Concordia University Department of Electrical and Computer Engineering Fundamentals of Control Systems (ELEC372) S. Hashtrudi Zad

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1 Concordia University Department of Electrical and Computer Engineering Fundamentals of Control Systems (ELEC372) S. Hashtrudi Zad Project: Analysis of the Performance of a Satellite Pitch Control System Due: Friday, Nov. 16, 2018, noon (in instructor s mailbox in EV5-175) The project must be done in groups of two or three. One report per group. Only original hardcopy of the report is accepted. The Attitude Determination and Control Subsystem (ADCS) of a spacecraft controls the orientation of the spacecraft in space. In this assignment, the control system for the pitch angle of a spacecraft is studied. 1 Satellite Model Fig. 1 depicts a satellite in a circular geostationary orbit at an altitude of approximately Earth θ Satellite Figure 1: Satellite in circular geostationary orbit. 36,000 km.. The period of a satellite in this type of orbit is the Earth s day (about 24 hours) and thus the angular velocity of the satellite in its orbit is ω o rad/s. A satellite 1

2 in a circular equitorial geostationary orbit will hover over a spot on Earth and hence will be useful for communications. The satellite s attitude is controlled using a momentum wheel. (Sample actuator and sensor data sheets are enclosed.) In this assignment, we investiagte the design of the system that controls the pitch angle (θ). The linearized model of the pitch motion is I d2 θ dt 2 = T(t) = T c(t)+t d (t) where I = 400 N.m.s 2 is the momentum of inertial of the satellite about the pitch axis, T c (t) is the control torque (due to the momentum wheel) and T d (t) is the disturbance torque. Note that the pitch angle θ is in radians. At a geostationary orbit, the two main sources of disturbance are solar pressure torque and thruster misalignment torque. We ignore thrust maneuvers and thus only consider solar pressure torque. The distrubance torque along the pitch axis is T d (t) = 10 4 cosω o t (N.m). Note that the disturbance is periodic, with a period equal to the satellite s period. 2 Problem Statement Fig. 2 shows the block diagram of the pitch angle control system. The desired reference pitch θ ref (s) + K (s) T m (s) 1 T d (s) T c (s) + + G(s) θ(s) Figure 2: Pitch control system. is θ ref = 0 rad. The transfer function of the satellite is G(s) = θ(s) T(s) = 1 Is 2 K (s) is the controller, T m (s) is the torque on the momentum wheel (exerted by a motor) and T c (s) is the control torque (T c = T m ). The block diagram of Fig. 2 can be redrawn in the familiar form of Fig. 3 where K(s) = K (s). It is desired to design K(s) (and hence the controller K (s)) so that the following design specifications are satisfied. 2

3 θ ref (s) + K(s) T d (s) T c (s) + + G(s) θ(s) Figure 3: Pitch control system redrawn. (DS1) The closed loop system must be stable. (DS2) The settling time of response to step inputs must be less than 300s. (DS3) The percentage of overshoot of response to step inputs must be less than 25%. (DS4) The pitch angle accuracy must be at least 0.05 deg; that is the effect of disturbance on the output in steady state should be less than 0.05 deg. (DS5) As with other satellite subsystems, the ADCS is subject to a power budget. Hence it is desirable to minimize the power consumption of the ADCS (i.e., the sum of power consumptions of the actuators, sensors and processing electronics). The following three controllers have been proposed for the above problem: K 1 (s) = s K 2 (s) = s+1 4s+1 K 3 (s) = s+1 s+2 Choose the controller that best satisfies the design specifications DS1 to DS5. You may use a combination of analytical calculations and computer simulation using MATLAB s Control System Toolbox in your analysis. All simulations have to be done using MATLAB s Control System Toolbox and the m- files must be included in the report. The students are encouraged to use Simulink or Linear System Analysis app for simulations additionally but these results do not replace Control System Toolbox simulations. 3 Report Prepare a report explaining your results. First start by providing a brief review of the problem. In the next section describe your methodology: 3

4 (i) The criteria used to evaluate the controllers. (ii) The method used to evaluate each criterion (e.g., analytical, computer simulation, etc.) and the reason for choosing the method. Then in following sections apply the methodolgy to evaluate the controllers(one section for each controller). For analytical evaluations provide the calculations. For computer simulations provide the information such as input signals and computer code. Describe any assumption made in your analysis. Next provide your final decision with explanation (You must choose one controller.) Finally, name two important sources of inaccuracy (i.e., difference between your simulation results and the corresponding actual values) in your analysis. Your report should contain the following four graphs for each controller. 1. The output θ(t) in response to a step reference input of 5 deg = 5π/180 rad. 2. The control torque T c (t) in response to a step reference input of 5 deg = 5π/180 rad. 3. The output θ(t) in response to disturbance T d (t). 4. The control torque T c (t) in response to disturbance T d (t). Finally note the following. The simulations for the responses to step inputs should cover up to a few hundreds of seconds when the response settles. The simulations for the periodic disturbance should last for about one orbit period (24 hours), or perferrably two periods (48 hours), to fully demonstrate the behaviour in steady state. For the purpose of plotting, convert the pitch angle from radians to degrees. All plots should be properly labeled. Do not forget to indicate the units used for each axis. 4 Appendix Data sheet for SSTL reaction wheels ( Data sheet for Sodern horizon sensor ( 4

5 SSTL Microwheels The 10SP-M and 100SP-O reaction wheels are configured to provide a highly agile 3-axis attitude control solution for Earth observation or space science missions. 10SP-M microwheels use a dry lubrication technology to deliver a maximum torque of 11 mnm, while the 100SP-O is oil lubricated, delivering a maximum torque of 110 mnm. The 100SP-O control electronics are heavily based upon the 10SP-M integral design. Fifty-four 10SP microwheels have been flown to date, accumulating 248 years of in-orbit operation; a further seventy-three 10SP microwheels and twenty-one 100SP microwheels are waiting launch delivery either on SSTL or third party missions. SSTL has flight-proven the 10SP-M for use on high resolution imaging spacecraft, but can provide microvibration isolation system mounts as an option. Benefits Flight proven Low cost 12 months typical delivery 7+ years design life Small and lightweight High momentum to mass ratio Fly the subsystems we fly! Features Dry lubrication technology (10SP-M) or oil lubrication (100SP-O), with hermetically sealed motor unit Integrated electronics controller Operates in torque or speed control mode v005 April 2013

6 SSTL Microwheels Performance Design life Angular momentum Max speed (+/-) Speed accuracy Max torque (peak) Environmental Conditions Operating temperature Survival temperature Radiation Random vibration (qualification) First mode Mechanical Mass Volume Moment of inertia (wheel) Static unbalance Dynamic unbalance Lubrication Electrical & Control Integrated electronics Control mode Power (standby) : 20 C Power (5000rpm) : 20 C Power (maximum torque) : 20 C Supply voltage(s) Data interface Telemetry data examples 10SP-M 7.5 years 0.42 Nms 5000 rpm <0.1 rpm rms N.m -20 to +50 C -30 to +60 C 5 krad 18 grms (all axes) >400 Hz 0.96 kg Ø109x101 mm kg.m² <0.1 gcm <0.2 gcm² Dry Yes Output Speed up to 5Hz ~1.5 W ~ 2.8 W ~ 13 W 5V / 22-34V DC (single supply also available) CAN bus or RS422 Speed, Motor current Electronics Temperature 100SP-O 7.5 years 1.5 Nms 5000 rpm <0.055 rpm rms 0.11 N.m -20 to +50 C -30 to +60 C 5 krad 15 grms (all axes) * >300 Hz 2.6 kg Ø120x120 mm kg.m² <0.2 gcm <0.3 gcm² Oil Yes Output Speed or Torque up to 5Hz ~ 1.2 W ~ 10 W ~ 113 W 17-35V DC CAN bus or RS422 Speed, Motor current Electronics & Motor Temperature * Mechanism levels tested. Life & electronics qualifications tested at lower values. Electronics can accept 10SP-M levels based on heritage design. SSTL is ISO9001:2008 certified 10SP-M Heritage Manufacture to: UK-DMC-2 (2009) ECSS Q-ST-70-08C Deimos-1 (2009) ECSS Q-ST-70-38C NigeriaSat-2 (2011) All work overseen by ESA trained assembly ExactView-1 (2012) staff Third party missions Available as part of SSTL s AOCS suite 100SP-O Heritage TechDemoSat-1 (launching 2013) Kazakhstan (launching 2014) DMC3 Constellation (launching 2014) Product specification may be subject to change without notification Surrey Satellite Technology Ltd. Magnetorquers Magnetometers Sun Sensor Inertial Sensors Star Trackers Reaction Wheels GPS Receivers Tycho House, 20 Stephenson Road, Surrey Research Park, Guildford, Surrey, GU27YE, United Kingdom Tel: +44(0) Fax:+44(0) subsystems@sstl.co.uk Web:

7 STD 15 EARTH SENSOR The STD 15 is a dual conical scanning Earth Sensor able to meet the more stringent requirements and environmental constraints of GEO missions. Scanning Infrared Horizon Sensor for GEO Orbits Since 1991, more than 100 units have been delivered in the world for the STD 15/16 product line. Most do them have been launched and operated on board telecommunication satellites, such as: TC2-A, TC2-B, TC2-C, TC2-D, HISPASAT 1A, HISPASAT 1B, HOT BIRD 2, HOT BIRD 3, HOT BIRD 4, HOT BIRD 5, HOT BIRD 7, WORLDSTAR 1, WORLDSTAR 2, SINGASAT 1, NILESAT 1, NILESAT 2, RESSAT, SESAT, ASTRA 2B, HELASAT, EXPRESS-AM, W3A.

8 STD 15: PROVEN TECHNOLOGIES FOR MEASURING PITCH AND ROLL ON BOARD GEO SATELLITES: An optronic sensor with a rotating mirror and fixed mirrors ϕ 4 Trace 2 ϕ 3 Earth disk Roll axis An infrared bolometer to detect Earth to Space and Space to Earth transition A dual track scanning pattern to increase accuracy ϕ 1 Pitch axis Trace 1 ϕ 2 Electronic functions for driving the scanning mechanism as well as operating the bolometer and data processing Scanning Format PERFORMANCES Altitude range: km Operating depointing range: - Nominal: Pitch range: ± 12 deg (Roll = 0) - Roll range : ± 2.9 deg (Pitch = 0) - Extended: Pitch range: ± 15.6 deg (Roll = 0) - Roll range : ± 14.5 deg (Pitch = 0) Output data rate: 1.25 Hz Accuracy budget: 3 σ - bias: deg - typical noise: deg. ENVIRONMENTAL CHARACTERISTICS Operating temperature: -25 C, +55 C Storage temperature: -40 C, +60 C Vibration: Hz : - Z axis: 16.9 g.rms - X, Y axis: 13.2 g.rms MECHANICAL INTERFACES Operating temperature: -25 C, +55 C Height: 168 mm - width: 206 mm - length: 206 mm Mass: 3.4 kg ELECTRICAL INTERFACES Typical consumption: 6.5 W Power supply: 20 to 55 Volts Output data: 1553 protocole RELIABILITY < Fits LIFE-SPAN 15 years in GEO orbit. 20, avenue Descartes Because of constant improvement to our product, LIMEIL-BREVANNES CEDEX FRANCE specifications are subject to change without notice. Tél.33 (0) Fax : 33 (0) Printed in France - AGENAE 33 (0) ISO 9001 C