sunil_Spacecraft_Payload_Control_report.pdf

REMOTESENSINGSCANNINGMIRRORCONTROLLERDESIGN M.Tech.Dissertation

Submitted in partial fulfillment of the requirements for the degree of

MasterofTechnology

by

K Sunil Kumar

(09311023)

Under the Guidance of Prof. Hari B Hablani

Department of Aerospace Engineering

INDIAN INSTITUTE OF TECHNOLOGY, BOMBAY

June 2011

iii

Acknowledgement

I would like to express my sincere gratitude towards my guide Prof. Hari B Hablani invaluable

guidance, motivation, constant support and encouraging independent thinking. My thanks to all

my family members, who have always encouraged and supported me in my pursuits. My sincere

thanks to all the people, who directly or indirectly have helped in my project. My special thanks

to Khadar Basha.

Sunil Kumar K

Roll no: 09311023

iv

Abstract Remote sensing satellites play a major role in monitoring the Earths air, ocean, and the land

from space. Satellite remote sensing is widely used as a tool in many parts of the world for the

management of the resources. Many countries are concerned about ecosystem and natural

resources, and to address this concern, series of remote sensing satellites have been launched. A

thorough literature review of opto-mechanical sensors is conducted which reveals that scanning

thematic mappers are used commonly for remote sensing of the Earth. This project report

therefore is concerned with the control of scan motion of a thematic mapper. Cross-track and in-

track profiles are formulated to scan successive rectangular strips of the ground. MATLAB codes

are developed to generate these cross-track and in-track command profiles of the sensor. To

impart this desired scan motion to the thematic mapper, several controllers are designed,

satisfying the specification of turnaround and settling down the instrument on a coasting rate in

11 ms with a tracking accuracy better than 1 millidegree. A proportional-derivative (PD), a PD

with feed-forward, a proportional-integral-derivative (PID), a PID with rate estimate, and a

double-lag compensator are designed to meet the performance specifications. The time-domain

and the frequency-domain results are furnished in the report. Sensor noise is modeled as white

noise with a standard deviation of 4% of the in-track angle amplitude of 0.016 degree, that is, a

white noise with 0.6 millidegree (1 ). In order to achieve the performance specifications, the payload scan angle is measured with a frequency of 5 kHz in cross-track and 10 kHz in in-track.

The optical sensors resolvers and Hall-Effect sensors are identified to provide these high-

frequency measurements. MATLAB SIMULINK software is used to simulate these controllers.

An attempt is made to formulate multi-body dynamics of the spacecraft bus and the hinged

sensor modeled as two articulated rigid bodies at an articulation point.

v

Contents

List of figures vii

List of Tables xi

1 Introduction 1

1.1 Background and Motivation 1

1.2 Objective 2

1.3 Chapter wise content 2

2 Remote Sensing 4

2.1 Introduction 4

2.2 Applications of Remote Sensing 5

2.3 Remote Sensors 7

2.3.1 Classification of Remote Sensing 7

2.3.2 Opto-Mechanical Sensors 8

2.4 Literature Review on Thematic Mapper 11

2.4.1 LANDSAT program 11

2.4.2 Scan Mirror Assembly (SMA) 14

2.4.3 Scan Line Corrector (SLC) 17

3 Analysis of scan motion 20

3.1 Spherical Geometry method 20

3.2 Cross-track and In-track pointing commands for scanning 25

3.2.1 Extremities of In-track and Cross-track motions 31

3.3 Results 34

3.3.1 In-track and Cross-track results 34

3.3.2 Analytical results based on Spherical Geometry 36

vi

4 Scanning Mirror Controller Design Analysis 42

4.1 Introduction 42

4.2 Time Domain Design Analysis 43

4.2.1 PD controller Design 43

4.2.2 PID controller Design 58

4.2.3 Sample Rate selection 70

4.2.4 PID Rate Estimate controller 76

4.2.5 White Noise 82

4.3 Frequency Domain Analysis 85

4.3.1 Double Lag Compensator 85

4.4 Sensors and Actuators 95

4.5 Scanner ground pattern of different controllers 97

5 Multi-body Dynamics 101

6 Conclusion and Future Work 105

6.1 Conclusion 105

6.2 Future work 107

References 108

vii

List of Figures Figure 2.1: Different processes involved in remote sensing 4

Figure 2.2: Schematic of operation of an opto-mechanical sensor 10

Figure 2.3.1 Landsat orbit 11

Figure 2.4: Landsat 7 satellite as viewed from sun side 12

Figure 2.5: optical systems and detector projection on ground track 13

Figure 2.6: Scan Assembly Mirror 15

Figure 2.6: Scan Mirror Assembly operational requirements 16

Figure 2.7: Scan Mirror Assembly subassemblies 17

Figure 2.8: Scan line corrector function 18

Figure 3.1: Definition of angular relationships between satellite, target and Earth center 20

Figure 3.2: Ground track and sensor scan motion on the surface of the Earth 22

Fig 3.3: Relation between different unit vector 23

Figure 3.4: Relation between sub satellite coordinates and spot coordinates

of sensor (mirror) 24

Figure 3.5: Relation between geometry as viewed from spacecraft and from

the center of the Earth 25

Figure 3.6: Relation between geometry of satellite motion and scan motion 29

Figure 3.7: Correction for satellite motion 32

Figure 3.8: Cross-track command 34

Figure 3.9: In-track command 35

Figure 3.10: Compensated motion with respect to LVLH frame 35

Figure 3.11: Scan pattern of the scanning mirror on the surface of the Earth 36

Figure 3.12: Un-compensated scan motion of the scanning mirror 37

Figure 3.13: Compensated scan motion of the scanning mirror 38

Figure 3.14: Relation between true anomaly Vs spacecraft and sensor

latitude and longitude 38

Figure 3.15 Variation of spot distance with respect to time 39

Figure 3.16 Variation of tilt and elevation angle with respect to distance 39

Figure 3.17 Variation of elevation with respect to tilt angle 40

Figure 3.18 Variation of true anamoly with respect to cross track 40

viii

Figure 3.19 Variation of Sensor Latitude and longitude with respect

to space craft latitude 41

Figure 4.1: An open-loop control system 42

Figure 4.2: A system with feedback and feedforward control 43

Figure 4.3: A closed-loop system with unit feedback PD controller in forward path 44

Figure 4.4: PD controller open loop frequency response plots 46

Figure 4.5: PD controller closed loop frequency response plots 47

Figure 4.6: PD controller error plots for cross-track motion (0.9-damping ratio) 48

Figure 4.7: PD controller error plots for in-track motion at 0.9 damping ratio 50

Figure 4.8: Scan motion of the mirror using PD controller for 0.9 damping ratio

and enlarged scan motion 51

Figure 4.9: Simulink model of PD controller 52

Figure 4.10: In-track and cross-track loop with null steady-state error for position,

Velocity, and parabolic input commands 53

Figure 4.11: Simulink model of feedforward PD controller 54

Figure 4.12: Cross-track and in-track error plots for PD feedforward controller 55

Figure 4.13: Feedforward PD controller scanning motion output of the sensor

(Damping ratio -0.9) 56

Figure 4.14: Scan motion of the sensor using PD feedforward controller by

varying inertia 57

Figure 4.15: PID controller 58

Figure 4.16: Scan motion of the mirror using PID controller

(] = 0.9 and differentG ) and enlarged plot 62

Figure 4.17: cross-track error using PID controller (damping ratio 0.9 and differentG ) and enlarged plot 63

Figure 4.18: In-track error using PID controller (damping ratio 0.9 and different G ) and enlarged plot 64

Figure 4.19: PID controller open-loop frequency response plots 65

Figure 4.20: PID controller closed-loop frequency response plots 66

Figure 4.21: Scan motion of the sensor using PID controller

(] =0.7 and different G values) and enlarged plot 68

ix

Figure 4.22: cross-track error (a) and in-track error (b) using PID controller

(] =0.7 and different G values) 69

Figure 4.23: PID controller (zeta=0.9) with sample rate output 72

Figure 4.24: Cross-track error (a), In-track error (b) of PID controller (zeta=0.9)

with sample rate 73

Figure 4.25: PD (zeta=0.9) feedback and feedforward with sample rate 74

Figure 4.26: Cross-track error (a), intrack error (b) of PD controller with sample rate 75

Figure 4.27: Bode diagram (a) and block diagram (b) for PID compensator 76

Figure 4.28: PID rate estimate controller open-loop frequency response 78

Figure 4.29: PID rate estimate controller closed-loop frequency response 79

Figure 4.30: PID rate estimate controller (G =0.9 and ] =0.9) Scan motion 80

Figure 4.31: In-track and cross-track error plot for PID rate estimate controller 81

Figure 4.32: White noise with standard deviation-4% of the in-track angle 82

Figure 4.33: PID (G =0.9 and ] =0.9) rate estimate with white noise 83

Figure 4.34: cross-track and in-track error of PID (G =0.9 and ] =0.9) controller

with white noise 83

Figure 4.35: PD (damping ratio-0.9) feedforward with white noise 84

Figure 4.36: Closed loop block diagram of the plant and second order

lag compensator 85

Figure 4.37: Mirror scan motion using double lag controller and enlarged plot 88

Figure 4.38: Cross-track and in-track error using double lag compensator 89

Figure 4.39: Double lag compensator open loop frequency response 90

Figure 4.40: Closed loop frequency response of doable lag compensator

for (a) cross-track (b) In-track 91

Figure 4.41: Double lag compensator nyquist plots 92

Figure 4.42: Scan motion with sensor noise of double lag compensator

and enlarged plot 93

Figure 4.43: Cross-track and in-track error profiles with sensor noise (White noise)

of double lag compensator 94

Figure 4.44: Controller output of scan motion on ground track 97

Figure 4.45: Variation of Elevation and Tilt angle Vs slant range of

x

PD and PID controller 98

Figure 4.46: Elevation angle variation with respect to tilt angle of

PD and PID controller 98

Figure 4.47: Variation of slant range with respect to time 99

Figure 4.41: Variation of Latitude and longitude of sensor with respect to

latitude of spacecraft 99

Figure 4.42: Latitude and longitude of spacecraft and sensor with respect

to true anomaly 100

Figure 5.1: System of two connected rigid bodies 101

xi

List of Tables 2.1: Landsat orbit parameters 12

2.2: SMA (Scan Mirror Assembly) characteristics 16

2.3: Scan line corrector (SLC) design parameters 18

4.1: Variation of 'DK ,'K P as damping coefficient changes for cross-track motion 45

4.2: Variation of 'DK ,'K P as damping coefficient changes for in-track motion 49

4.3: proportional, integral and derivative gain values for cross-track controller 60

4.4: proportional, integral and derivative gain values for in-track controller 61

4.5: Sample rate for different parameters of PID controller 71

4.6: q values for parameters damping ratio and integral gain ratio 77

4.7: Raster scan parameters 86

6.1: comparison of different controller parameters 106

1

Chapter-1

Introduction

1.1 Background and Motivation:

A careful assessment of changes that occur in the environment and in coastal ecosystems forms a

major milestone for effective coastal ecosystem management and leads to sustainable utilization

of coastal resources. All these can be achieved only through the collection of accurate, reliable

and comprehensive set of scientific data. Remote sensing is the technique of deriving

information about objects on the surface of the earth without physically coming into contact with

them. Remote sensing technology in recent years has proved to be of great importance in

acquiring data for effective resources management and hence could also be applied to coastal

environment monitoring and management.

The LANDSAT program provides repetitive acquisition of high resolution multispectral data of

the Earth's surface on a global basis. The data from the Landsat spacecraft constitute the longest

record of the Earth's continental surfaces as seen from space. It is a record unmatched in quality,

detail, coverage, and value. The INSAT series was designed to provide combined

telecommunications, direct TV broadcast, and meteorological service, using INSAT services

early warnings of impending disasters (floods, storms) and could directly reach to the civilian

population even in remote areas [26].

The Thematic mapper is a second generation Earth resources sensor and it was placed in orbit

aboard LandsatD spacecraft in July of 1982. It is predecessors of MSS (Multi Spectral scanner)

and the major difference is MSS collects data during west to east direction along a scan

line.Thematic Mapper(TM) acquires data during both forward(west to east) and reverse (east to

west)sweeps of its scanning mirror . After the TM, ETM+ (Enhanced Thematic Mapper plus) is

used and carries Scan Line Corrector (SLC) which is used to correct scanning motion of the

scanning mirror. With the exception of a brief test on September 7, 2003, the SLC has remained

off since that time. The Landsat Data Continuity Mission (LDCM) is the future of the landsat

satellite where Operational Land Imager (OLI) is used as payload by replacing ETM+. For

2

almost 40 years, Landsat satellites have collected data of the Earths surface to support the global

change research and applications [20].

These mission either LANDSAT, METEOSAT, INSAT, SPOT are using opto-mechanical

sensors where mechanical scanning is involved. The scanning mechanism also has to be

considered as one of the basic element of imaging systems in the optical sensors. These

mechanisms currently facing challenges like controller design, multi-body dynamics effect of

that mechanism on the spacecraft attitude. The current work addresses one such scanning

mechanism and ground track of such mechanisms by using spherical geometry methodology,

design a controller to track the scanning mechanism and analysis of multi-body dynamics of the

spacecraft and payload.

1.2 Objectives:

Keeping in view of all these the present study has been planned with the following objectives.

To study different kind of sensors used in Remote sensing satellite and scanning mechanism by an opto-mechanical sensor.

To analyze the sensor coordinates relative to the subsatellite point of the spacecraft by using spherical geometry method

To analyze the cross-track and in-track pointing commands for scanning To design a controller to track the scan pattern of the scan mirror by using different

controllers and analyze the controller with white noise

To analyze multi-body dynamics of the spacecraft and payload by considering 3 Degrees of Freedom(DOF) for spacecraft and 2 DOF for payload (scan mirror)

1.3 Chapter wise contents:This report organized in 6 chapters. First chapter presents introduction, background and

objectives. Second chapter gives a brief overview of remote sensing followed by classification of

remote sensing and different kinds of remote sensors. Detail description on opto-mechanical

sensors, thematic mapper and literature review on Landsat is discussed in this chapter. The third

chapter presents the analysis of scan motion by using spherical geometry method to find out

sensor position (sensor coordinates) on the Earth fixed frame. The in-track and cross-track

3

analysis for scan motion is briefly discussed in this chapter and implement these commands into

spherical geometry analysis to get sensor coordinates.

Fourth chapter describes about different types of controller used to track the scan motion of the

mirror. The time domain and frequency domain design of controllers followed by different

sensors used to feedback the position of the scanning mirror is briefly discussed. Sample rate

selection for feedback the signal and White noise also included with the sensor, to make more

realistic investigation on the controller behavior. Fifth chapter discusses the multi-body

dynamics of the spacecraft with articulate payload with two degrees of freedom and some future

work related to multi-body dynamics also specified in this chapter. A summary of the results,

conclusions and a few recommendations for future work are presented in Chapter 6.

2.1 Intr

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The first requirement (A in fig.2.1) for remote sensing is to have an energy source which

illuminates or provides electromagnetic energy to the target of interest. As the energy travels (B)

from its source to the target, it will come in contact with and interact with the atmosphere it

passes through. This interaction may take place a second time as the energy travels from the

target to the sensor. Once the energy makes its way to the target through the atmosphere, it

interacts with the target depending on the properties of both the target (C) and the radiation.

After the energy has been scattered by, or emitted from the target, we require a sensor (remote -

not in contact with the target) (D) to collect and record the electromagnetic radiation. The energy

recorded by the sensor has to be transmitted (E), often in electronic form, to a receiving and

processing station where the data are processed into an image (hardcopy and/or digital). The

processed image is interpreted (F), visually and/or digitally or electronically, to extract

information about the target which was illuminated. The final element of the remote sensing

process is achieved when we apply (G) the information we have been able to extract from the

imagery about the target in order to better understand it, reveal some new information, or assist

in solving a particular problem [27].

There are two main types of remote sensing: passive remote sensing and active remote sensing.

In passive remote sensing, passive sensors are used and they detect natural radiation that is

emitted or reflected by the object or surrounding area being observed. Reflected sunlight is the

most common source of radiation measured by passive sensors. Examples of passive remote

sensors include film photography, infrared, charge-coupled devices, and radiometers.

Active collection, on the other hand, emits energy in order to scan objects and areas whereupon a

sensor then detects and measures the radiation that is reflected or backscattered from the target.

RADAR is an example of active remote sensing where the time delay between emission and

return is measured, establishing the location, height, speeds and direction of an object.

2.2 Applications of Remote Sensing: Coastal areas, the place where the waters of the seas meet the land are indeed unique places in

our global geography. They are endowed with a very wide range of coastal ecosystems like

mangroves, coral reefs, lagoons, sea grass, salt marsh, estuary etc. They are unique in a very real

economic sense as sites for port and harbor facilities that capture the large monetary benefits

6

associated with waterborne commerce and are highly valued and greatly attractive as sites for

resorts and as vacation destinations. The combination of freshwater and salt water in coastal

estuaries creates some of the most productive and richest habitats on earth; the resulting bounty

in fishes and other marine life can be of great value to coastal nations. In many locations, the

coastal topography formed over the millennia provides significant protection from hurricanes,

typhoons, and other ocean related disturbances. But these values could diminish or even be lost,

if they are not managed. Pollution of coastal waters can greatly reduce the production of fish, as

can degradation of coastal nursery grounds and other valuable wetland habitats.

To achieve this, an understanding of the coastal processes that influence the coastal

environments and the ways in which they interact is necessary. It is advantageous to adopt a

holistic or systematic approach for solving the coastal problems, since understanding the

processes and products of interaction in coastal environments is very complicated. A careful

assessment of changes that occur in the coastal environments and in coastal ecosystems forms a

major milestone for effective coastal ecosystem management and leads to sustainable utilization

of coastal resources. All these can be achieved only through the collection of accurate, reliable

and comprehensive set of scientific data. Remote sensing technology in recent years has proved

to be of great importance in acquiring data for effective resources management and hence could

also be applied to coastal environment monitoring and management [5].

Agriculture plays major role in economies of both developed and undeveloped countries. The

production of food is important to everyone and producing food in cost effective manner is the

goal of every farmer, regional agricultural agency. A farmer needs to be informed to be efficient

and that includes having the knowledge and information to forge a viable strategy for forming

operation. Satellite and air born images are used as mapping tools to classify crops examine their

health and viability, and monitor farming practices. Agriculture applications of remote sensing

includes crop type assessment, crop type classification, crop estimation, mapping of soil

characteristic and management practices.

Forests are valuable resources providing food, shelter, wild life habitat, fuel, and daily supplies

like medicinal ingredients and paper. Forest plays a major role in carbon dioxide supply and

exchange, acting as key link between atmosphere, geosphere and hydrosphere. International and

domestic forestry applications where remote sensing can be utilized include sustainable

7

development, biodiversity, monitoring deforestation, wild life habitat assessment and other

environmental concerns.

Remote sensing is used as a tool to extract information about land surface structure, composition.

Multispectral data can provide information on lithology, rock composition based on spectral

reflectance. Hydrology is related to many other applications of remote sensing, particularly

forestry, agriculture and land cover, since water is a vital component in each of these disciplines.

Land use of application of remote sensing are natural resource management, base line mapping

for GIS input, routing and logistics planning for seismic, research, extraction activities and

identification of landing strips, roads, clearing, bridges, land/water interface [27].

2.3 Remote Sensors: Remote sensors are the instruments that measure the properties of electromagnetic radiation

leaving a medium due to scattering or emission. Information could be collected over a special

extent including the angular dependence of the observation and as a function of distance along

the line of sight of the instrument.

2.3.1 Classification of Remote Sensors:

As mentioned earlier that passive remote sensing used passive sensors which sense natural

radiation, either emitted or reflected from the Earth. It is convenient to classify sensors as those

operating in optical-infrared region and those operating in the microwave region. Imaging

sensors give 2-dimensional spatial distribution of the emitted or reflected intensity of

electromagnetic radiation, while non-imaging sensors measure the intensity of radiation within

field of view. In active remote sensing, active sensors are used to produce electromagnetic

radiation of a specific wavelength or band of wavelengths .The interaction of this radiation with

the target could then be studied by sensing the scattered radiation from the targets [5].

An optical-infrared (OIR) sensor covers a wavelength region extending from 0.4m to 20m.

The reception and analysis are carried out by instruments like lenses, mirrors, prisms. These

sensors are further classified into photographic and electro-optical. In the photographic system,

the images are formed directly on to a film where as in electro-optical sensors; the optical image

is first converted into an electrical signal and further processed to record the data.

8

The microwave region of interest to remote sensing covers the electromagnetic radiation of

wavelength. However these sensors can operate irrespective to the radiation of the sun. Thus, the

microwave sensors can operate during day and night. The atmosphere is more transparent to the

microwaves, than to optical rays, thus providing weather monitoring capability. But the current

work is dealt with the optical-infrared sensors only.

In photographic cameras, where image is formed in conventional manner by lens, recording are

restricted to particular wavelength within the visible region. The camera may be an instrument in

which the image is captured in a film or a charge coupled device (CCD). Alternately, it may be

like television camera which could be referred as return beam vidion (RBV) cameras in which

image is converted into signal that is superimposed on a carrier wave and transmitted to distant

receiver. In case of non-photographic cameras or electro-optical sensors, no lens is involved that

means no image is formed or image is formed in completely different manner from the method

used in a camera with lens and instrument is able to operate at longer wavelengths in the infrared

part of the spectrum.

Multispectral scanner (MSSs) is optical-mechanical scanner that is widely used in remote

sensing and it is able to operate both in the visible and infrared ranges of wavelengths. MSS is

like a simple radiometer; first it splits the beam of received radiation into a number of spectral

ranges and secondly by adding the important features of scanning. The image is not formed all at

once as it is in camera but is built up by scanning. In most cases, this scanning is achieved using

a rotating mirror; in other either whole satellite spin or a push-broom technique using a one-

dimensional CCD array is employed. The push broom scanner is one of the scanning systems

that have no moving parts and its one-dimensional array of CCDs that is used in place of a

scanning mirror to achieve cross-track scanning.

2.3.2 Opto-Mechanical Scanners:

Most of the limitations associated with photographic and TV imaging systems are overcome in

opto-mechanical scanners. Mechanical scanning is involved in some of the Opto-mechanical

sensors like MSS, Thematic mapper (TM), Enhanced Thematic Mapper plus (TM). Most of the

remote sensors acquire data using scanning systems, which employ a sensor with a narrow field

of view that sweeps over the terrain to build up and produce a two-dimensional image of the

9

surface. A scanning system used to collect data over a variety of different wavelength and is

most commonly used in scanning system.

The spectral range of photographic systems is restricted to the visible and near-infrared regions

while MSS systems can extend this range into the thermal infrared. They are also capable of

much higher spectral resolution than photographic systems. Multi-band or multispectral

photographic systems use separate lens systems to acquire each spectral band. This may cause

problems in ensuring that the different bands are comparable both spatially and radiometrically

and with registration of the multiple images.

The radiation emitted or reflected from the scene is intercepted by a scan mirror, diverts the

radiation to a collecting telescope. In the normal case the scan mirror is inclined at 45deg. to the

optical axis of the telescope. The telescope focuses the radiation on to a detector. The detector

receives radiation from an area on the ground which is determined by detector size and focal

length of the optics. By rotating the scan mirror, the detector starts looking at adjacent picture

elements on the ground. There are two main methods of scanning employed to acquire

multispectral image data across-track scanning and along-track scanning [5].

The rotation of scan mirror collects radiation from a strip on the ground whose width equals to a

pixel and is at right angles to the nadir track. If the rate of rotation of the scan mirror is adjusted

such that by the time the platform moves through one picture element, the scan mirror set to start

of the next scan line, then successive and contiguous scan lines can be produced. Thus in the

cross-track direction, the information is collected from each pixel to produce one line of image

and in the along-track direction, successive lines of image in a contiguous fashion are produced

by the platform motion as shown in fig.2.2. To produce multispectral imaginary, the energy

collected by the telescope is channeled to a spectral dispersing system-spectrometer. Such

systems which can generate imagery simultaneously in more than one spectral band are called

Multi-spectral Scanners (MSS).

In opto-mechanical imager scanning can be carried out either in the object plane or in the image

plane. In the image plane scanner, the scan mirror is kept after the collecting optics near to the

focal plane and the mirror detects each point in the focal plane to the detector. Such a system

requires the collecting optics corrected for the total field of view, which is quite difficult. Though

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11

2.4 Literature Review on Thematic Mapper:

The TM relies heavily on the technology of the MSS, it is designed to achieve finer special

resolution, sharper spectral separation, and greater radiometric accuracy and resolution. The

following section gives us detailed description of scanning parameters of TM which was used in

LANDSAT. The TM acquires data in seven spectral bands covering the visible, near-infrared,

middle-infrared, and thermal infrared regions of the electromagnetic spectrum.

2.4.1 LANDSAT program:

The Landsat Program has provided high

spatial resolution data of the Earth's surface to

a broad and varied user community, including

agribusiness, global change researchers, state

and local governments, commercial users,

military, and the international community.

Landsat images provide information meeting

the broad and diverse needs of business,

science, education, government, and national

security.

The mission of the Landsat Program is to

provide repetitive acquisition of high

resolution multispectral data of the Earth's surface on a global basis. Landsat represents the only

source of global, calibrated, high spatial resolution measurements of the Earth's surface that can

be compared to previous data records. The data from the Landsat spacecraft constitute the

longest record of the Earth's continental surfaces as seen from space. It is a record unmatched in

quality, detail, coverage, and value.The Landsat platforms carry multiple remote sensor systems

and data relay systems along with attitude-control and orbit-adjust subsystems, power supply,

and receivers for ground station commands and transmitters to send the data to ground receiving

stations.

12

The injected spacecraft is a 1940kg satellite designed for a

705-km, sun synchronous, earth mapping orbit with a 16-day

repeat cycle. Its payload is a single nadir-pointing instrument,

the Enhanced Thematic Mapper. The LANDSAT-D is an-

experimental Earth-recourses monitoring system that utilize the

capabilities of TM, which is the principal instrument on the

LANDSAT-D spacecraft. The LANDSAT-D spacecraft was

launched into a circular near-polar sun-synchronous orbit [25].

Table 2.1: Landsat orbit parameters [25]

Figure 2.4: Landsat 7 satellite as viewed from sun side [25]

The TM design provides for a nadir-viewing, eight-band multispectral scanning radiometer

capable of providing high-resolution image information of the Earth's surface when operated

from Landsat-7, a 3 axis stabilized spacecraft located in a near polar, sun-synchronous and

circular orbit at a 705 km nominal altitude, with an orbit inclination of 98.2 degrees. The TM is

designed to collect, filter and detect radiation from the Earth in a swath 185 km wide as it passes

overhead and provides the necessary cross-track scanning motion while the spacecraft orbital

motion provides an along-track scan.

Altitude 705km

Inclination 98.2 deg.

Repeat period 16 days

Orbits/repeat

period

233

Trace spacing 172 km

13

The Landsat TM, MSS instrument achieves its 185-kilometer cross-track ground swath by using

a bi-directional scan mirror to traverse the instrument line-of-sight through a 15.4-degree cross-

track field of view. On descending passes, the mirror alternately scans west-to-east (forward

scan) and then east-to-west (reverse scan). The active Earth-imaging portion of each scan lasts

for, nominally, 60,743 micro seconds. During this time, the Landsat spacecraft advances

approximately 410 meters down track. If uncompensated, this spacecraft motion would add an

along-track component to the scan mirror's cross-track trajectory, leading to a zig-zag scanning

pattern that overlaps where one scan end adjoins the next scan start, and leaves gaps where one

scan end adjoins the previous scan start. The maximum gap at the edge of the TM swath is the

distance traveled in two active scans plus one mirror turnaround period (11.57 milliseconds), less

the width of one scan (480 meters). This is approximately 420 meters. The thematic mapper

acquires data in seven spectral bands covering visible, near Infrared, middle infrared, thermal

infrared. [14].

The scanning mechanism operating at 7Hz

provides the cross-track scan; where as the

orbital velocity provides the scan along the

track.A Ritchey-Chretien telescope focuses

the energy onto a pair of motion

compensation mirrors (i.e. scan line

corrector) where it is redirected to the focal

planes as shown in the figure 2.5. The scan

line corrector is required due to the

compound effect of a long-track orbital

motion and cross-track scanning which leads

to significant overlap and under lap in

ground coverage between successive scans.

Figure 2.5: optical systems and detector projection on ground track [14]

14

To achieve the required level of scan mirror angular position knowledge and control, the TM

scan mirror assembly includes a device, known as the scan angle monitor (SAM). The SAM

provides timing pulses to the scan mirror control electronics at fixed angles representing the

beginning, middle, and end ofeach earth-view active scan [15]. The SAM timing pulses serve

two functions: 1) to initiate and halt the collection of earth-view image data during the active

scan time and 2) to allow the scanmirror control electronics to monitor the scan mirror velocity

and maintain the desired active scan time. When operating in SAM mode, the SAM timing

pulses are used to compute the deviations from the ideal scan start to midscan and midscan to

scanend times for each active scan so that the active scan times arenearly the same for each

mirror sweep. In this operating mode, the active scan angle is held fixed by the SAM and the

amount oftime required to traverse this fixed angle is controlled to withina few detector sample

time periods. The amount of time the scanmirror takes to reverse direction between scans is not

controlled [22].

2.4.2 Scan Mirror Assembly (SMA): The heart of the TM is the Scan Mirror Assembly (SMA). The SMA performs the following four primary functions:

Delivering a linear earth scan into the TM telescope. Controlling the active scan time. Synchronizing the video data at the multiplexer. Collecting scan error data for correction and engineering data for analysis on the ground.

An object-space scan mirror sweeps the TM line of sight back and forth seven times each second

in a direction normal to the orbital ground track to form a raster of 16 lines in bands1 through 5

and band7, and four lines in band6. Data are collected during both the forward (west to east) and

reverse scan (east to west) scans with a scanning efficiency of 85percent. The scan velocity is

essentially constant during both directions of scan for two reasons:

1) Torque is applied to the scan mirror only during the turnaround times (not during the active

scans)

2) The scan mirror floats in a nearly inertia-free manner during the active scan through the use

of magnets through the use of magnets which compensate for the flex pivot spring forces.

The bands are displaced with respect to each other in their focal planes and in effect are scanned

across the same earth point at different times. Because of this characteristic during active scan,

15

linearity and stability of the scan rate important. While hitting turnaround bumper springs, the

Scan Mirror Assembly (SMA), the mechanical scanning mirror, produces as much as 23,000 gs

peak and impart 4 ft-lb of torque to the spacecraft; less than 11 milliseconds later, the scanning

mirror must start collecting picture image data not influenced by structural self-produced

vibration [15].

The Scan Mirror Assembly (SMA) provides the cross-track scanning motion to develop the 185-

km long scene swath. The SMA consists of a flat mirror supported by flex pivots on each side

(which have compensators to equalize pivot reaction torque), a torque (induction motor), and a

scan angle monitor (SAM), 2 leaf spring bumpers and scan mirror electronics (SME). The

motion of the mirror in each direction is stopped by the bumper, and is boosted by precision

torque pulses during the turnaround period. The amount of torque applied is controlled by the

SME microprocessor as determined from the SAM mirror angle pulses.

Figure 2.6: Scan Assembly Mirror [15]

The resulting active scan in each direction is closely controlled to 60,743 micro seconds. SAM

mirror angle pulses are used by the multiplexer to synchronize the detected scene data. There are

redundant sets of scan mirror electronics (SME), SME 1 and SME 2. SME 2 is an identical back

up electronic package to SME-1. Additionally, both SMEs have a primary SAM mode of

operation and a back up Bumper Mode of operation.

16

Figure 2.6: Scan Mirror Assembly operational requirements [15]

Activescanamplitude

7.695degrees

Scanperiod

142,925microseconds

Scanningfrequency

6.997Hz

Activescanperiod

60,743microseconds

Turnaroundtime

10,719microseconds

Objectplanescanrate

4.42191rad/sec

Table 2.2: SMA characteristics

The scan mirror oscillates by rebounding between the bumper assemblies. If there are no

restoring torquess between rebounds, a constant angular velocity will be obtained. The restoring

torque due to the spring constant and nonlinearity of the flexural pivot is compensated almost

perfectly

impulses

The desi

readings

proportio

scan erro

The SMA

portion o

(SAM) s

scan line

relative t

2.4.3: S

A second

detector

scan mir

previous

structura

detectors

(SLC) is

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are supplied

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A was desig

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to the SMA/T

Scan Line

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swath cause

rror turnarou

set. The S

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an electro-o

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Figure 2.

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iguous and

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the mirror, to

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17

orque

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or the

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rector

irrors

18

set at an angle on a shaft. The shaft, driven by a torquer which has primary and redundant

tachometers, rotates about an axis normal to the axis of the scan mirror in a saw tooth fashion.

The SLC is positioned behind the primary optics and compensates for the in-track motion of the

spacecraft that occurs during an active SMA cross track scan. A rectilinear scan pattern is

produced using the SLC instead of the zig-zag pattern that would be produced without it fig.2.8.

Scan frequency 13.99Hz

Scan rate in object space 9,610 rad/sec

SLC rotation rate 576.7 rad/sec

SLC linear scan angle 32.02 rad

Table 2.3: Scan line corrector (SLC) design parameters

Figure 2.8: Scan line corrector function [14]

19

The SLC retraces, moving from its end-of-scan full aft position to its scan-start full forward

position, during the turnaround time while the scan mirror is changing directions. The SLC

adjusts the TM along-track pointing so that, if the scan mirror were not moving, it would view a

constant location during each active scan period. This along-track "staring" makes the scan

mirror's cross-track scans nearly perpendicular to the spacecraft ground track, minimizing end-

of-scan overlap and gaps.

20

Chapter-3

Analysis of scanning motion

The Landsat thematic mapper acquires data during both forward and reverse sweeps of its scan

mirror. The scan velocity is essentially constant during both directions of scan for two reasons:

1) Torque is applied to the scan mirror only during the turnaround times (not during the active

scans), 2) The scan mirror floats in a nearly inertia-free manner during the active scan through

the use of magnets through the use of magnets which compensate for the flex pivot spring forces.

.So the torque should be applied during turnaround times not during active scans. So using

spherical geometry method, target latitude and longitude of target point has been detected by

using the relationship between target, satellite and earth center. The following sections gives

brief idea about this method and it is taken from the ref. [2].

3.1 Spherical Geometry method: Spherical geometry method is used to get target point location in terms of Latitude and Longitude. The following fig.3.1shows the angular relation between satellite, target and Earth center [7].

Figure 3.1 : Definition of angular relationships between satellite, target and Earth center

The most common problem in space mission geometry is to determine the relative geometry of

objects on the earth surface as seen from the spacecraft. One of the methods is to use the given

21

coordinates of a target on the Earth to determine its coordinates in the spacecraft field of view.

Another method is to determine the intercept point on the surface of the Earth corresponding sub

satellite point of the spacecraft coordinates.

The spherical-Earth approximation is adequate for most mission geometry applications. The

Earths oblateness has two distinct effects on the shape of the Earth as seen from space. First, the

Earth appears somewhat oblate rather than round, and second, the center of the visible oblate

Earth is displaced from the true geometric center of the Earth.

The spacecraft is at a point P and the corresponding sub satellite point on the surface of the

Earth is S with a distance r from the surface of the Earth. The spacecraft sensor is pointing

towards E on the surface of the Earth with a distance d from the surface of the Earth and tilt

angle T with respect to the sub satellite point .Elevation angle , measured at the target between the spacecraft and the local horizontal, Earth centered angle , measured at the Earth from the sub satellite point to the target point as shown in the figure 3.1.

From law of sines: sin(90 ) sin sin

E

Tr d R

+ = =

From above relation cos sin sinE

r r Td R

= =

d in terms of is given by 2 2 2 2 cosE Ed R r rR = +

d can also written in terms of : sin cosdr

= 2

2 2cos 1 sin 1 cosdr

= =

then 2 2 2cos sinE Ed r R R = Tilt angle is given the relation cos cos cosIT CTT = where IT = intrack angle; CT =crosstrack angle

From fig. (3.1): cos sinE

r TR

= ; then cos sinEd r T R =

22

Arc on the ground is given by sin cos sinE

d d Tr R

= =

The Line of sight (LOS) vector which is pointing towards target point and it is perpendicular to

the ground track of the spacecraft. The relation between unit vector along the LOS ( lu ) and unit

vector along the spacecraft nadir ( nadiru ) is given by the following section.

Figure 3.2: Ground track and sensor scan motion on the surface of the Earth

Unit vector ( lu ) along = cos

sincos

IT CT

CT

CT

; nadir unit vector ( nadiru )=

001

[sin cos sin cos cos ]l nadir IT CT o CT o CT IT ou u i j k k = + = sin cos sinIT CT o CT oj i and l nadiru u = sin 1nlT ; where 1nl =unit vector along l nadiru u 2sin T = 2 2 2sin cos sinIT CT CT +

This equation is equivalent to the equation cos cos cosIT CTT =

23

Figure 3.3: Relation between different unit vector

From above relations sinl nadiru u

T

= 1nl = sin sin cossin sin

CT IT CTo oi jT T

+

Hence tan = sintan

IT

CT

The relation between , CT and IT is given as sintan tanIT

CT

= ;

where = angle between direction of motion of the spacecraft and unit vector along l nadiru u From above relation, if IT =0, then the angle = 0 and tilt angle is equal to cross-track angle.

Azimuth of the spacecraft orbit ( xaz ): 1tan

cos tanxAz

u i= where u=argument of latitude;

and i = inclination angle of spacecraft orbit

Spacecraft latitude ( ) : sin sin sinu i = ;

Inertial longitude ( ): cos sin sin cos costancos cos sin cos sin

u u iu u i

+ =

Where is ascending node angle

24

Figure 3.4: Relation between sub-satellite coordinates and spot coordinates of sensor (mirror)

From law of sines: sin sinsincos sin cos

s E

E

az az

= =

But from fig 3.3 it is shown that 2 x s

az az + + = ;

sin cos( )s xaz az= +

From triangle NSE spot latitude is given by: sin sin cos cos sin sin( )E xaz = + +

For spot longitude: consider sin sincos sin

s

E

az

= ; hence sinsin sincos

s

E

az =

Relative longitude cos( )sin sincos

x

E

az + =

To determine target latitude and longitude of the scanning motion, we should know the cross-

track and in-track pointing commands for scanning. The following section gives a brief analysis

about cross-track and in-track commands for scanning.

25

3.2 Cross-track and In-track pointing commands for scanning:

Consider some inertial frame in the orbit plane, and true anomaly angle () is measured from the frame.

Figure 3.5: Relation between geometry as viewed from spacecraft and from the center of the

Earth

The satellite attitude is often expressed in a frame of reference in which the local vertical is

normal to the Earths ellipsoid (geodetic reference), rather than pointing to the Earths center

(geocentric reference).The current development is based on geocentric reference. The following

flow chart shows the several steps involved in transformations from inertial frame of reference to

line of sight (LOS) reference.

The first step in transforming to the Line of sight frame is to rotate the inertial frame counter-

clock wise around the z-axis by the angle .This is achieved by the transforming

26

cos sin 0sin cos 00 0 1

o

o

o

l lb bn n

= where l bn is inertial vector, o o ol b n - rtn vector

The next transformation involves rtn frame of reference to orbit frame of reference,the relation is

given as

0 1 0 sin cos 00 0 1 = 0 0 11 0 0 cos sin 0

o o

o o

o

X l lY b bZ n n

=

o oX Y Z - orbit frame of reference

The third step in transforming to intermediate LOS frame of reference is to rotate the orbit frame

counter-clock wise around the y-axis by the in-track angle IT .The resultant transformation is given by

'

'

'

cos 0 sin0 1 0

sin 0 cos

o IT IT o

o o

o IT IT o

X XY YZ Z

=

= 1 00 1 0

0 1

IT o

o

IT o

XYZ

= sin cos cos sin 0

0 0 1sin cos cos sin 0

IT IT

IT IT

lbn

+ +

The final step in transforming to LOS frame of reference is to rotate intermediate LOS frame

counterclock wise around the x-axis by the cross-track angle CT . The resultant coordinates are

'

'

'

1 0 00 cos sin0 sin cos

l o

l CT CT o

l CT CT o

X XY YZ Z

=

Where l l lX Y Z - line of sight vector; ' ' 'o o oX Y Z - intermediate LOS frame vector

27

I I IX Y Z l bn= (Inertial frame of reference)

IZ n = (Rotate inertial frame counter-clock wise around IZ axis by the angle) o o ol b n (Similar to Radial, transverse, normal (RTN) frame)

o o oX Y Z (orbit frame of reference) where ; ;o o o o o ol Z b X n Y= = =

IT oY (Rotate orbit frame counter-clock wise around Y-axis by the angle IT ) ' ' 'o o oX Y Z (Line of sight intermediate frame)

'CT oX (Rotate intermediate frame counter-clock wise around Y-axis by the Cross-track angle CT ) l l lX Y Z (Line of sight frame of reference)

The line of sight vector in LOS frame 00

l

l

l

XYZ

=

So 0

[ ][ ] 0

LOSo

o IT CT

o

XYZ

= =

1 0 1 0 0 00 1 0 0 cos sin 0

0 1 0 sin cos

IT

CT CT

IT CT CT

o

o

o

XYZ

=

1 00 1 0

0 1

IT

IT

0sin

cosCT

CT

=

cossin

cos

IT CT

CT

CT

LOS vector is given by pr r = +

where r - vector from Earth center to spacecraft as shown in fig.3.5 ; pr = vector from Earth

center to target point.

28

The scan motion is along normal direction (n ) at some particular time, suppose at *t t= , then the

corresponding true anomaly angle is * ,then *

*

l lb bn n

=

The scanning is along n at a fixed vertical direction ( *l ) so *

p E nr r l z n= + this relation is only at

the time of scanning only. pr =

* *

0

l b n

E

n

r

z

F

where Er = Earths radius; nz = scanning motion of

sensor with respect to Earth surface

Now the spacecraft orbit frame at *t t= , = * , then pr = * * *0 X Y Z

n

E

zr

F

To determine instantaneous orbit frame then transform the orbit frame at *t t= , = * rotate it about z-axis by the angle * = . The following flow chart shows the transforming to the instantaneous orbit frame of reference

from satellite orbit frame at *t t= , = * , and also transforming to the instantaneous rtn orbit frame from RTN frame at *t t= , = * .

* *l b n (rtn frame at *t t= , = * ) * * *X Y Z (The satellite orbit frame at *t t= , = * )

* n = * *Z = o ol b n (The instantaneous o o oX Y Z (instantaneous orbit frame)

rtn orbit frame at t)

29

Figure 3.6: Relation between geometry of satellite motion and scan motion

The vector pr in orbit frame is given by

* * [ ]cos sin 0sin cos 0 0

0 0 1

o

l b n

E

p

n

scanningrr

z

=

F

F

cossin

o ol b nE

E

n

rr

z

=

o ol b nE

E

n

rrz

(the instantaneous rtn orbit frame at t)

Transforming to instantaneous orbit frame, as we know the relation RTN frame and orbit frame is ; ;o o o o o ol Z b X n Y= = =

Hence o

prF =

X Y Zo o oE

n

E

rzr

F

(the instantaneous orbit frame)

30

Line of sight vector by using above relations pr r = +

= 00

o o o X Y Zo o oX Y ZE

n

E

rz

r r

+

F

=E

n

E

rz

r r

The above vectors is used only during scanning of the sensor (mirror) that means it is instantaneously while scanning of the mirror taking place and equate this vector to the satellite orbit frame of reference. It is given by

pr r = + =E

n

E

rz

r r

=

cossin

cos

IT CT

CT

CT

From the above relation crosstrack angle is given by 1 1sin tann nCTE

z zr r

= = and also

In-track angle is given by ;cos

EIT

CT

r =

To find angular velocity vector ( ) = 2

We know that pr r = + and also pr r = + * ( )p E n or r l z t t n= + = *E nr l z n+ ;

Because * *l b n is a frozen frame and ignoring Earths rotation: pr = nz n = n oz j where o o oi j k - Orbit frame unit vector

r = vb = ovi (v- velocity of the satellite)

So o n ov i z j = = 0

X Y Zo o o

n

vz

F

Transform this orbit frame vector to line of sight vector ( l l lX Y Z ) frame: = [ ] [ ] ooIT X CT Y F

= 1 0 1 0 00 1 0 0 cos sin

0 1 0 sin cos 0

IT

CT CT n

IT CT CT

vz

= cos sin

sin cosn CT IT CT

n CT IT CT

vz vz v

31

Then = [... ... ... ]l l l lk i j k + + where li lj lk - unit vector triad in the LOS frame

The angular velocities: , ,o IT CT ; where o - orbit angular velocity , IT - in-track angular velocity , CT - cross-track angular velocity = ' 'o o IT o CT lj j i + + where ' '[ , ]o o o lj j i i= = = '( )o IT o CT lj i + + Transformation matrix from orbit frame of reference to LOS frame of reference is

1 0 00 cos sin0 sin cos

CT CT

CT CT

, so 'oj =

0cossin

l

CT

CT

F

and li = 100

l

F

substitute these relations in

so = ( )o IT + 0

cossin

l

CT

CT

F

+ 00

l

CT

F

= ( ) cos( )sin

l

CT

o IT CT

o IT CT

+ +

F

but = 2

= 1 [ ( cos sin )]l l n CT IT CTvj i z v + +

by comparing above vector: CT = 1 [ cos sin ]n CT IT CTz v + and IT = cos oCTv +

3.2.1 Extremities of intrack and crosstrack motions: The analysis which is discussed so far is for coasting (scanning) period, to determine turnaround

limits for the intrack commands it is better to know correction for satellite motion in Local

vertical and Local Horizontal (LVLH) frame . Figure 3.7 shows correction of satellite motion in

LVLH frame and th_it_mx = maximum in-track angle, th_ct_mx = maximum crosstrack angle

Turnaround: in-track angle

At time t = ot initial conditions are - ,IT mx , ,IT mx and final conditions ,IT mx , ,IT mx First half with positive acceleration , then intrack rate commands are given by

, ( )IT IT mx IT ot t = +

32

Figure 3.7: correction for satellite motion

By integrating above in-track rate, then ( )IT t = 2, , 1( ) ( )2IT mx IT mx o IT ot t t t + During first half turnaround period ( a ) in-track commands are , ,IT a IT mx IT a = + ; ,IT a = , ,IT mx IT mx a 212 IT a + The next half with negative acceleration (- IT ) ,then in-track and intrack rate are

IT = ,IT a - IT (t - ot ) and IT = ,IT a + , ( )IT a ot t - 12 IT2( )ot t

for the next half turnaround period ( a ) then ,2IT a = ,IT a - IT a = ,IT mx as desired

,2IT a = , ,IT a IT a a + - 212 IT a ,IT mx

,2IT a = , ,IT mx IT mx a 212 IT a + +( ,IT mx IT a + ) a - 21

2 IT a

= ,IT mx - 2 ,IT mx a + 2IT a ,IT mx

so 2IT a = , ,2( )IT mx IT mx a + then , ,22( )IT mx IT mx aITa

+=

33

then ,IT a = ,IT mx + 2a ,IT mx

During coasting (scanning):

I

prF =

cos sin 0sin cos 0

0 0 1

o ol b nE

E

n

rrz

=

(cos sin )(sin cos )

I Il b nE

E

n

rr

z

+

Consider Ib component: (sin cos )Er = sin( )Er = *sinEr During turnaround period pr = r +

oo o o

o

X Y ZE

n

E

rz

r r

= =

F

F Correct during scanning only, 00

o o oX Y Z

rr

=

o F =

cossin

cos

oo o oX Y Z

IT CT

CT

CT

=

F

this is correct for any IT , CT

then pr =cos

sincos

oo o oX Y Z

IT CT

CT

CT r

=

F

=coscos

sin

o ol b nCT

IT CT

CT

r

The next step is transforming to o ol b n orbit frame target vector ( pr ) is to rotate the inertial frame counterclockwise around the z-axis by the angle .This transformation is given by o ol b npr = [ ]Z Ipr F But here to find inertial frame from o ol b n orbit frame ,this can be done by

I

prF = [ ]Z o ol b npr

I

prF =

cos sin 0sin cos 0

0 0 1

coscos

sin

o ol b nCT

IT CT

CT

r

=

cos ( cos ) sin ( cos )sin( cos ) cos cos

sin

CT IT CT

CT IT CT

CT

rr

+

Consider the Ib component:

sin( cos ) cos cosCT IT CTr + = sin cos sin( )CT ITr + (for 1IT ) For small = ( )ITr altitude + = ( ) ITr h h +

34

3.3 Results: Figures 3.8, 3.9 shows the cross-track and in-track results for scan analysis by using Landsat parameters which is mentioned in section 2.4.1 by using data like turnaround time, cross-track angle, orbit rate, spacecraft velocity.

3.3.1 In-track and cross-track Results:

An object-space scan mirror sweeps the TM line of sight back and forth seven times each second

in a direction normal to the orbital ground track. Data collected during forward and reverse scan

and scan velocity is essentially constant [15]. So in cross-track profile at the time of scan period

the velocity of the mirror is constant and at the time of turnaround velocity changes with respect

to time. The angle, rate, acceleration profiles are shown in fig.3.8

Figure 3.8 : cross-track command

The cross-track angle command which is shown in the fig.3.8, we can approximate as sinusoidal

with an amplitude 8.56 D [(7.7(coasting)+2*0.43(turnaround)] at 7Hz frequency and in-track

angle command can be approximate as saw tooth signal. However, this approximation can be

use in the analysis of robust controller design which is discussed in the further section.

0 0.2 0.4 0.6 0.8 1-10

-5

0

5

10

Time (s)

CT

(deg

)

crosstrack command

0 0.2 0.4 0.6 0.8 1-400

-200

0

200

400

Time (s)

rat

e CT

(deg

/s)

0 0.2 0.4 0.6 0.8 1-5

0

5x 104

Time (s)

acc

CT

(deg

/s2 )

35

Figure 3.9: In-track command

Figure 3.10: compensated motion with respect to LVLH frame

If we combine the in-track and cross-track motion, and feed it to the scan mirror then the resultant motion

is simulated. The SLC correction for orbital motion to the mirror with respect to the spacecraft (LVLH

frame) is shown in fig.2.8. The SLC jumps ahead during the scan turnaround so that the next set of

0 0.2 0.4 0.6 0.8 1-0.02

-0.01

0

0.01

0.02

Time (s)

IT (d

eg)

intrack command

0 0.2 0.4 0.6 0.8 1-5

0

5

10

Time (s)

rat

e IT

(deg

/s)

0 0.2 0.4 0.6 0.8 1-2000

-1000

0

1000

2000

Time (s)

acc

IT (d

eg/s

2 )

-10 -8 -6 -4 -2 0 2 4 6 8 10-0.02

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0.02

CT (deg)

it (d

eg)

36

scan lines is contiguous and parallel with the previous set which is compensated motion as

shown above fig.3.11.

The TM scans cross-track swaths of 187km as mentioned in section 2.4.1, downrange of the scan

motion with respect to normal to the orbit and sensor motion on the surface of the Earth in km is

shown in fig.3.11.

Figure 3.11: Scan pattern of the scanning mirror on the surface of the Earth

3.3.2 Analytical Results based on Spherical Geometry:

Implement the above in-track and cross-track commands in spherical geometry method, so that

we can easily find out the coordinates of the scanning motion of the sensor (scan mirror). The

orbit parameter of Landsat spacecraft are taken from [15]. But the inclination angle of the

spacecraft is considered as 90 D instead of 98.2 D because it is easier to analyze the motion of the

spacecraft and sensors, and rests of the parameters are remain same.

-150 -100 -50 0 50 100 1500

2

4

6

8Scan Pattern

normal to orbit (km)

Dow

nran

ge (k

m)

0 0.2 0.4 0.6 0.8 1 1.2 1.4-200

-100

0

100

200

Time (s)

zn (k

m)

37

357.8 358 358.2 358.4 358.6 358.8 359 359.2 359.4 359.6 359.80

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Latit

ude(

deg)

Longitude(deg)

spacecraft subsatellite pointsub-satellite point starting pointsensor scanning motionsensor's ground track starting point

Suppose if there is no in-track motion and only cross-track is given to the mirror, then we can

expect the resultant motion as zig-zag manner as it mentioned in section 2.4.3.The simulated

result is shown in fig. 3.12.

Figure 3.12: Un-compensated scan motion of the scanning mirror

If the in-track angle is also include to the mirror motion then the resultant motion has smooth

turnaround curves at the end of each active scan and also the active scans are parallel to each

other for successive scans. This is happens on the surface of the Earth, anyhow in this simulation

we neglected the Earth rotation because the simulation is carried out for 1sec.If we observe this

corrected motion in local vertical and local horizontal frame (spacecraft point of view) it is as

fig.3.10. That means in-track is not only corrects the motion at turnarounds but also at the

(coasting) active scan. These results are expected and simulated result is shown in the fig.3.13.

The variation of spacecraft latitude, longitude and sensor latitude, longitude with respect to the

true anomaly has been found out and the results are in Earth-fixed frame.

38

0 0.02 0.04 0.06 0.08357

358

359

360

true anomaly(deg)

spot

long

itude

(deg

)

0 0.02 0.04 0.06-0.05

0

0.05

0.1

true anomaly(deg)

spot

latit

ude(

deg)

0 0.02 0.04 0.06 0.080

0.05

0.1

true anomaly(deg)

latit

ude(

deg)

0 0.02 0.04 0.06358.761

358.762

358.763

358.764

true anomaly(deg)

Long

itude

(deg

)

Figure 3.13: Compensated scan motion of the scanning mirror

Figure 3.14: Relation between true anomaly Vs spacecraft and sensor latitude and longitude

357.8 358 358.2 358.4 358.6 358.8 359 359.2 359.4 359.6 359.8-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Latit

ude(

deg)

Longitude(deg)

satellite ground tracksatellite ground track starting pointsensor ground tracksensor's ground track starting point

39

Figure 3.15: variation of spot distance with respect to time

Figure 3.16: variation of tilt and elevation angle with respect to distance

0 0.2 0.4 0.6 0.8 1 1.2 1.4705

706

707

708

709

710

711

712

713

Time (sec)

Spo

t dis

tanc

e(K

m)

705 706 707 708 709 710 711 712 7130

5

10

Distance(Km)

Tilt

angl

e(de

g)

705 706 707 708 709 710 711 712 71380

85

90

Distance(Km)

Ele

vatio

n an

gle(

deg)

40

Figure 3.17: Variation of elevation angle with respect to tilt angle

Figure 3.18: Variation of true anomaly with respect to cross-track angle

0 1 2 3 4 5 6 7 8 981

82

83

84

85

86

87

88

89

90

Tilt angle of mirror(deg)

Ele

vatio

n an

gle(

deg)

-10 -8 -6 -4 -2 0 2 4 6 8 100

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

thetaCT (deg)

(Tru

e A

nom

aly,

deg

)

41

Figure 3.19: variation of sensor latitude and longitude with respect to the spacecraft latitude

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08-0.05

0

0.05

0.1

Latitude of spacecraft(deg)

Latit

ude

of s

cani

ng m

irror

(deg

)

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08357

358

359

360

Latitude of spacecraft(deg)Lon

gitu

de o

f sca

ning

mirr

or(d

eg)

42

Chapter 4

Controller Design Analysis for Scanning Mirror

4.1 Introduction:

A control system is a dynamic system that contains a controller as an integral part. The device

that generates the signal according to control law and controls the response of the plant is called

controller. The purpose of the controller is to generate control signals, which will drive the

process to be controlled in the desired manner. Certain command inputs given to the controller

and the plant is expected to behave in a desired manner, under control. In feedback control, the

plant has to be monitored and its response needs to be measured using sensors, for feeding back

into the controller. Then, the controller compares the sensed signal with a desired response as

specified externally and uses the error to generate a proper control signal.

There are different types of control systems, depend on the loop of the system like open loop

control system, closed loop control system, feed-forward control system. If the plant is stable and

completely, accurately known and if the inputs to the plant can be precisely generated and

applied, then accurate control might be possible even without feedback control. Under these

circumstances, a measurement is not needed and thus, we have an open-loop control system. In a

feedback control system, the control loop has to be closed, by measuring the system response and

employing that information to generate control signals to correct any output errors. Hence,

feedback control is also known as closed-loop control. In feedforward control, unknown inputs

are measured and that information, along with desired inputs, is used to generate control signals

that can reduce errors due to these unknown inputs or variation in them.

Figure 4.1: An open-loop control system

Controller Signal

conditioning ActuatorPlant

Set point

(Reference

input)

Controlled Variable (Output)

43

Reference Output input

Figure 4.2: A system with feedback and feedforward control

The current work dealt with different types of the controllers like PD (Proportional-derivative),

PID (Proportional-Integral-Derivative), Double-lag compensator. PD, PID controller design

comes under time-domain analysis, where as Double-Lag compensator comes under frequency

domain analysis.

4.2 Time Domain Design Analysis:

The time-domain design of the control systems refer to the utilization of the time-domain

properties and specifications of the system to be designed. The time domain characteristics of a

linear control system are represented by the transient and steady state responses of the system

when certain test signals are applied. In this case the in-track and cross-track commands which are

simulated by using analysis (section-3.2) .Qualitatively, the damping ratio and the natural

frequency can be used to indicate the relative stability of the system.

4.2.1 PD controller Design:

With ideal derivative compensation, a pure differentiator is added to the forward path of the

feedback control. Proportional derivative (PD) consists of feeding the error (proportional) plus the

derivative of the error forward to the plant.

Controller Plant

Measurement for

feedback

Measurement for

feedforward

44

The transfer function of PD controller ( )cG s = KP + DK s;

The transfer function of the Plant ( )pG s = 21

Js; where J is mass moment of inertia

The closed-loop transfer with unit feedback of the overall system is given by

( )1 ( ) ( )

c

c p

G sG s G s+ =

' '

2 ' '

KK

P D

D P

K ss K s

++ +

where 'K P = 1KPJ

; 'DK = 1

DJK;

Controller ( )cG s plant ( )pG s

Reference + controller output input (Actual output)

(-)

Figure 4.3: A closed-loop system with unit feedback PD controller in forward path

The closed loop characteristic equation 1 ( ) ( ) c pG s G s+ = 2 ' 'KD Ps K s+ + ; (4.1)

The characteristic equation of standard form of the second ordered system is given as

2 22 n ns s + + (ref.10) (4.2) The dynamic behavior of the second-order system can then be described in terms of two

parameters , and n or c . If 0

45

Control frequency ( c ) = 8 scan frequency = 112 = 351.853 rad/sec By using equations 4.1, 4.2 'DK = 2 c , 'K P = 2c

'DK ,

'K P values are depends on , c , where as changes from 0.1 to 1 for a fixed c value. 'DK ,

'K P can get by using another method which is used in PID controller design and it will be

discuss in further section.

c = 8 c = 9 c = 10 zeta 'K D

'K P 'K D

'K P 'K D

'K P 0.1 70.37184 123804.318 79.16832 156689.839 87.9648 193444.2460.2 140.74368 123804.318 158.33664 156689.839 175.9296 193444.2460.3 211.11552 123804.318 237.50496 156689.839 263.8944 193444.2460.4 281.48736 123804.318 316.67328 156689.839 351.8592 193444.2460.5 351.8592 123804.318 395.8416 156689.839 439.824 193444.2460.6 422.23104 123804.318 475.00992 156689.839 527.7888 193444.2460.7 492.60288 123804.318 554.17824 156689.839 615.7536 193444.2460.8 562.97472 123804.318 633.34656 156689.839 703.7184 193444.2460.9 633.34656 123804.318 712.51488 156689.839 791.6832 193444.2461 703.7184 123804.318 791.6832 156689.839 879.648 193444.246

Table 4.1: Variation of 'DK , 'K P as damping coefficient changes for cross-track motion

Let consider damping ratio as 0.7 and c = 8 then substitute these values in closed-loop transfer function is 2

351.859 492.6492.6 351.859

ss s

++ +

Loop transfer function is ' '

2

K P DK ss+ = 2351.859 492.6ss

+

It is mentioned in the ref. [15] that the geometric accuracy of SMA for cross-track scan motion is

20 RAD (1.14millidegree). The time domain results shown in the fig.4.6, that the cross-track error is more than the permissible limit. The open loop and closed loop frequency response of the

PD controller is shown in the fig.4.4, 4.5. The phase margin of the system is 73.5deg, and the gain

margin is infinity. The double integrator plant is stable for infinite gain with PD controller.

46

.

Figure 4.4: PD controller Bode plots

-40

-20

0

20

40

60

80M

agnitu

de (d

B)

101

102

103

104

-180

-135

-90

Phas

e (d

eg)

crosstrack PD compensator bode plot

Frequency (rad/sec)

-20

0

20

40

60

80

Mag

nitu

de (d

B)

intrack PD compensator bode plot

Frequency (rad/sec)10

110

210

310

4-180

-135

-90

System: cPhase Margin (deg): 73.5Delay Margin (sec): 0.000777At frequency (rad/sec): 1.65e+003Closed Loop Stable? No

Phas

e (d

eg)

47

Figure 4.5: closed loop frequency response for cross-track and in-track PD controller

10-2 100 102 104 10610-10

10-8

10-6

10-4

10-2

100

102

(rad/sec)

Mag

nitu

decrosstrack closed-loop frequency response

magnitude=0.707

10-2 100 102 104 10610

-10

10-8

10-6

10-4

10-2

100

102

(rad/sec)

Mag

nitu

de

intrack closed-loop frequency response

magnitude=0.707

48

Figure 4.6: PD controller error plots for cross-track motion (0.9-damping ratio)

0 0.2 0.4 0.6 0.8 1-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

time(sec)

cros

stra

ck(d

eg)

crosstrack motion for 10Wcrosstrack motion for 8W

active scan

permissable error1milli degree

active scan

0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 0.22 0.24

-0.15

-0.1

-0.05

0

0.05

0.1

time(sec)

cros

stra

ck(d

eg)

crosstrack motion for 10Wcrosstrack motion for 8W

active scan active scan

permissableerror 1millidegree

49

But in case of SLC (scan line corrector) which imparts in-track motion to the mirror has different

specifications and scan mirror assembly parameters are not valid. So the frequency of SLC is

14Hz, the