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Control Theory
- Course name: Control Theory
- Code discipline:
- Subject area: ['Introduction to Linear Control, Stability of linear dynamical systems', 'Controller design', 'Sensing, observers, Adaptive control']
Short Description
Prerequisites
Prerequisite subjects
Prerequisite topics
Course Topics
| Section | Topics within the section |
|---|---|
| Introduction to Linear Control, Stability of linear dynamical systems |
|
| Controller design. |
|
| Sensing, observers, Adaptive control |
|
Intended Learning Outcomes (ILOs)
What is the main purpose of this course?
Linear Control Theory is both an active tool for modern industrial engineering and a prerequisite for most of the state-of-the-art level control techniques and the corresponding courses. With this in mind, the Linear Control course is both building a foundation for the following development of the student as a learner in the fields of Robotics, Control, Nonlinear Dynamics and others, as well as it is one of the essential practical courses in the engineering curricula.
ILOs defined at three levels
Level 1: What concepts should a student know/remember/explain?
By the end of the course, the students should be able to ...
- methods for control synthesis (linear controller gain tuning)
- methods for controller analysis
- methods for sensory data processing for linear systems
Level 2: What basic practical skills should a student be able to perform?
By the end of the course, the students should be able to ...
- State-space models
- Eigenvalue analysis for linear systems
- Proportional and PD controllers
- How to stabilize a linear system
- Lyapunov Stability
- How to check if the system is controllable
- Observer design
- Sources of sensor noise
- Filters
- Adaptive Control
- Optimal Control
- Linear Quadratic Regulator
Level 3: What complex comprehensive skills should a student be able to apply in real-life scenarios?
By the end of the course, the students should be able to ...
- Turn a system of linear differential equations into a state-space model.
- Design a controller by solving Algebraic Riccati eq.
- Find if a system is stable or not, using eigenvalue analysis.
Grading
Course grading range
| Grade | Range | Description of performance |
|---|---|---|
| A. Excellent | 85-100 | - |
| B. Good | 70-84 | - |
| C. Satisfactory | 50-69 | - |
| D. Poor | 0-49 | - |
Course activities and grading breakdown
| Activity Type | Percentage of the overall course grade |
|---|---|
| Labs/seminar classes | 30 |
| Interim performance assessment | 20 |
| Exams | 50 |
Recommendations for students on how to succeed in the course
Resources, literature and reference materials
Open access resources
- Williams, R.L. and Lawrence, D.A., 2007. Linear state-space control systems. John Wiley & Sons.
- Ogata, K., 1995. Discrete-time control systems (Vol. 2, pp. 446-480). Englewood Cliffs, NJ: Prentice Hall.
Closed access resources
Software and tools used within the course
Teaching Methodology: Methods, techniques, & activities
Activities and Teaching Methods
| Learning Activities | Section 1 | Section 2 | Section 3 |
|---|---|---|---|
| Homework and group projects | 1 | 1 | 1 |
| Testing (written or computer based) | 1 | 0 | 0 |
| Reports | 1 | 1 | 1 |
| Midterm evaluation | 0 | 1 | 0 |
| Discussions | 0 | 1 | 0 |
Formative Assessment and Course Activities
Ongoing performance assessment
Section 1
| Activity Type | Content | Is Graded? |
|---|---|---|
| Question | What is a linear dynamical system? | 1 |
| Question | What is an LTI system? | 1 |
| Question | What is an LTV system? | 1 |
| Question | Provide examples of LTI systems | 1 |
| Question | What is a MIMO system? | 1 |
| Question | Simulate a linear dynamic system as a higher order differential equation or in state-space form (Language is a free choice, Python and Google Colab are recommended Use built-in solvers or implement Runge-Kutta or Euler method | 0 |
Section 2
| Activity Type | Content | Is Graded? |
|---|---|---|
| Question | What is stability in the sense of Lyapunov? | 1 |
| Question | What is stabilizing control? | 1 |
| Question | What is trajectory tracking? | 1 |
| Question | Why the control for a state-space system does not include the derivative of the state variable in the feedback law? | 1 |
| Question | How can a PD controller for a second-order linear mechanical system can be re-written in the state-space form? | 1 |
| Question | Write a closed-loop dynamics for an LTI system with a proportional controller | 1 |
| Question | Give stability conditions for an LTI system with a proportional controller | 1 |
| Question | Provide an example of a LTV system with negative eigenvalues that is not stable | 1 |
| Question | Write algebraic Riccati equation for a standard additive quadratic cost | 1 |
| Question | Derive algebraic Riccati equation for a given additive quadratic cost | 1 |
| Question | Derive differential Riccati equation for a standard additive quadratic cost | 1 |
| Question | What is the meaning of the unknown variable in the Riccati equation? What are its property in case of LTI dynamics | 1 |
| Question | What is a frequency response? | 1 |
| Question | What is a phase response? | 1 |
| Question | Design control for an LTI system using pole placement | 0 |
| Question | Design control for an LTI system using Riccati (LQR) | 0 |
| Question | Simulate an LTI system with LQR controller | 0 |
Section 3
| Activity Type | Content | Is Graded? |
|---|---|---|
| Question | What are the sources of sensor noise? | 1 |
| Question | How can we combat the lack of sensory information? | 1 |
| Question | When it is possible to combat the lack of sensory information? | 1 |
| Question | How can we combat the sensory noise? | 1 |
| Question | What is an Observer? | 1 |
| Question | What is a filter? | 1 |
| Question | How is additive noise different from multiplicative noise? | 1 |
| Question | Simulate an LTI system with proportional control and sensor noise | 0 |
| Question | Design an observer for an LTI system with proportional control and lack of sensory information | 0 |
Final assessment
Section 1
- Convert a linear differential equation into a state space form
- Convert a transfer function into a state space form
- Convert a linear differential equation into a transfer function
- What does it mean for a linear differential equation to be stable?
Section 2
Section 3
- Write a model of a linear system with additive Gaussian noise
- Derive and implement an observer
- Derive and implement a filter
The retake exam
Section 1
Section 2
Section 3