final report updated

1

Summer Training

On

Control System Design

For

Dual Axis Gimbal Assembly

At

DRDO

Laser Science & Technology Centre

Defence Research & Development Organisation,

Metcalfe House, Delhi-54

In

Partial Fulfillment for Requirement of the Degree

Bachelor of Technology

In

Electrical and Electronics Engineering

Department of Electrical and Electronics Engineering

BHAGWAN PARSHURAM INSTITUTE OF TECHNOLOGY

Submitted by:

Farheen Hussain

5320804912

2

ACKNOWLEDGEMENT

It is my pleasure to be indebted to various people, who directly or indirectly contributed in the development of this work and who influenced my thinking, behavior and acts during the course of study.

I express my sincere gratitude to Shri Hari Babu Srivastava, Sc ‘G’ worthy Director for providing me an opportunity to undergo summer training at LASTEC (DRDO).

I am thankful to Mr. Ravindra Singh, Sc ‘F’ for his support, cooperation, and motivation provided to me during the training for constant inspiration, presence and blessings.

I also extend my sincere appreciation to Mr. Ashish Pandey, Sc ‘D’ who provided his valuable suggestions and precious time in accomplishing my training report.

Also I am thankful to my college, Bhagwan Parshuram Institute of Technology, for providing us such an opportunity. Because of this summer training we have learnt many new things and have got sharpen our skills.

Lastly, I would like to thank the almighty and my parents for their moral support and my friends with whom I shared my day-to-day experience and received lots of suggestions that my quality of work.

3

LASER SCIENCE AND TECHNOLOGY CENTREDEFENCE RESEARCH & DEVELOPMENT ORGANIZATION

MINISTRY OF DEFENCEMETCALFE HOUSE, NEW DELHI - 110054

Phone: (011) 23907-573, 543Website: www.drdo.gov.in

____________________________________________________________________

CERTIFICATE

This is to certify that Ms. Farheen Hussain, student of B.Tech (EEE) Bhagwan Parshuram Institute of technology (GGSIPU), New Delhi has successfully completed the dissertation entitled “Control System Design for Dual Axis Gimbal Assembly" and has worked under my supervision and guidance in Laser Science and technology Center (LASTEC), Defence Research & Development Organization (DRDO), Ministry of Defence, Metcalfe House, Delhi.

To the best of my knowledge, the work is original and has not been submitted elsewhere for any other academic attainment.

Mr. Ravindra Singh

Scientist ‘F’

Control electronics group

LASTEC, DRDO

4

TABLE OF CONTENT_______________________________________________

I. Abstract

1. Introduction

2. Control System Design

2.1 Azimuth Assembly Control System Design

2.1.1 Current Loop Control System Design

2.1.2 Stabilization Loop Control System Design

2.1.3 Position Loop Control System Design 2.2 Elevation Assembly Control System Design



2.2.3 Position Loop Control System Design

2.3 Overall Control System

3. Step response 4. Performance Analysis

5. Final result

I. ABSTRACT

5

This document proposes and describes an effective way of designing a control system for controlling the dual axis gimbal assembly. The designing of control system has been done using MATLAB software. Finally the results obtained after designing the controllers have been analyzed with respect to frequency domain parameters as well as time domain parameters. Gimbal is a mechanical structure which can have motions in more than one axis. Here, gimbal assembly which has to be controlled has motion in two axis, one in Azimuth and other one is in Elevation.

A common control system design configuration uses a rate or stabilization loop inside a position loop. The stabilization loop controls the rate of the gimbal assembly as per demanded. The outer position loop minimizes the positioning error of the gimbal assembly.

1. Introduction

6

In this report, we are going to discuss the procedure of control system design to meet the desired specifications. Classical design technique (frequency response) will be used. To begin with, we will consider the open loop frequency response of the gimbal assembly (plant) and motor. The plant model used for control design is a simplified, linearized model that allows us to apply classical design techniques. More accurate nonlinear plant models will be used later to validate the design and evaluate performance.

Furthermore, controllers are designed independently for azimuth and elevation, and the effect of cross-coupling in dynamics on performance is evaluated later. The philosophy adopted is to first design a very fast current loop which is being closed in the servo power amplifier itself then a fast stabilization (rate) loop, in which boresight gyros are used as sensors for rate feedback. The stabilization loop is then nested within a position (outer) loop that uses an encoder as a position sensor. The role of the stabilization loop is to attenuate jitter and stabilize the line of sight (LOS) against disturbances, while the main role of the position is to minimize the positioning error.

Control System Specifications for the cascaded gimbal assembly

Ø Position loop bandwidth : >5 HzØ Stabilization loop bandwidth : >30 HzØ Gain margin : > 6 dBØ Phase margin : > 30 degØ Controller Type : PI / Lead-lag Ø Disturbance Spectrum : 3 mrad at 1 Hz and less at

higher frequencies ( 20 dB/decade)

2. Control System DesignFor designing the control system, first we will start with the azimuth assembly.

7

2.1 Azimuth Assembly Control System Design

For designing the control system for azimuth assembly, we will start with designing the control system for current loop.


The Simulink model for the uncompensated plant is based on the mathematical formulation for modeling the rigid gimbal dynamics. While the Simulink block diagram derived directly from the equations is fairly involved, Fig. 2.1 shows the simplified transfer function model of the azimuth gimbal assembly. The important mechanical parameters are obtained from the FE model. Moment of inertia Iazimuth=51 kg-m2, Bviscous= 160.2 N-m-sec/rad (viscous friction coefficient). The Structural modes initially are neglected here during the modeling in rigid mode but later on it will be included. The Mega flux Series Allied Motion MF0510015A00 motor is modeled as a simple DC machine, with torque constant=4.11 N-m/Amp, L=0.675 mH, R=0.05 Ohm, back emf constant kb=4.11 V-sec/rad. For a brushless motor model, the above constants get scaled by appropriate constant factors representing conversion from line-line quantities to line-phase quantities. This does not change the time constant of the motor, it only requires scaling of the gain in the power amplifier (drive electronics) by appropriate factor. This will not affect the performance of the control system.

The peak torque of the motor is 2523 N-m. The peak current of the motor is 613 Amp. Assuming that 10 V DAC will be used for converting the digital control signal into analog signal which will be fed to Servo Power Amplifier, the scale factor for the current feedback can be selected as 10 V = 613 Amp. Now for designing the current loop controller, we will start with the uncompensated open loop bode plot where input is the voltage to the motor (V), while the output is the equivalent voltage corresponding to armature current.

8

Fig. 2.1 Transfer function model of uncompensated plant along with actuator (azimuth)

Fig. 2.2 shows the frequency response plot of the uncompensated open loop azimuth plant along with actuator model.

Bode Diagram

Frequency (Hz)

10-2

10-1

100

101

102

103

104

-225

-180

-135

-90

-45

0

45

Phas

e (d

eg)

-100

-50

0

50From: Sine Wave To: Current to Voltage Ratio

Mag

nitu

de (d

B)

Fig. 2.2 Uncompensated open loop Bode plotsGain at 1 KHz = - 48 dB

Since we are targeting the current loop bandwidth more than 1 KHz, hence we will target the gain cross-over frequency of the compensated open loop at 1 KHz. From Fig. 2.2, it can be observed that the open loop gain at 1 KHz is –48 dB. This indicates that more than 48 dB gain will be required to achieve adequate current loop bandwidth.

Now as we know, that motor winding transfer function is of first order, closing the current loop only with pure gain will give some steady state error. Hence we will use PI as current loop controller.

PI Compensation:

Assume a PI compensator in the form of (K [(1+s/a)/s]). Since we are targeting gain cut off frequency at 1 KHz which is quite high, we should place zero of the PI very close to

9

origin so that gain roll off ( -20 dB/decade) does not continue for higher frequencies. To start with, we will place zero at 1 rad/s. Now with this value of a, (1+s/a)/s part of PI compensator provides a gain of approx. 20*log10 (1/a) = 20*log10 (1/1) = 0 dB at 1 KHz. Hence for gain cross-over frequency at 1 KHz, K should be set in such a way that it gives 48-0 = 48 dB of gain at 1 KHz. Now if we take 48 of gain, it is equivalent to 260. Hence, K = 260.Hence, PI compensator takes the form as given below:

PI: 260* (s +1)/s

Figure 2.3 shows the compensated open loop bode plot.

Bode Diagram

Frequency (Hz)

10-3

10-2

10-1

100

101

102

103

104

-225

-180

-135

-90

-45

0

45

Phas

e (d

eg)

-20

0

20

40

60


Mag

nitu

de (d

B)

Fig. 2.3: Compensated open loop Bode plotsGain Margin= 14.1 dB, Phase Margin = 79.3 deg., Gain cut-off frequency = 999 Hz

From Fig. 2.3, it is clear that system with the particular PI controller is stable as both the gain margin and phase margin is positive.

Fig. 2.4 shows the block diagram of the closed current loop

10

Fig. 2.4: Closed current loop block diagram

Fig.2.5 shows bode plot of the closed current loop.

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

104

-225

-180

-135

-90

-45

0

45

Phas

e (d

eg)

-15

-10

-5


Mag

nitu

de (

dB)

Fig. 2.5 Azimuth closed current loop bode plot(Bandwidth = 1.3 KHz)

11


Now for designing the stabilization loop controller, we will start with the uncompensated open loop bode plot where input is the voltage to the motor (V), while the output is the angular rate.

Fig. 2.6 shows the frequency response plot of the uncompensated open loop azimuth plant along with actuator model and inner current loop.

Bode Diagram

Frequency (Hz)

10-2

10-1

100

101

102

103

104

-270

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

-80

-60

-40

-20

0

20From: Sine Wave To: Gain3

Mag

nitu

de (d

B)

Fig 2.6 Uncompensated open loop Bode plot (Velocity loop) Gain at 1 Hz = 12 dB& Gain at 35 Hz = -18 dB

From Fig. 2.6, it can be observed that the open loop gain at 1Hz is 12 dB, while the same at 35Hz is around –18 dB. This indicates that more than 18 dB gain will be required to achieve adequate stabilization loop bandwidth.

PI compensation

12

The first step in the stabilization loop compensator design is to choose adequate gain so as to give a cut-off frequency of around 35Hz. The gain required is approximately 18 dB, which translates to around 20. More importantly, the gain to overcome the worst case disturbances should be roughly equal to the ratio of the disturbance to the allowable residual jitter on the line-of-sight. The disturbance specification is 3 mrad at 1Hz, while the allowable jitter is 50 micro-radian. So 3 mrad / 50 micro-rad = 60, which is equivalent to 36 dB. Since the open loop uncompensated gain is 12 dB at 1Hz, the stabilization loop must provide at least 36-12 = 24 dB of gain to achieve the stabilization accuracy. `Now assume a PI compensator in the form of (K[(1+s/a)/s]).Since we are targeting gain cut off frequency at 35 Hz, we can place zero of the PI at 2 Hz (less than 1/10th of gain cut off frequency). Then the value of a will be 2*pi*2 = 12.57. Now with this value of a, (1+s/a)/s part of PI compensator provides a gain of -15 dB at 1 Hz & -22 dB at 35 Hz. Hence for 36 dB open loop gain at 1 Hz, K should be set in such a way that it gives 24+15 =39 dB of gain at 1 Hz & 22+18 = 40 dB of gain at 15 Hz. Now if we take 40 dB of gain, it is equivalent to 100. Hence, K = 100.Hence, PI compensator takes the form as given below:

PI: 100 (0.07957 s +1)/s

Fig. 2.7 shows the PI compensated open loop bode plot.

Bode Diagram

Frequency (Hz)

10-2

10-1

100

101

102

103

104

-270

-225

-180

-135

-90

Phas

e (d

eg)

-100

-50

0

50

100From: Sine Wave To: Gyro scale factor

Mag

nitu

de (d

B)

Fig. 2.7 Compensated open loop Bode plotGain Margin= 31.5 dB, Phase Margin = 84 deg., Gain at 1 Hz = 36.9 dB

13

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

104

-270

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

-80

-60

-40

-20

0


Mag

nitu

de (d

B)

Fig. 2.8 Azimuth closed velocity loop bode plot(Bandwidth = 39.9 Hz)

Fig. 2.8 shows the closed stabilization loop Bode plot. The stabilization loop bandwidth achieved in this case is around 39.9 Hz. Since the gyro bandwidth (100Hz) is much higher than the target closed loop bandwidth, it does not significantly affect the response at frequencies of interest for disturbance attenuation. On the other hand, it does act as a low pass filter for high frequency noise (>100Hz).

Fig. 2.9 shows the block diagram of the stabilization loop along with inner current loop for the azimuth plant.

14

Fig. 2.9 Stabilization loop block diagram with inner current loop

2.1.3 Position Loop Control System Design

Now for designing the position loop controller, we will start with the uncompensated open loop bode plot where input is the voltage to the motor (V), while the output is the angular position.Fig. 2.10 shows the frequency response plot of the uncompensated open loop azimuth plant along with actuator model and inner current & stabilization loops

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

-450

-360

-270

-180

-90

Phas

e (d

eg)

-120

-100

-80

-60

-40

-20

0From: Sine Wave To: Integrator

Mag

nitu

de (d

B)

. Fig 2.10 Uncompensated open loop Bode plot (Position loop)

Gain at 5 Hz = -45 dB

15

From Fig. 2.10, it can be observed that the open loop gain at 5 Hz is -45 dB. This indicates that 45 dB gain will be required to achieve adequate stabilization loop bandwidth. Now if we take 45 dB of gain, it is equivalent to 180. Hence, K = 180.

Fig. 2.11 shows the Gain compensated open position loop bode plot.

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

-450

-360

-270

-180

-90

Phas

e (d

eg)

-60

-40

-20

0

20


Mag

nitu

de (d

B)

Fig. 2.11 Compensated open loop Bode plotGain Margin= 24.1 dB, Phase Margin = 83.1 deg.

16

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

-450

-360

-270

-180

-90

0

Phas

e (d

eg)

-60

-50

-40

-30

-20

-10


Mag

nitu

de (d

B)

Fig. 2.12 Azimuth closed position loop bode plot(Bandwidth = 6 Hz)

Fig. 2.12 shows the closed position loop Bode plot. The stabilization loop bandwidth achieved in this case is around 6 Hz.

Fig. 2.13 shows the block diagram of the position loop along with inner current & stabilization loops for the azimuth plant.


17

2.2 Elevation Assembly Control System Design

2.2.1 Current Loop Design

As we have done for Azimuth assembly, in the similar steps we will do for elevation assembly. Fig. 2.14 shows the simplified transfer function model of the elevation gimbal assembly. Moment of inertia Ielevation= 0.5 kg-m2, Bviscous= 0.5*2*pi*.5 = 1.57 N-m-sec/rad (viscous friction coefficient). The Mega flux Series Allied Motion MF0210100A00 motor is modeled as a simple DC machine, with torque constant=1.56 N-m/Amp, L=6.5 mH, R=3.6 Ohm, back emf constant kb=1.56 V-sec/rad. For a brushless motor model, the above constants get scaled by appropriate constant factors representing conversion from line-line quantities to line-phase quantities. This does not change the time constant of the motor, it only requires scaling of the gain in the power amplifier (drive electronics) by appropriate factor. This will not affect the performance of the control system.

The peak torque of the motor is 15 N-m. The peak current of the motor is 9.57 Amp. Assuming that 10 V DAC will be used for converting the digital control signal into analog signal which will be fed to Servo Power Amplifier, the scale factor for the current feedback can be selected as 10 V = 9.57 Amp. Now for designing the current loop controller, we will start with the uncompensated open loop bode plot where input is the voltage to the motor (V), while the output is the equivalent voltage corresponding to armature current.

Fig. 2.14 Transfer function model of uncompensated plant along with actuator (elevation)

Fig. 2.15 shows the frequency response plot of the uncompensated open loop elevation plant along with actuator model.

18

Bode Diagram

Frequency (Hz)

10-2

10-1

100

101

102

103

104

-225

-180

-135

-90

-45

0

45

Phas

e (d

eg)

-50

-40

-30

-20

-10From: Sine Wave To: Current to Voltage Ratio

Mag

nitu

de (d

B)

Fig. 2.15 Uncompensated open loop Bode plotsGain at 1 KHz = - 32 dB

Since we are targeting the current loop bandwidth more than 1 KHz, hence we will target the gain cross-over frequency of the compensated open loop at 1 KHz. From Fig. 2.15, it can be observed that the open loop gain at 1 KHz is –32 dB. This indicates that more than 32 dB gain will be required to achieve adequate current loop bandwidth.

Now as we know, that motor winding transfer function is of first order, closing the current loop only with pure gain will give some steady state error. Hence we will use PI as current loop controller.

PI Compensation:

Assume a PI compensator in the form of (K [(1+s/a)/s]). Since we are targeting gain cut off frequency at 1 KHz which is quite high, we should place zero of the PI very close to origin so that gain roll off ( -20 dB/decade) does not continue for higher frequencies. To start with, we will place zero at 2 rad/s. Now with this value of a, (1+s/a)/s part of PI compensator provides a gain of approx. 20*log10 (1/a) = 20*log10 (1/2) = -6 dB at 1 KHz. Hence for gain cross-over frequency at 1 KHz, K should be set in such a way that it gives

19

32+6 = 38 dB of gain at 1 KHz. Now if we take 38 of gain, it is equivalent to 80. Hence, K = 80.Hence, PI compensator takes the form as given below: PI: 80* (0.5s +1)/s PI: 40* (s +2)/s

Fig. 2.16 shows the compensated open loop bode plot.

Bode Diagram

Frequency (Hz)

10-2

10-1

100

101

102

103

104

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

-20

0

20

40


Mag

nitu

de (d

B)

Fig. 2.16 Compensated open loop Bode plotsGain Margin= 13.9 dB, Phase Margin = 83.3 deg., Gain cut-off frequency = 1.03 KHz

From figure 2.16, it is clear that system with the particular PI controller is stable as both the gain margin and phase margin is positive.

Fig. 2.17 shows the block diagram of the closed current loop.

20

Fig. 2.17 Closed current loop block diagram

Fig. 2.18 shows bode plot of the closed current loop.

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

104

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

-30

-25

-20

-15

-10

-5


Mag

nitu

de (d

B)

Fig. 2.18 Elevation closed current loop bode plot(Bandwidth = 1.21 KHz)

21


Now for designing the stabilization loop controller, again we will start with the uncompensated open loop bode plot where input is the voltage to the motor (V), while the output is the angular rate.

Fig. 2.19 shows the frequency response plot of the uncompensated open loop elevation plant along with actuator model and inner current loop.

Bode Diagram

Frequency (Hz)

10-2

10-1

100

101

102

103

104

-270

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

-80

-60

-40

-20

0


Mag

nitu

de (d

B)

Fig. 2.19 Uncompensated open loop Bode plot (Velocity loop) Gain at 1 Hz = 7 dB& Gain at 35 Hz = -23 dB

From Fig. 2.19, it can be observed that the open loop gain at 1Hz is 7 dB, while the same at 35Hz is around –23 dB. This indicates that more than 23 dB gain will be required to achieve adequate stabilization loop bandwidth.

22

PI compensation

The first step in the stabilization loop compensator design is to choose adequate gain so as to give a cut-off frequency of around 35Hz. The gain required is approximately 23 dB, which translates to around 15. More importantly, the gain to overcome the worst case disturbances should be roughly equal to the ratio of the disturbance to the allowable residual jitter on the line-of-sight. The disturbance specification is 3 mrad at 1Hz, while the allowable jitter is 50 micro-radian. So 3 mrad / 50 micro-rad = 60, which is equivalent to 36 dB. Since the open loop uncompensated gain is 7 dB at 1Hz, the stabilization loop must provide at least 36-7 = 29 dB of gain to achieve the stabilization accuracy. Now assume a PI compensator in the form of (K[(1+s/a)/s]).Since we are targeting gain cut off frequency at 35 Hz, we can place zero of the PI at 3 Hz (less than 1/10th of gain cut off frequency). Then the value of a will be 2*pi*3 = 18.85. Now with this value of a, (1+s/a)/s part of PI compensator provides a gain of -15.5 dB at 1 Hz & -25.5 dB at 35 Hz. Hence for 36 dB open loop gain at 1 Hz, K should be set in such a way that it gives 29+15.5 =44.5 ≈ 45 dB of gain at 1 Hz & 23+25.5 = 48.5 dB of gain at 35 Hz. Now if we take 48.5 dB of gain, it is equivalent to 260. Hence, K = 260.Hence, PI compensator takes the form as given below:

PI: 260 (0.05305 s +1)/s

Fig. 2.20 shows the PI compensated open loop bode plot.

23

Bode Diagram

Frequency (Hz)

10-2

10-1

100

101

102

103

104

-270

-225

-180

-135

-90

Phas

e (d

eg)

-100

-50

0

50


Mag

nitu

de (d

B)

Fig. 2.20 Compensated open loop Bode plotGain Margin= 32 dB, Phase Margin = 82.5 deg., Gain at 1 Hz = 39.8 dB

24

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

104

-270

-225

-180

-135

-90

-45

0

Phas

e (d

eg)

-60

-40

-20

0


Mag

nitu

de (d

B)

Fig. 2.21 Elevation closed velocity loop bode plot(Bandwidth = 39.9 Hz)

Fig. 2.21 shows the closed stabilization loop Bode plot. The stabilization loop bandwidth achieved in this case is around 39.9 Hz. Since the gyro bandwidth (100Hz) is much higher than the target closed loop bandwidth, it does not significantly affect the response at frequencies of interest for disturbance attenuation. On the other hand, it does act as a low pass filter for high frequency noise (>100Hz).

Fig. 2.22 shows the block diagram of the stabilization loop along with inner current loop for the elevation plant.

25


2.2.3Position Loop Control System DesignNow for designing the position loop controller, we will start with the uncompensated open loop bode plot where input is the voltage to the motor (V), while the output is the angular position.Fig. 2.23 shows the frequency response plot of the uncompensated open loop azimuth plant along with actuator model and inner current & stabilization loops.

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

-450

-360

-270

-180

-90

Phas

e (d

eg)

-120

-100

-80

-60

-40

-20


Mag

nitu

de (d

B)

Fig 2.23 Uncompensated open loop Bode plot (Position loop) Gain at 5 Hz = -44.5 dB

26

From Fig. 2.23, it can be observed that the open loop gain at 5 Hz is -44.5 dB. This indicates that 44.5 dB gain will be required to achieve adequate stabilization loop bandwidth. Now if we take 44.5 dB of gain, it is equivalent to 170. Hence, K = 170.

Fig. 2.24 shows the Gain compensated open position loop bode plot.

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

-450

-360

-270

-180

-90

Phas

e (d

eg)

-60

-40

-20

0

20


Mag

nitu

de (d

B)

Fig. 2.24 Compensated open loop Bode plotGain Margin= 24.4 dB, Phase Margin = 84.2 deg.

27

Bode Diagram

Frequency (Hz)

10-1

100

101

102

103

-450

-360

-270

-180

-90

0

Phas

e (d

eg)

-60

-50

-40

-30

-20

-10


Mag

nitu

de (d

B)

Fig. 2.25 Azimuth closed position loop bode plot(Bandwidth = 5.73 Hz)

Fig. 2.25 shows the closed position loop Bode plot. The stabilization loop bandwidth achieved in this case is around 6 Hz.

Fig. 2.26 shows the block diagram of the position loop along with inner current & stabilization loops for the azimuth plant.


28

2.3 Overall control system

Fig. 2.27 shows the overall control system block diagram with 1% cross-coupling between azimuth and elevation dynamics in the simplified plant model.

Fig. 2.27 Overall control system Simulink model

29

3. Step response

Figure 2.28 shows a qualitative closed loop step response plot for azimuth and elevation velocity loops.

Commanded Value: 2 V Gyro Scale factor = 5.73 V/rad/s = 100 mV/deg/s

Hence 2V voltage command corresponds to 20 deg/s angular speed.

Time Domain Parameters

Azimuth Velocity loop step response

Azi

mut

h R

ate

(deg

. /s

)

Time (sec)

Rise time = 15 msSettling time = 80 msPeak overshoot = 4 %Steady State Error = 0.01 %

Elevation Velocity loop step response

30

Fig. 2.28 Step response of overall control system (qualitative)

Time Domain Parameters

Elevation Velocity loop step response

Elev

atio

n R

ate

(deg

. /s

)

Time (sec)

Rise time = 14.5 msSettling time = 110 msPeak overshoot = 10 %Steady State Error = 0.01 %

31

4. PERFORMANCE ANALYSIS

Azimuth assembly:

Current loop:

Uncompensated open loop: Gain at 1 kHz =-48dB

Compensated open loop: Gain Margin= 14.1 dBPhase Margin = 79.3 degGain cut-off frequency = 999 Hz

Azimuth closed current loop:Bandwidth = 1.3 KHz

Stabilization Loop:

Uncompensated open loop (Velocity loop):Gain at 1 Hz = 12 dBGain at 35 Hz = -18 dB

Compensated open loop:Gain Margin= 31.5 dBPhase Margin = 84 degGain at 1 Hz = 36.9 dB

Azimuth closed velocity loopBandwidth = 39.9 Hz

Position Loop:

Uncompensated open loop (Position loop):Gain at 5 Hz = -45 dB

Compensated open loop:Gain Margin= 24.1 dBPhase Margin = 83.1 deg

Azimuth closed position loop:Bandwidth = 6 Hz

32

Elevation Assembly:

Current Loop Design

Uncompensated open loop:

Gain at 1 KHz = - 32 dBCompensated open loop:

Gain Margin= 13.9 dBPhase Margin = 83.3 degGain cut-off frequency = 1.03 KHz

Elevation closed current loop:Bandwidth = 1.21 KHz

Stabilization Loop Control System Design:

Uncompensated open loop (Velocity loop):Gain at 1 Hz = 7 dBGain at 35 Hz = -23 dB

Compensated open loop:Gain Margin= 32 dBPhase Margin = 82.5 degGain at 1 Hz = 39.8 dB

Elevation closed velocity loop:Bandwidth = 39.9 Hz

Position Loop Control System Design:

Uncompensated open loop (Position loop):Gain at 5 Hz = -44.5 dB

Compensated open loop:Gain Margin= 24.4 dBPhase Margin = 84.2 deg

Azimuth closed position loop:Bandwidth = 5.73 Hz

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5. FINAL RESULT

Characteristics Specified Values Achieved Values Azimuth elevationRate loop Position loop rate loop position loop

Gain Margin >6 dB 31.5 dB 24.1 dB 32 dB 24.4 dBPhase Margin >30 deg. 84 deg. 83.1 deg. 82.5 deg 84.2 deg.Bandwidth >30 Hz

(rate loop)> 5 Hz(position loop)

39.9 Hz 6 Hz 39.9 Hz 5.73 Hz

final report updated

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Transcript of final report updated