF GUIDANCE SYSTEMS

        Purpose and Function

               Every missile guidance system consists of an attitude control system and a flight path control system. The attitude control system functions to maintain the missile in the desired attitude on the ordered flight path by controlling the missile in pitch, roll, and yaw. The attitude control system operates as an auto-pilot, damping out fluctuations that tend to deflect the missile from its ordered flight path. The function of the flight path control system is to determine the flight path necessary for target interception and to generate the orders to the attitude control system to maintain that path.

       TYPES OF GUIDANCE SYSTEMS

              Missile guidance systems may be classified into two broad categories: missiles guided by man-made electromagnetic devices, and those guided by other means.

All of the missiles that maintain electromagnetic radiation contact with man-make sources may be further subdivided into two subcategories.

Control guidance missiles:

           Control guidance missiles are those that are guided on the basis of direct electromagnetic radiation contact with friendly control points.

Radar Control Guidance: Radar control guidance may be subdivided into two separate categories. The first category is simply referred to as the command guidance method. The second is the beam-rider method, which is actually a modification of the first, but with the radar being used in a different manner.

Command guidance:The term command is used to describe a guidance method in which all guidance instructions, or com-mands, come from sources outside the missile. The guidance sys- tem of the missile contains a receiver that is capable of re- ceiving instructions from ship or ground stations or from air- craft. The missile flight-path control system then converts these commands to guidance information, which is fed to the attitude control system.

Beam-rider Method:The main difference between the beam-rider method and the radar command guidance method is that the characteristics of the missile-tracking radar beam are not varied in the beam-rider system. The missile has been designed so that it is able to formulate its own correction signals on the basis of its position with respect to the radar scan axis.

Homing guidance missiles:

Homing guidance systems control the flight path by employing a device in the weapon that reacts to some distinguishing feature of the target. Homing devices can be made sensitive to a variety of energy forms, including RF, infrared, reflected laser, sound, and visible light. In order to home on the target, the missile or torpedo must determine at least the azimuth and elevation of the target by one of the means of angle tracking mentioned pre-viously. 

Active Homing: In active homing, the weapon contains both the transmitter and receiver. Search and acquisition are conducted as with any tracking sensor. The target is tracked employing monostatic geometry in which the returning echo from the target travels the same path as the transmitted energy

Semi active Homing: In semiactive homing, the target is illuminated by a tracking radar at the launching site or other control point. The missile is equipped with a radar receiver (no transmitter) and by means of the reflected radar energy from the target, formulates its own correction signals as in the active method.

Passive Homing: Passive homing depends only on the target as a source of tracking energy.

 Retransmission Homing or Track Via Missile (TVM). Re-transmission homing is a blending of the characteristics of both command and semiactive homing guidance. In command guidance, missile steering commands are computed at the launch point using target position and missile position data derived from launch point sensors.

GUIDED FLIGHT PATHS

                A guided missile is usually under the combined influence of natural and man-made forces during its entire flight. Its path may assume almost any form. Man-made forces include thrust and directional control as shown in figure 16-14. The vector sum of all the forces, natural and man-made, acting on a missile at any instant, may be called the total force vector. 

Preset Flight Paths.

Preset flight paths are of two types: constant and programmed.

Constant: A preset guided missile path has a plan that has been fixed beforehand. This plan may include several different phases, but once the missile is launched, the plan cannot be changed. The phases must follow one another as originally planned. The simplest type of preset guided missile path is the constant preset. Here, the missile flight has only one phase.

Programmed: A missile could be guided in a preset path against a fixed target; the joint effect of missile power and gravity would then cause the path to become a curve. A missile following a preset path may be guided in various ways--for in-stance, by an autopilot or by inertial navigation. The means of

propulsion may be motor, jet, or rocket.

Variable Flight Paths:

The guided flight paths of greatest interest are those that can vary during flight. In general, the heading of the weapon is a function of target position and velocity. These parameters are measured by continuous tracking, and the resultant missile flight path is determined, assuming that the target motion will remain unchanged until new data is received.

Pursuit: The simplest procedure for a guided missile to follow is to remain pointed at the target at all times. The mis-sile is constantly heading along the line of sight from the mis-sile to the target, and its track describes a pursuit path with the rate of turn of the missile always equal to the rate of turn of the line of sight. Pure pursuit paths are highly curved near the end of flight, and often the missile may lack sufficient

Constant Bearing: At the opposite extreme to a pursuit path is a constant-bearing or collision path. The missile is aimed at a point ahead of the target, where both the missile and target will arrive at the same instant. The line of sight to this point does not rotate relative to the missile. The missile path is as linear as the effect of gravity and aerodynamic forces allow. If the target makes an evasive turn or if the target's velocity changes, a new collision course must be computed and the missile flight path altered accordingly.

Proportional Navigation: The more advanced homing mis-siles will employ some form of proportional navigation. The mis-sile guidance receiver measures the rate of change of the line of sight (LOS) (bearing drift, if you will) and passes that informa-tion to the guidance computer, which in turn generates steering commands for the autopilot. The missile rate of turn is some fixed or variable multiple of the rate of change of the LOS. This multiple, called the navigation ratio, can be varied during mis-sile flight to optimize performance.

Line of Sight: Defined as a course in which the missile is guided so as to remain on the line joining the target and point of control. This method is usually called "beam riding."

Overview

Electronic systems operate on two types of signals.

1. Continuous-Time (CT) signals or discrete-time (DT) signals. A continuous-time system is one in which the input signals are defined along a continuum of time, such as an analogue signal which “continues” over time producing a continuous-time signal. But a continuous-time signal can also vary in magnitude or be periodic in nature with a time period T. Generally, most of the signals present in the physical world which we can use tend to be continuous-time signals. For example, voltage, current, temperature, pressure, velocity, etc.
2. Discrete-time system is one in which the input signals are not continuous but a sequence or a series of signal values defined in “discrete” points of time. This results in a discrete-time output generally represented as a sequence of values or numbers. A continuous-time signal, x(t) can be represented as a discrete set of signals only at discrete intervals or “moments in time”. Discrete signals are not measured versus time, but instead are plotted at discrete time intervals, wheren is the sampling interval. As a result discrete-time signals are usually denoted as x(n) representing the input and y(n)representing the output.

         

           In feedback systems, the output signal is “fed back” and either added to or subtracted from the original input signal. The result is that the output of the system is continuously altering or updating its input with the purpose of modifying the response of a system to improve stability. A feedback system is also commonly known as a Closed-loop System. 

If the feedback loop reduces the value of the original signal, the feedback loop is known as “negative feedback”. If the feedback loop adds to the value of the original signal, the feedback loop is known as “positive feedback”.

Transfer Functions:

            Transfer Function is defined as the ratio of the Laplace transform of the output variable to the Laplace transform of the input variable, with all zero initial conditions.

A transfer function has the following properties:

·  The transfer function is defined only for a linear time-invariant system. It is not defined for nonlinear                systems.

·  The transfer function between a pair of input and output variables is the ratio of the Laplace transform of        the output to the Laplace transform of the input.

·  All initial conditions of the system are set to zero.

·  The transfer function is independent of the input of the system.

To derive the transfer function of a system, we use the following procedures:

1. Develop the differential equation for the system by using the physical laws, e.g. Newton’s laws and Kirchhoff’s laws.
2. Take the Laplace transform of the differential equation under the zero initial conditions.
3. Take the ratio of the output Y(s) to the input U(s). This ratio is the transfer function.

The part in the denominator of the transfer function which indicates us the position of poles in the system is known as Characteristic Equation.

Root Locus:

              Path of  poles of a close loop transfer function of characteristic equation as a function if gain.

         For Example:

          Transfer function  

         Locus on Real Axis

We have n=3 poles at s = 0, -3, -2.

         Cross Imag. Axis

Locus crosses imaginary axis at 2 values of K. Locus crosses where K = 0, 30.2, corresponding to crossing imaginary axis at s=0, ±2.45j, respectively.

    For Example 2:

    Transfer function

       Completed Root Locus

We have n=2 poles at s = 2, -1.  We have m=1 finite zero at s = -3.

         Cross Imag. Axis

Locus crosses where K = 0.646, 1, corresponding to crossing imaginary axis at s=0, ±0.994j, respectively.

Response of Control System

Steady state occurs after the system becomes settled and at the steady system starts working normally. Steady state response of control system is a function of input signal and it is also called as forced response. 
The transient state response of control system gives a clear description of how the system functions during transient state and steady state response of control system gives a clear description of how the system functions during steady state.

Steady State Error : It can be defined as the difference between the actual output and the desired output as time tends to infinity.

It is clear that the steady state response of control system depends only on the time constant ‘T’ and it is decaying in nature. 

Let us consider the block diagram of the second order system.

Now we will see the effect of different values of ζ on the response. We have three types of systems on the basis of different values of ζ.

1. Under damped system : A system is said to be under damped system when the value of ζ is less than one. In this case roots are complex in nature and the real parts are always negative. System is asymptotically stable. Rise time is lesser than the other system with the presence of finite overshoot.
2. Critically damped system : A system is said to be critically damped system when the value of ζ is one. In this case roots are real in nature and the real parts are always repetitive in nature. System is asymptotically stable. Rise time is less in this system and there is no presence of finite overshoot.
3. Over damped system : A system is said to be over damped system when the value of ζ is greater than one. In this case roots are real and distinct in nature and the real parts are always negative. System is asymptotically stable. Rise time is greater than the other system and there is no presence of finite overshoot.
4. Oscillations : A system is said to be sustain damped system when the value of zeta is zero. No damping occurs in this case.

PID:

PID control stands for proportional plus derivative plus integral control. PID control is a feedback mechanism which is used in control system. This type of control is also termed as three term control. By controlling the three parameters – proportional, integral and derivative we can achieve different control actions for specific work.
let's take a look at how the PID controller works in a closed-loop system using the schematic shown above. The variable () represents the tracking error, the difference between the desired input value () and the actual output (). This error signal () will be sent to the PID controller, and the controller computes both the derivative and the integral of this error signal. The control signal () to the plant is equal to the proportional gain () times the magnitude of the error plus the integral gain () times the integral of the error plus the derivative gain () times the derivative of the error.