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CourseAerospace, UAM, Drones & Space Applications open

LQR course in orbital control

Online course of 300 hours in LQR for orbital control: 6 modules covering linear optimal control, linearised relative orbital dynamics, LQR for station-keeping, formations and rendezvous, and estimation and LQG, with an assigned technical tutor.

Duration3 months
ModeOnline
LanguageEnglish
Start datesSet by the faculty
AwardSEIUM Institute certificate
Enrol now View syllabus Ask an advisor
Virtual lab · try it before you enrol

Take the controls.

Run a real engineering trade-off from this field. Move the sliders, watch the model react in real time and beat the challenge.

SIM · LIVE ●
Learning outcomes

What you will be able to do

01

Formulate linear quadratic optimal control problems.

02

Model linearised relative orbital dynamics.

03

Design LQR controllers for station-keeping.

04

Apply LQR to formation flying and rendezvous.

05

Integrate state estimators into LQG schemes.

06

Assess the trade-off between fuel consumption and accuracy.

07

Develop a complete LQR controller for an orbital scenario.

Profile

Who it's for

  • Control engineers applying optimal control to space systems.
  • GNC engineers.
  • Orbital dynamics engineers.
  • Formation flying engineers.
  • Control software engineers.
  • Optimal control researchers.
  • Engineering or science graduates aiming to enter the space industry.
Standards & tools

What you'll work with

  • ECSS-E-ST-60-10C (control performance)
  • ECSS-E-ST-60-30C (satellite attitude and orbit control system requirements)
  • ECSS-E-ST-60C (control engineering)
  • ECSS-E-HB-60A (control engineering handbook)
  • ECSS-E-ST-40C (space software engineering)
  • ECSS-E-ST-10-09C (reference coordinate systems)
  • MATLAB Control System Toolbox
  • Simulink
  • Python with python-control
  • Basilisk
  • GMAT
Syllabus

6 modules

  1. 1.1State-space representation
  2. 1.2Controllability and observability
  3. 1.3Quadratic cost function
  4. 1.4Algebraic Riccati equation
  5. 1.5Optimal feedback gain
  6. 1.6Robustness properties of LQR
  7. 1.7Choice of Q and R matrices
  8. 1.8Discrete-time LQR
  9. 1.9LQR with input constraints
  10. 1.10Workshop: LQR gain calculation for a double integrator
  1. 2.1Clohessy-Wiltshire equations
  2. 2.2Tschauner-Hempel equations
  3. 2.3Effect of J2 on relative motion
  4. 2.4LVLH and Hill frames
  5. 2.5Natural relative motion and closed orbits
  6. 2.6Model discretisation
  7. 2.7Validity of the linearisation
  8. 2.8Relative orbital elements
  9. 2.9Models with differential drag
  10. 2.10Practical exercise: relative motion simulation with Clohessy-Wiltshire
  1. 3.1Error model with respect to a reference orbit
  2. 3.2Station-keeping control in LEO
  3. 3.3Drift control in GEO
  4. 3.4Trajectory tracking with LQR
  5. 3.5Integral action and LQI
  6. 3.6Saturation and discrete thrust
  7. 3.7Comparison with impulsive control
  8. 3.8Propellant budget
  9. 3.9Selection of the control period
  10. 3.10Lab: LQR station-keeping control
  1. 4.1Formation flying with LQR
  2. 4.2Formation reconfiguration
  3. 4.3Final rendezvous approach
  4. 4.4Passive safety constraints
  5. 4.5Time-varying LQR
  6. 4.6Finite horizon and differential Riccati equation
  7. 4.7Decentralised control
  8. 4.8Fuel consumption versus accuracy
  9. 4.9Multi-satellite formations
  10. 4.10Case study: rendezvous with LQR in the Hill frame
  1. 5.1Kalman filter in relative navigation
  2. 5.2Separation principle
  3. 5.3LQG controller
  4. 5.4Loss of robustness in LQG
  5. 5.5Loop transfer recovery (LTR)
  6. 5.6Process and measurement noise
  7. 5.7On-board implementation
  8. 5.8Monte Carlo validation
  9. 5.9Tuning of filter covariances
  10. 5.10Case study: LQG design with differential GNSS navigation
  1. 6.1Scenario definition
  2. 6.2Linearised model
  3. 6.3Weight selection
  4. 6.4Controller design
  5. 6.5State estimator
  6. 6.6Non-linear simulation
  7. 6.7Consumption analysis
  8. 6.8Comparison of alternatives
  9. 6.9Report and presentation
  10. 6.10Final project: final review with the tutor
Methodology, software & labs

How you'll learn

100% online training on the SEIUM campus, with downloadable material, recorded classes and an assigned technical tutor. No fixed timetables: you progress at your own pace within each intake, making it compatible with work.

Each module combines theory, guided reading of the original standard and applied exercises. The working software is MATLAB Control System Toolbox, Simulink, Python with python-control, Basilisk and GMAT, in free, academic or evaluation versions. Practical work is based on real procedures: LQR station-keeping control with discrete propulsion, rendezvous in the Hill frame with time-varying LQR and LQG design with relative navigation. Assessment is continuous per module plus the final project.

Standards covered: ECSS-E-ST-60-10C, ECSS-E-ST-60-30C, ECSS-E-ST-60C, ECSS-E-HB-60A, ECSS-E-ST-40C, ECSS-E-ST-10-09C.

Assigned technical tutor:every module ends with a deliverable that your tutor marks individually.
Standards-based learning:guided reading of ECSS-E-ST-60-10C, ECSS-E-ST-60-30C and ECSS-E-ST-60C applied to real cases, not as a theoretical annex.
Industry software:MATLAB Control System Toolbox, Simulink, Python with python-control, Basilisk and GMAT, in free, academic or evaluation versions.
Final project:a complete LQR controller for an orbital scenario, from the linearised model to non-linear validation, reviewed by your tutor.
Flexible format:100% online, no fixed timetables, compatible with full-time work.
Capstone project

Build it end to end

Your final project follows the real engineering workflow, step by step, reviewed by your tutor.

LQR gain design
Compute and tune LQR gains on a reference model.
Relative motion model
Simulate relative motion with the Clohessy-Wiltshire equations.
Station-keeping controller
Design an LQR station-keeping controller with discrete thrust.
Rendezvous and LQG
Close the loop with an estimator for a rendezvous in the Hill frame.
Final project
Deliver a complete LQR orbital controller with consumption analysis, reviewed by your tutor.
Career opportunities

Where this takes you

Control engineerGNC engineerOrbital dynamics engineerFormation flying engineerControl software engineerOptimal control researcher
Admissions & scholarships

Requirements

  • No prior qualification is required.
  • Internet connection and a computer able to run the programme software.
  • English sufficient to read technical standards.

Ready to start?

Send your application today. Our admissions team replies within 72 hours with your study plan and funding options.

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FAQ

Frequently asked questions

The programme totals 300 hours over 3 months. You set your own pace within each intake, and your tutor helps you plan the workload around your job.

You work with MATLAB Control System Toolbox, Simulink, Python with python-control, Basilisk and GMAT, using free, academic or evaluation versions. Your tutor indicates the free alternative wherever one exists.

A SEIUM Institute certificate, awarded on passing the continuous assessment and the final project. It is SEIUM's own qualification, not an official state degree; its recognition depends on the programme completed and the regulations of each country.

Yes. Modules passed are recognised in a higher programme in the same area (postgraduate diploma or master's). Ask about the recognition policy when you enrol.

No prior qualification is required; you need an internet connection, a computer able to run the programme software and English sufficient to read technical standards.

Start dates are set by SEIUM's faculty for each intake. Our admissions team will confirm the next available date when you apply.

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