Multivariable control
Summary
This course covers methods for the analysis and control of systems with multiple inputs and outputs, which are ubiquitous in modern technology and industry. Special emphasis will be placed on discrete-time systems due to their relevance to digital and embedded control architectures.
Content
Several industries across engineering (e.g. manufacturing, energy, chemical, and transportation) rely on the simultaneous utilization of multiple sensing and actuation channels. Multivariable systems are also relevant for emerging technologies, such as the internet of things, and for fields beyond engineering, such as biology or finance. The first part of this course will provide methods for analyzing multi-input multi-output dynamical systems in the state-space form. The focus will be on linear discrete-time models which offer a reference framework for digital control architectures. To this purpose, several concept of basic system theory will be recalled and developed in detail. The second part will cover popular methods for designing multivariable controllers and illustrate their application to various classes of systems.
Keywords
Multivariable systems, feedback control, state-space models, optimal control, LQR, Kalman filtering, LQG
Learning Prerequisites
Required courses
Linear algebra, Control systems
Important concepts to start the course
- State-space models
- Linear systems in continuous and discrete time
- Basic concepts of stability
- Feedback control
Learning Outcomes
By the end of the course, the student must be able to:
- Construct and analyse a discrete-time model for a dynamic system, A5
- Analyze a multivariable dynamic system and design an appropriate controller for the system, A10
- Assess / Evaluate the stability, performance and robustness of a closed-loop system, A12
- Propose several control solutions, formulate the trade-offs, choose the options, A14
Transversal skills
- Demonstrate the capacity for critical thinking
- Use a work methodology appropriate to the task.
Teaching methods
Ex-cathedra, exercises
Assessment methods
Written final exam.
In addition to the exam: graded group assignments on paper and computer during the semester.
Supervision
| Office hours | No |
| Assistants | Yes |
| Forum | No |
Resources
Virtual desktop infrastructure (VDI)
No
Bibliography
- Course slides on Moodle
Moodle Link
In the programs
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Multivariable control
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Multivariable control
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Multivariable control
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Multivariable control
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Multivariable control
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Multivariable control
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional
- Semester: Fall
- Exam form: Written (winter session)
- Subject examined: Multivariable control
- Lecture: 2 Hour(s) per week x 14 weeks
- Exercises: 2 Hour(s) per week x 14 weeks
- Type: optional