Fundamentals of Naval Weapons Systems

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Fundamentals of Naval Weapons Systems

Chapter 1 Naval Weapons Systems Chapter 2 Energy Fundamentals Chapter 3 Elements of Feedback Control Chapter 4 Computational Systems Chapter 5 Automatic Tracking Systems Chapter 6 Track-While-Scan Concepts Chapter 7 Electronic Scanning and the Phased Array Chapter 8 Principles of Underwater Sound Chapter 9 Underwater Detection and Tracking Systems Chapter 10 Visible and Infrared Spectrum Chapter 11 Countermeasures Chapter 12 Military Explosives Chapter 13 Warheads Chapter 14 Fusing Chapter 15 Guidance and Control Chapter 16 Weapon Propulsion and Architecture Chapter 17 Launching Systems Chapter 18 Reference Frames and Coordinate Systems Chapter 19 Ballistics and the Fire Control Problem Chapter 20 Command, Control, and Communication

Supplements: Communication Supplement Nuclear Effects Nuclear Supplement Bandwidth Ring Laser Gyros HF Radio Propagation Towed Array Sonar System Superhetrodyne Seasonal Variation in SVP's Interferometry

Chapter 1 Introduction Introduction 1 1 Naval Weapons Systems 1 Introduction

OBJECTIVES: At the conclusion of this chapter the student will:

1. Understand the basic purpose of any weapon system through an analysis of the Fire Control Problem.

2. Be able to identify and explain the six fundamental steps/tasks that comprise the Fire Control Problem.

3.

Understand the basic concepts of the "detect to engage" sequence.

4.

Be familiar with the basic components that comprise a modern weapons system.

The international situation has deteriorated and the United States and Nation X have suspended diplomatic relations. The ruler of Nation X has threatened to annex the smaller countries bordering Nation X and has threatened hostilities toward any country that tries to stop him. You are assigned to a guided missile cruiser which is a member of Battle Group Zulu, currently stationed approximately 300 nautical miles off the coast of Nation X. The Battle Group Commander has placed the Battle Group on alert by specifying the Warning Status as Yellow, in all warfare areas, meaning that hostilities are probable.

You are standing watch as the Tactical Action Officer (TAO) in the Combat Information Center (CIC), the nerve center for the ship's weapons systems. Dozens of displays indicate the activity of ships and aircraft in the vicinity of the Battle Group. As the TAO you are responsible for the proper employment of the ship's weapons systems in the absence of the Commanding Officer. It is 0200 and you are in charge of a multi-million dollar weapon system and responsible for the lives and welfare of your shipmates.

The relative quiet of CIC is shattered by an alarm on your Electronic Warfare (EW) equipment indicating the initial detection and identification of a possible incoming threat by your Electronic Support Measures (ESM) equipment. The wideband ESM receiver detects an electromagnetic emission on a bearing in the direction of Nation X. Almost instantaneously the emitter's parameters are interpreted by the equipment and compared with radar parameters stored in the memory of the ESM equipment. On a display screen the information and a symbol indicating the emitter's approximate line of bearing from your ship is presented. You notify the Commanding Officer of this new development. Meanwhile the information is transmitted to the rest of the Battle Group via radio data links.

Moments later, in another section of CIC, the ship's long range two-dimensional air search radar is just beginning to pick up a faint return at the radar's maximum range. The information from the air search radar coupled with the line of bearing from your ESM allow you to localize the contact and determine an accurate range and bearing. Information continues to arrive, as the ESM equipment classifies the J-band emission as belonging to a Nation X attack aircraft capable of carrying anti-ship cruise missiles.

The contact continues inbound, headed toward the Battle Group, and within minutes is within range of your ship's three-dimensional search and track radar. The contact's bearing, range, and altitude are plotted to give an accurate course and speed. The range resolution of the

pulse compressed radar allows you to determine that the target is probably just one aircraft. You continue to track the contact as you ponder your next move.

As the aircraft approaches the outer edge of its air launched cruise missile's (ALCM) range, the ESM operator reports that aircraft's radar sweep has changed from a search pattern to a single target track mode, indicating imminent launch of a missile. In accordance with the Rules of Engagement (ROE) in effect, you have determined that this action shows hostile intent on the part of the target, and decide to defend the ship against immienent attack. You inform your CIC team of your intentions, and select a weapon, in this case a surface to air missile, to engage the target. You also inform the Anti-Air Warfare Commander of the indications of hostile intent, and he places you and the other ships in Air Warning Red, attack in progress.

As the target closes to the maximum range of your weapon system, the fire control or tactical computer program, using target course and speed, computes a predicted intercept point (PIP) inside the missile engagement envelope. This information is and the report that the weapon system has locked on the target is reported to you. You authorize batteries released and the missile is launched toward the PIP. As the missile speeds towards its target at Mach 2+, the ship's sensors continue to track both the aircraft and the missile. Guidance commands are sent to the missile to keep it on course.

Onboard the enemy aircraft, the pilot is preparing to launch an ALCM when his ESM equipment indicates he is being engaged. This warning comes with but precious few seconds, as the missile enters the terminal phase of its guidance. In a desperate attempt to break the radar lock he employs evasive maneuvering. It's too late though, as the missile approaches the lethal "kill radius," the proximity fuze on the missile's warhead detonates its explosive charge sending fragments out in every direction, destroying or neutralizing the target. This information is confirmed by your ship's sensors. The radar continues to track the target as it falls into the sea and the ESM equipment goes silent.

The Fire Control Problem

What has just been described above is not something out of a war novel, but rather a scenario of a possible engagement between a hostile force (the enemy attack aircraft) and a Naval Weapons System (the ship). This scenario illustrates the concept of the "detect to engage" sequence, which is an integral part of the modern Fire Control Problem. Although the scenario was one of a surface ship against an air target, every weapon system performs the same functions: target detection, resolution or localization, classification, tracking, weapon selection, and ultimately neutralization. In warfare, these functions are accomplished from

submarines, aircraft, tanks and even Marine infantrymen. The target may be either stationary or mobile; it may travel in space, through the air, on the ground or surface of the sea, or even beneath the sea. It may be manned or unmanned, guided or unguided, maneuverable or in a fixed trajectory. It may travel at speeds that range from a few knots to several times the speed of sound.

The term weapons system is a generalization encompassing a broad spectrum of components and subsystems. These components range from simple devices, operated manually by a single man, accomplishing one specific function, to a complex array of subsystems, interconnected by computers, and data communication links that are capable of performing several functions or engaging numerous targets simultaneously. Although each subsystem may be specifically designed to solve a particular part of the fire control problem, it is these components operating in concert that allows the whole system to achieve its ultimate goal - the neutralization of the target.

Components

All modern naval weapons systems, regardless of the medium they operate in or the type of weapon they employ, consist of the basic components that allow the system to detect, track and engage the target. Sensor components must be designed for the environments in which the weapon system and the target operate. These components must also be capable of coping with widely varying target characteristics, including target range, bearing, speed, heading, size and aspect.

Detecting the Target

There are three phases involved in target detection by a weapons system. The first phase is surveillance and detection, the purpose of which is to search a predetermined area for a target and detect its presence. This may be accomplished actively, by sending energy out into the medium and waiting for the reflected energy to return, as in radar, and/or passively, by receiving energy being emitted by the target, as by ESM in our scenario. The second phase is to measure or localize the target's position more accurately and by a series of such measurements estimate its behavior or motion relative to ownship. This is accomplished by repeatedly determining the target's range, bearing, and depth or elevation. Finally, the target must be classified, that is, its behavior must be interpreted so as to estimate its type, number, size and most importantly identity. The capabilities of weapon system sensors are measured by the maximum range at which they can reliably detect a target and their ability to distinguish individual targets in a multi-target group. In addition, sensor subsystems must be able to

detect targets in a medium cluttered with noise, which is any energy sensed other than that attributed to a target. Such noise or clutter is always present in the environment due to reflections from rain or the earth's surface or as a result of deliberate radio interference or jamming. It is also generated within the electronic circuitry of the detecting device.

Tracking the Target

Sensing the presence of a target is an essential first step to the solution of the fire control problem. To successfully engage the target and solve the problem, updates as to the target's position and its velocity relative to the weapon system must be known or estimated continuously. This information is used to both evaluate the threat represented by the target and to predict the target's future position and a weapon intercept point so the weapon can be accurately aimed and controlled. In order to obtain target trajectory information, methods must be devised to enable the sensor to follow or track the target. This control or "aiming" may be accomplished by a collection of motors and position sensing devices called a servo system. Inherent in the servo process is a concept called feedback. In general, feedback provides the system with the difference between where the sensor is pointing and where the target is actually located. This difference is called system error. The system then takes the error and through a series of electro-mechanical devices moves the sensor and/or weapon launcher in the proper direction and at a rate such that the error is reduced. It is the goal of any tracking system to reduce this error to zero. Realistically this isn't possible so when the error is minimal the sensor is then said to be "on target." Sensor and launcher positions are typically determined by devices that are used to convert mechanical motion to electrical signals. Synchro transformers and optical encoders are commonly used in servo systems to detect the position and control the movement of power drives and indicating devices. The power drives then move the radar antennas, directors, gun mounts, and missile launchers.

The scenario presented in the beginning of this chapter was in response to a single target. In reality, this is rarely the case. The modern "battlefield" is one in which sensors are detecting numerous contacts, friendly and hostile, and information is continually being gathered on all of them. The extremely high speed, precision, and flexibility of modern computers enable the weapons systems and their operators to compile, coordinate, evaluate the data, and then initiate an appropriate response. Special-purpose and general-purpose computers enable a weapons system to detect, track, and predict target motion automatically. These establish the target's presence and define how, when, and with what weapon the target will be engaged.

Engaging the Target

Effective engagement and neutralization of the target requires that a destructive mechanism, in this case a warhead, be delivered to the vicinity of the target. How close to the target a warhead must be delivered depends on the type of warhead and the type of target. In delivering the warhead, the aiming, launch, and type of propulsion system of a weapon, and the forces which the weapon are subjected to enroute to the target need to be considered. The weapon's capability to be guided or controlled after launch dramatically increases its accuracy and probability of kill from a single weapon. The use of guidance systems also dramatically complicates system designs. These factors as well as the explosive to be used, the fuzing mechanism, and warhead design are all factors in the design and effectiveness of a modern weapon.

Conclusion

As can be seen, solving the fire control problem, from target detection to neutralization, requires a complex integration of numerous components which must operate together to achieve the goal. At the functional center of every weapon system is a human being, who is engaged in the employment of that system. Today's high technology naval weapons systems require that a Naval/Marine Corps Officer be competent in the scientific and engineering principles that underlie their design, operation and employment. Understanding the basic rules for evaluating or predicting a weapon system's performance are necessary as an aid to the imaginative use of tactics. Unless every weapons system operator possesses a thorough understanding of the physical processes that define the performance of equipment, our operating forces will be unable to make full use of their assets and exploit the weaknesses and limitations of the enemy.

QUESTIONS

1. List and briefly explain the six tasks that must be resolved in order to solve the Fire Control Problem.

2. What are the two basic ways in which a sensor initially detects the presence of a target? Give an example of each.

3. What are the two ways a detecting device's (sensor) capability is measured?

Chapter 2

Energy Fundamentals 1 1 Naval Weapons Systems Sensors

Introduction

The first requirement of any weapon system is that it have some means of detecting a target. This function of the Fire Control Problem, as well as several others, is accomplished by the weapon system sensor. In order to detect, track and eventually nuetralize a target, the weapon system must be capable of sensing some unique characteristic that differentiates or identifies it as a target. One such characteristic is the energy that is either emitted or reflected by the target. Once the energy is detected the weapon system sensor can perform some of the other functions of the Fire Control Problem, namely the localization, identification and tracking of the target. The information thus obtained by the sensor can then be furnished to the other components of the weapons system.

This section is heavily directed toward the properties of radar energy, but the principles presented in Chapter 2 are the same for all other types of electromagnetic energy--such as radio, infrared, visible light, and X-rays. Sound energy, though not electromagnetic, also exhibits many of these same properties, as will be described later in this section. It is imperative that a solid foundation in the principles of energy transmission and propagation be acquired in order to fully understand the design and use of the various types of modern weapons-system sensors.

2

Radar

Energy Fundamentals

OBJECTIVES

1.

Understand the relationship between wavelength and the speed of wave propagation.

2. Understand the concept of the generation of electromagnetic energy and the relationship between the E and H fields in an electromagnetic wave.

3. Be acquainted with the concepts of time and distance as they affect wave phase angle and constructive and destructive interference.

4.

Understand the principles of reflection, refraction, ducting and polarization.

5.

Know how antenna and target height affect detection range.

6.

Know the relationship between frequency and wave propagation path.

CHARACTERISTICS OF ENERGY PROPAGATION

The Nature of Waves

The detection of a target at tactically advantageous ranges can only be accomplished by exploiting energy that is either emitted by or reflected from the target. The form of energy that has proven to be the most suitable is energy wzves. This type of energy radiates or propagates from a source in waves, in much the same way as waves spread out concentrically from the point of impact of a pebble dropped in water. A small portion of the surface is elevated above the normal level of the pond by the force of pebble impact. This elevated portion is immediately followed by another portion that is below the normal level of the pond,

conserving the water medium. Together the two parts appear as a small portion of a sine wave function that is perpendicular to the surface of the pond. The disturbance seems to move equally in all directions, and at a constant speed away from the point of impact. This type of activity is known as a transverse travelling wave.

While the waves created by this familiar example are two-dimensional, electromagnetic energy radiated from a point in a vacuum travels in three-dimensional waves--i.e., concentric spheres. The fact that, unlike sound, electromagnetic waves travel through a vacuum reminds us that the wave does not depend upon a substantive medium, but rather upon "fields" of potential force, that is the electric and magnetic fields that make up the electromagnetic wave. In the study of radiated energy, it is often difficult to envision expanding spheres of concentric wave fronts as they propagate through space. To model the wave and keep track of its progress, it is convenient to trace the two dimensional ray paths rather than the waves. A ray is formed by tracing the path of a hypothetical point on the surface of a wave front as it propagates through a medium. This trace forms a sinusoid and models a transverse travelling wave. No matter what type of weapon system is being discussed, energy waves are usually involved at some point in the detection, tracking, and nuetralization of the target. It is therefore very important to understand some fundamental concepts and descriptive properties of energy waves, because it is fundamental to all our modern weapons systems.

Frequency

Perhaps the single most important property that distinguishes between the different forms of radaited energy is frequency. Nearly all wave activity is periodic, menaing that the disturbance forming the wave happens over an over again in usually rapid succession. If the number of disturbances that occur over a given time (usually one second) are counted, then we have a measure that describes the periodic structure or frequency of that wave. As mentioned previously, a wave disturbance produces a maximum (crest) followed by a minimum (trough) value. By counting the number of maximums and minimums per second gives us the frequency which is measured in cycles per second or hertz (Hz), named in honor of Heinrich Hertz who in 1887 was the first to produce and detect electromagnetic waves in the radio frequency range. In the case of sound, frequency is the rate at which the medium is successively compressed and expanded by the source. For electromagnetic energy such as radio, radar, and light, it is the rate at which the electric and magnetic fields of a propagating wave increase and decrease in intensity. Since radiated energy is composed of periodic waves, these potential force fields can be represented by sine or cosine waves.

To help understand the significance of frequency as a descriptive parameter, it may be helpful to know that the push tones on your telephone, radio waves, heat, light, x-rays and gamma radiation may all be described as radiated sinusoidal waves. It is the frequency that distinguishes one of these energy forms from the other. Discriminating one form of radiated energy from another on the basis of frequency alone is called a spectrum. Figure 2.1 shows how the various forms of wave energy relate to frequency. Audio frequencies are low numbers, ranging from about 10 to 20,000 Hz. At about 20,000 Hz the nature of waves change from the more mechanical sound waves to electromagnetic waves, which comprise the remainder of the spectrum. At the lower frequencies are radio, television, radar and microwave ransmissions. This radio band is very wide ranging from 20 thousand (kilo) to about 200 million (Mega) Hz fro radio and television, and to 100 billion (Giga) Hz for radar and microwaves. At yet higher frequencies the energy forms become heat, then visible light, followed by x-rays and finally gamma radiation. The entire spectrum has covered 20 orders of mamgnitude, and yet the sinusoidal wave form of the radaited energy has remained the same!

Velocity

The velocity that waves spread from their source can vary dramatically with the form of the energy and with the medium the energy is spreading through. The velocity at which the energy propagates can vary from a few meters per second as in the case of the wave on the surface of the pond to 300 million (3x108) meters per second for the velocity of an electromagnetic wave in a vacuum. For an electromagnetic wave travelling in other mediums the speed may be substantianally reduced. For example, electromagnetic energy flowing alog a wire, or light passing though a lens may have a velocity that is only about 3/4 that of the velocity in a vacuum.

As a wave passes through mediums with different propagation velocities, the path of the wave may be significantly altered. It is therefore useful to have a relative measure of the effect of different mediums and materials on wave speed. The measure of this difference in propagation velocity is called the index of refraction. The index of refraction is simply the ratio of a wave in a standard medium or material (usually designated as c) divided by the velocity of the wave in the medium being examined. For sound waves the standard velocity is usually the velocity in a standard volume of air or seawater. For electromagnetic waves, the standard is the propagation velocity in a vacuum. As an example, if the velocity of light in a galss lens were 3/4 of the velocity in a vacuum, the index of refraction would be 3x108 m/sec divided 2.25x108 m/sec, giving an index of refraction of 1.33. For radar frequencies and above, the index of refraction of air is very close to 1.0 and therefore the velocity difference in the two mediums is usually ignored in the timing of radar echoes to determine target range.

Wavelength

We have seen that all travelling waves consist of a periodically repeating structure, and that the wave propagates at some idetifiable velocity. A new descriptive parameter that combines the two measurements of frequency and velocity will now be examined. If the distance between two easily identifiable portions of adjacent waves, such as the crests, is measured, then we have measured the the wave travels during one complete wave cycle. This distance is known as wavelength (). Notice that the wavelength depends on how fast the wave is moving (wave velocity) and how often the the disturbances are coming (wave frequency). From physics we know that distance (wavelength) equals velocity (c) multiplied by time. Figure 2.2 shows a wave as it would exist at any one instant in time over a distance r, in the direction of propagation. The time interval required for the wave to travel exactly one wavelength, that is for the displacement at point r4 to return to the same value as it had at the beginning of that time interval, is known as the period and is given the symbol T. This time period is also equal to the reciprocal of the frequency of oscillation. From these observations, an inverse relationship between frequency and wavelength can be written, as seen below:

where:

c = Wave propagation velocity in a particular medium (meters/sec)

= wavelength (meters)

f = frequency (Hz)

T= period (sec)

Wavelength is very important in the design of radio and radar antennas, because of its relationship to antenna size. Referring to figure 2.1 radio frequency wavelengths range from thousands of meters at the low end of the spectrum to fractions of a centimeter at the high frequency end. Infrared and light energ have ver small wavelengths in the nanmeter (1x10-9 m) range. X-rays and gamma rays have wavelengths even smaller, in the picometer (1x10-12 m) to femtometer (1x10-15 m) range. Both the efficiency of a radar or radio antenna and its ability to focus energy depends on the wavelength since the antenna's ability to form a narrow beam (its directivity) is directly related to the antenna size measured in wavelengths. That is, a physically small antenna will have very good directivity when used at a high frequency (short wavelength), but would not be able to form as narrow a beam if used to transmit at a lower

frequency. In addition, the size of the antenna is directly proportional to the wavelength of the energy being transmitted.

Amplitude

Amplitude may be defined as the maximum displacement of any point on the wave from a constant reference value. It is easy to picture the amplitude of say waves on the surface of the water. It would be the height of the water at a crest of a wave above the average level of the water, or the level of the water when it is still. The amplitude of an electromagnetic wave is more complicated, but it is sufficient to think of it as associated with the intensity of the two fields that compose it, the electric and magnetic. When depicting an electromagnetic wave as a sine wave it is the electric field intensity, in volts per meter (v/m) that is plotted. In figure 2.2 the amplitude varies from +A to -A. The stronger the electromagnetic wave (i.e. the radio signal) the greater the field intensity. The power of the electromagnetic wave is directly proportional to the square of the electric field intensity. The crests and troughs of the wave are simply reversals of the polarity (the positive to negative voltage direction in space) of the electric field.

Phase

The final property of a wave to be discussed is its phase. Phase is simply how far into a cycle a wave has moved from a reference point. Phase is commonly expressed in degrees or radians, 360 degrees or 2 radians corresponding to a complete cycle of the wave. Referring back to figure 2.2 as an illustration, there is no field intensity at the origin, at the instant in time for which the wave is drawn. At the same instant in time, a crest or peak in field intensity is being experienced at point r1 , a trough or oppositely directed peak intensity at point r2 , another "positive zero crossing" at r3 and another crest at r4. The wave at r1 is one quarter cycle out of phase with that at the origin, three quarters of a cycle out of phase at r2, and back in phase at r3. Points that are separated by one wavelength (r3 and the origin, r4 and r1) experience in phase signals as the propagating wave passes by. Based on the way in which phase is measured, we can say that the signal seen at r1 is 90o out of phase with the origin.

Now consider a wave propagating to the right. Figure 2.3 illustrates a propagating sine wave by showing, in three steps in time, the wave passing four observation points along the r axis. The

increments of time shown are equal to one quarter of the period of a cycle, t = T/4. Just as we can plot a wave by looking at it as the wave exists at some instant in time, we can also plot a propagating wave as a function of time as seen at one point in space. Figure 2.4 illustrates this by showing the position of the wave at points r4, r2 and r1. The signals at r4 and r1 are in phase, whereas the signal at r2 is out of phase with the signal at r4 by 90o.

The signal at r2 is also said to lead the signal at r4. This is because the waveform at r2 crosses the horizontal axis (at t2) and reaches its peaks (at t3) before the waveform at r4. Similarily, we can say that the signal at r4 lags the signal at r2 by 180o.

A sine wave can also be thought of as being generated by a rotating vector or phasor as shown in figure 2.5(a). At the left is a vector whose length is the amplitude of the sine wave and which rotates counter clockwise at a rotation rate () of 360o or 2 radians each cycle of the wave. This rotating vector representation is very useful when it is necessary to add the intensities of the fields (amplitudes) of multiple waves arriving at a point. This method of adding two or more rotating vectors is known as phasor algebra and is illustrated in figure 2.5(b). In figure 2.5(b), two vectors of equal amplitude and rotation rate, with vector one leading vector two by 30o, are shown. The resultant is the vector addition of the two vectors/waves and is illustrated by the dashed vector/waveform. When multiple waves are involved, as in most radar applications, it is easier to add the vectors together to create a new vector, the resultant, than to add the waves themselves.

Coherency

Any pure energy that has a single frequency will have the waveform of a sinusoid and is termed coherent energy. In addition any waveform which is composed of multiple frequencies and whose phase relationships remain constant with time is also termed coherent. For pulses of electromagnetic energy (as in radar) coherence is a consistency in the phase of a one pulse to the next. That is, the first wavefront in each pulse is separated from the last wavefront of the preceeding pulse by an integer number of wavelengths (figure 2.6). Examples of coherent signals used in radar are:

- a short pulse of a constant frequency signal.

- a short pulse of a frequency modulated signal.

- the series or "train" of such pulses used over a long period of time.

Noncoherent energy is that which involves many frequency components with random or unknown phase relationships among them. Sunlight and the light emitted by an incandescent light are examples of noncoherent energy. Both are white light, that is they contain numerous frequencies, are random in nature and the phase relationships among them change with time. Coherent energy has two major advantages over noncoherent energy when employed in radars. These advantages will be addressed and explained later in this section under the Radar Equation topic. Radars of older design used noncoherent signals, since at the time of their development, the technology was not available to produce a sufficiently powerful coherent signal. The high performance radars used today make use of coherent signals.

The Wave Equation

In order to derive an equation that completely defines the amplitude and hence the strength of the electric field in terms of time and distance, it is helpful to begin by investigating the simplified example of a sine wave at a single instant in time (figure 2.2). The displacement of the wave in the y direction can be expressed as a function of the distance from the source (r) and the maximum amplitude (A).

The y displacement is solely a function of the lateral (r) displacement from the origin since the sine wave is shown at one instant in time.

In figure 2.3 the wave is propagating to the right and the displacement is seen at different points along the r axis as the time changes. At any given point along the r axis (for example r4) the displacement varies as the frequency of oscillation. The number of cycles that pass by any point during an elapsed time t is equal to the frequency multiplied by the elapsed time. To determine the actual change in phase angle that has occurred at this point after a time t the full cycle of oscillation is equal to 360o or 2 radians must be also taken into consideration. This change in phase is expressed by:

It is now possible to express the displacement in y of this propagating sine wave as a function of distance from the source (r), elapsed time (t), frequency (f) and the maximum amplitude (A):

Substituting in the relationship of equation 2-1, equation 2-4 becomes:

or

ELECTROMAGNETIC WAVES

Maxwell's Theory

Maxwell's Equations state that an alternating electric field will generate a time-varying magnetic field. Conversely, a time-varying magnetic field will generate a time-varying electric field. Thus, a changing electric field produces a changing magnetic field that produces a changing electric field and so on. This means that some kind of energy transfer is taking place in which energy is transferred from an electric field to a magnetic field to an electric field and so on indefinitely. This energy transfer process also propagates through space as it occurs. Propagation occurs because the changing electric field creates a magnetic field that is not confined to precisely the same location in space, but extends beyond the limit of the electric field. Then the electric energy created by this magnetic field extends somewhat farther into space than the magnetic field. The result is a traveling wave of electromagnetic energy. It is important to note that these fields represent potential forces and differ from mechanical waves (i.e. ocean waves or sound) in that they do not require a medium to propagate. As such they are capable of propagating in a vacuum.

Generation of Electromagnetic Waves

An elementary dipole antenna is formed by a linear arrangement of suitable conducting material. When an alternating electric voltage is applied to the dipole, several phenomena occur that result in electromagnetic radiation. An electric field that varies sinusoidally at the same frequency as the alternating current is generated in the plane of the conductor. The maximum intensity of the generated electric field occurs at the instant of maximum voltage.

It was stated at the beginning of this section that an alternating electric field will produce a magnetic field. The dipole antenna just described must therefore be surrounded by a magnetic field as well as an electric one. A graphical illustration of this field is shown in figure 2.7. Since

the current is maximum at the center of the dipole, the magnetic field is strongest at this point. The magnetic field is oriented in a plane at right angles to the plane of the electric field and using the right-hand rule, the direction of the magnetic field can be determined as illustrated in figure 2.7.

The elementary dipole antenna of the foregoing discussion is the basic radiating element of electromagnetic energy. The constantly changing electric field about the dipole generates a changing magnetic field, which in turn generates an electric field, and so on. This transfer of energy between the electric field and the magnetic field causes the energy to be propagated outward. As this action continues a wave of electromagnetic energy is transmitted.

The Electromagnetic Wave

In order to provide further insight into the nature of electromagnetic radiation, a sequential approach to the graphical representation of electromagnetic fields will be undertaken.

Figure 2.8 illustrates the waveform of both the electric (E) and magnetic (H) fields, at some distance from the dipole, as they are mutually oriented in space. The frequency of these waves will be identical to the frequency of the voltage applied to the dipole. From previously developed relationships, the electric and magnetic field strengths at any distance r and time may be defined as:

and

where

Eo = maximum electric field strength

Ho = maximum magnetic field strength

c = speed of light = 3 X 108 meters/sec

r = distance from the origin

t = time since origination (or some reference)

Phase Shifted Equation

Consider two dipole antennas, each of which is operating at the same frequency, but located such that one antenna is a quarter of the wavelength farther away from a common reference point as shown in figure 2.9. For simplicity, only the E field from each antenna is shown. The electric field strength at point P from antenna one is depicted in equation 2-7(a). In this particular case the wave from antenna one leads antenna two by the distance they are seperated, 1/4 wavelength or 90o. For antenna number two, the field strength equation becomes:

which can be further reduced to:

E~=~E_o~sin~ LEFT

Chapter 3 Elements of Feedback Control

3

Elements of Feedback Control

3.1 OBJECTIVES AND INTRODUCTION

Objectives

1. Know the definition of the following terms: input, output, feedback, error, open loop, and closed loop.

2. Understand the principle of closed-loop control.

3. Understand how the following processes are related to the closed-loop method of control: position feedback, rate feedback, and acceleration feedback.

4. Understand the principle of damping and its effect upon system operation.

5. Be able to explain the advantages of closed-loop control in a weapon system.

6. Be able to model simple first-order systems mathematically.

Introduction

The elements of feedback control theory may be applied to a wide range of physical systems. However, in engineering this definition is usually applied only to those systems whose major function is to dynamically or actively command, direct, or regulate themselves or other systems. We will further restrict our discussion to weapons control systems that encompass the series of measurements and computations, beginning with target detection and ending with target interception.

3.2 CONTROL SYSTEM TERMINOLOGY

To discuss control systems, we must first define several key terms.

Input. Stimulus or excitation applied to a control system from an external source, usually in order to produce a specified response from the system.

- Output. The actual response obtained from the system.

Feedback. That portion of the output of a system that is returned to modify the input and thus serve as a performance monitor for the system.

Error. The difference between the input stimulus and the output response. Specifically, it is the difference between the input and the feedback.

A very simple example of a feedback control system is the thermostat. The input is the temperature that is initially set

into the device. Comparison is then made between the input and the temperature of the outside world. If the two are different, an error results and an output is produced that activates a heating or cooling device. The comparator within the thermostat continually samples the ambient temperature, i.e., the feedback, until the error is zero; the output then turns off the heating or cooling device. Figure 3-1 is a block diagram of a simple feedback control system.

Other examples are:

(1) Aircraft rudder control system

(2) Gun or missile director

(3) Missile guidance system

(4) Laser-guided projectiles

(5) Automatic pilot

3.3 CLOSED AND OPEN-LOOP SYSTEMS

Feedback control systems employed in weapons systems are classified as closed-loop control systems. A closed-loop system is one in which the control action is dependent on the output of the system. It can be seen from figure 3-1 and the previous description of the thermostat that these represent examples of closed-loop control systems. Open-loop systems are independent of the output.

3.3.1 Characteristics of Closed-Loop Systems

The basic elements of a feedback control system are shown in figure 3-1. The system measures the output and compares the measurement with the desired value of the output as prescribed by the input. It uses the error (i.e., the difference between the actual output and desired output) to change the actual output and to bring it into closer correspondence with the desired value.

Since arbitrary disturbances and unwanted fluctuations can occur at various points in the system, a feedback control system must be able to reject or filter out these fluctuations and perform its task with prescribed accuracies, while producing as faithful a representation of the desired output as feasible. This function of filtering and smoothing is achieved by various electrical and mechanical components, gyroscopic devices, accelerometers, etc., and by using different types of feedback. Posi- tion feedback is that type of feedback employed in a system in which the output is either a linear distance or an angular displacement, and a portion of the output is returned or fed back to the input. Position feedback is essential in weapons control systems and is used to make the output exactly follow the input. For example: if, in a missilelauncher control system, the position feedback were lost, the system response to an input signal to turn clockwise 10o would be a continuous turning in the clockwise direction, rather than a matchup of the launcher position with the input order.

Motion smoothing by means of feedback is accomplished by the use of rate and acceleration feedback. In the case of rate (velocity) feedback, a portion of the output displacement is differentiated and returned so as to restrict the velocity of the output. Acceleration feedback is accomplished by differentiating a portion of the output velocity, which when fed back serves as an additional restriction on the system output. The result of both rate and acceleration

feedback is to aid the system in achieving changes in position without overshoot and oscillation.

The most important features that negative feedback imparts to a control system are:

(1) Increased accuracy--An increase in the system's ability to reproduce faithfully in the output that which is dictated by an input.

(2) Reduced sensitivity to disturbance--When fluctuations in the relationship of system output to input caused by changes within the system are reduced. The values of system components change constantly throughout their lifetime, but by using the self-cor-recting aspect of feedback, the effects of these changes can be minimized.

(3) Smoothing and filtering--When the undesired effects of noise and distortion within the system are reduced.

(4) Increased bandwidth--When the bandwidth of any system is defined as that range of frequencies or changes to the input to which the system will respond satisfactorily.

3.3.2 Block Diagrams

Because of the complexity of most control systems, a shorthand pictorial representation of the relationship between input and output was developed. This representation is commonly called the block diagram. Control systems are made up of various combinations of the following basic blocks.

Element. The simplest representation of system components. It is a labeled block whose transfer function (G) is the output divided by the input.

Summing Point. A device to add or subtract the value of two or more signals.

Splitting Point. A point where the entering variable is to be transmitted identically to two points in the diagram. It is sometimes referred to as a "take off point."

Control or Feed Forward Elements (G). Those components directly between the controlled output and the referenced input.

Reference variable or Input (r). An external signal applied to a control system to produce the desired output.

Feedback (b). A signal determined by the output, as modified by the feedback elements, used in comparison with the input signal.

Controlled Output (c). The variable (temperature, position, velocity, shaft angle, etc.) that the system seeks to guide or regulate.

Error Signal (e). The algebraic sum of the reference input and the feedback.

Feedback Elements (H). Those components required to establish the desired feedback signal by sensing the controlled output.

Figure 3-3 is a block diagram of a simple feedback control system using the components described above.

In the simplified approach taken, the blocks are filled with values representative of component values. The output (c) can be expressed as the product of the error (e) and the control element (G).

c = eG (3-1)

Error is also the combination of the input (r) and the feedback (b).

e = r - b (3-2)

But feedback is the product of the output and of the feedback element (H).

b = cH (3-3)

Hence, by substituting equation (3-3) into equation (3-2)

e = r - cH

and from equation (3-1)

e = c/G

c/G = r - cH

c = Gr - cGH

c + cGH = Gr

c=Gr

1 +GH (3-5)

(3-4)

It has then been shown that figure 3-3 can be reduced to an equivalent simplified block diagram,

G , shown below.

1 + GH

c = rG

1 + GH (3-6)

In contrast to the closed loop-system, an open-loop system does not monitor its own output, i.e., it contains no feedback loop. A simple open-loop system is strictly an input through a control element. In this case:

c = rG

The open-loop system does not have the ability to compensate for input fluctuations or control element degradation.

3.3.3 Motor Speed Control System

If the speed of a motor is to be controlled, one method is to use a tachometer that senses the speed of the motor, produces an output voltage proportional to motor speed, and then subtracts that output voltage from the input voltage. This system can be drawn in block diagram form as shown in figure 3-5. In this example

r = input voltage to the speed control system

G = motor characteristic of 1,000 rpm per volt of input

c = steady state motor speed in rpm

H = the tachometer characteristic of 1 volt per 250 rpm motor speed

Example. This example assumes that the input signal does not change over the response time of the system. Neglecting transient responses, the steady state motor speed can be determined as follows:

r = 10 volts

c = (e)(1000) rpm

e = c volts

1000

b = c volts

250

e=r-b

= 10 - c volts

250

Equating the two expressions for e and solving for c as in equation (3-4)

c = 10 - c volts

1000

250

c + 4c = 10,000 rpm

c = 2,000 rpm

Finally the error voltage may be found

e = c = 2 volts

1000

or by using the simplified equivalent form developed earlier as equation (3-6):

c = r G = 10V 1000 rpm/V = 2000 rpm

1 + GH 1 + 1000 rpm 1V

V 250 RPM

e = c = 2000 rpm = 2 volts

G 1000 rpm

V

3.4 RESPONSE IN FEEDBACK CONTROL SYSTEMS

In weaponry, feedback control systems are used for various purposes and must meet certain performance requirements. These requirements not only affect such things as speed of response and accuracy, but also the manner in which the system responds in carrying out its control function. All systems contain certain errors. The problem is to keep them within allowable limits.

3.4.1 Damping

Weapons system driving devices must be capable of developing suf-ficient torque and power to position a load in a minimum rise time. In a system, a motor and its connected load have sufficient inertia to drive the load past the point of the desired position as govern-ed by the input signal. This overshooting results in an opposite error signal reversing the direction of rotation of the motor and the load. The motor again attempts to correct the error and again overshoots the desired point, with each reversal requiring less correction until the system is in equilibrium with the input stimu-lus. The time required for the oscillations to die down to the desired level is often referred to as settling time. The magnitude of settling time is greatly affected by the degrees of viscous friction in the system (commonly referred to as damping). As the degree of viscous friction or damping increases, the tendency to overshoot is diminished, until finally no overshoot occurs. As damping is further increased, the settling time of the system begins to increase again.

Consider the system depicted in figure 3-6. A mass is attached to a rigid surface by means of a spring and a dashpot and is free to move left and right on a frictionless slide. A free body diagram of the forces is drawn in figure 3-7.

Newton's laws of motion state that any finite resultant of external forces applied to a body must result in the acceleration of that body, i.e.:

F = Ma

Therefore, the forces are added, with the frame of reference carefully noted to determine the proper signs, and are set equal to the product of mass and acceleration.

F(t) - Fspring - Fdashpot = Ma (3-7)

The force exerted by a spring is proportional to the difference between its rest length and its instantaneous length. The proportionality constant is called the spring constant and is usually designated by the letter K, with the units of Newtons per meter (N/m).

Fspring = Kx

The force exerted by the dashpot is referred to as damping and is proportional to the relative velocity of the two mechanical parts. The proportionality constant is referred to as the damping constant and is usually designated by the letter B, with the units of Newtons per meter per second N- sec.

m

Fdashpot = Bv

Noting that velocity is the first derivative of displacement with respect to time and that acceleration is the second derivative of displacement with respect to time, equation (3-7) becomes

F(t) - Kx - Bdx = Md2x

rearranging

dt dt2 (3-8)

Md2x + Bdx + Kx = F(t)

dt2 dt

or

d2x + B dx + Kx = F(t) (3-9)

dt2 M dt M M

This equation is called a second-order linear differential equation with constant coefficients.

Using the auxiliary equation method of solving a linear differential equation, the auxiliary equation

of (3-9) is:

s2 + Bs + K = 0

MM

(3-10)

and has two roots

-B + B2 - 4K

MMM

s = (3-11)

2

and the general solution of equations (3-9) is of the form

x(t) = C1es1t + C2es2t

(3-12)

where s1 and s2 are the roots determined in equation (3-10) and C1 and C2 are coefficients that can be determined by evaluating the initial conditions.

It is convenient to express B in terms of a damping coefficient as follows:

B = 2 MK

or

=B

2 MK

Then equation (3-10) can be written in the form:

0 = s2 + 2ns + n2 (3-13)

where

n = K and is the natural frequency of the system.

M

and

=B

M(2n)

=B

2 MK

For the particular value of B such that = 1 the system is critically damped. The roots of equation (3-10) are real and equal (s1 = s2), and the response of the system to a step input is of the form

x(t) = A(1 - C1te-s1t - C2e-s2t)

(3-14)

The specific response is shown in figure 3-8a.

For large values of B (>1), the system is overdamped. The roots of equation (3-10) are real and unequal, and the response of the system to a step input is of the form

x(t) = A(1 - C1te-s1t - C2e-s2t)

Since one of the roots is larger than in the case of critical damp-ing, the response will take more time to reach its final value. An example of an overdamped system response is shown in figure 3-8b.

For small values of B such that