## Journal of lectures

**Lecture 1: 12th February, 2020.
**- Presentation of the subject.

– Lesson 1.1. Sections 1-6

– Lesson 1.1. Examples 1-7 + Last example of slides (magnetic suspension system)

**Lecture 2: 19th February, 2020.
**- Lesson 1.2. Sections 1-4

– Lesson 1.2. Examples 1-6 + one additional example of Jordan diagonalization of a 4-order system with different real poles and a complex conjugate pair.

**Lecture 3: 26th February, 2020.
**- Lesson 1.3. Sections 1-4

– Exercises lesson 1.1: Exercise 1(b), 7(d).

– In the case of block diagrams, we studied which lines and derivatives can be chosen as state variables, in general.

– Exercises lesson 1.2: Exercise 6.

– I propose you to solve the next exercises (lesson 1.2): Exercise 5(a), exercise 8.

**Lecture 4: 4th March, 2020.
**- Exercises lesson 1.2: Exercise 5(a), 8.

–Â We solved an example of lesson 1.3: From the difference equation of a discrete-time system, obtain several state-space representations.

–Â Introduction to the unit 2: Controllability and observability of a dynamic system.

– I propose you to solve the next exercises (lesson 1.3): Exercise 5(c), exercise 6.

**Lecture 5: 11th March, 2020.
**-Â Lesson 2.1. Controllability. We studied the whole lesson.

– I propose you to solve the next exercises (lesson 2.1): Exercise 1, 2 and 3.

**Lecture 6: 18th March, 2020. ONLINE LESSON.
**- Lesson 1.3. Exercise 6.

–Â Lesson 2.1. Exercises 1, 2, 3.

– We have studied these concepts through a videoconference. You can find next the recording of the videoconference and the materials I have generated during it.

- Recording of the videoconference.
- Solution to exercise 6, lesson 1.3.
- Solution to exercise 1, lesson 2.1.
- Solution to exercise 2, lesson 2.1.
- Solution to exercise 3, lesson 2.1.

**Lecture 7: 25th March, 2020. ONLINE LESSON.**

– Lesson 2.2.Â Sections 1, 2, 3.

– We have studied these concepts through a videoconference. You can find next the recording of the videoconference and the materials I have generated during it.

- Recording of the videoconference.
- Lesson 2.2 with annotations.
- Solution toÂ exampleÂ 4, lesson 2.2 (continuation).

**Lecture 8: 1st April, 2020. ONLINE LESSON.**

Part 1:

– Lesson 2.2.Â Section 4 and example 5.

– We have studied these concepts through a videoconference. You can find next the recording of the videoconference and the materials I have generated during it.

- Recording of the videoconference.
- Lesson 2.2 with annotations, part 2.
- Solution toÂ example 5, lesson 2.2.Â Â Part (a)Â Â Â Part (b)

Part 2:

– Exercises UnitÂ 2. Exercise 7.

– Introduction to unit 3

– Lesson 3.1.Â Sections 1, 2 and 3.

– We have studied these concepts through a videoconference. You can find next the recording of the videoconference and the materials I have generated during it.

- Recording of the videoconference.
- Solution toÂ exerciseÂ 7, unit 2.Â Â Wording.Â Â Solution
- Lesson 3.1 with annotations, part 1.

**Lecture 9: 8th April, 2020. ONLINE LESSON.**

Part 1:

–Â Practical session:

- Recording of the videoconference.
- Remind that the deadline of the report of Laboratory 4 is 22nd April.

Part 2:

–Â We finished lesson 3.1. We did examples 1, 2 and we introduced example 3.

– We have studied these concepts through a videoconference. You can find next the recording of the videoconference and the materials generated during it.

- Recording of the videoconference.
- Review lesson 3.1, sections 1, 2.
- Lesson 3.1 with annotations, part 2.Â Â Â Control Steps.
- Lesson 3.1. Section 4: Discrete control placing all poles at z=0.
- Lesson 3.1.Â Example 1 and 2.Â Â Â Wording.Â Â Â Solution
- Lesson 3.1.Â Example 3.Â Â Â Wording.Â Â Â Introduction

I recommend you to finishÂ example 3 (computer control with T=0.1 sec.), following the list of steps (column 2).

Finally, remind that we talked about the dates of the Continuos Evaluation.

**Lecture 10: 22nd April, 2020. ONLINE LESSON.**

Part 1:

–Â Practical session:

Part 2:

–Â WeÂ did the example 3 of lesson 3.1. We studied how to simulate it as similar as possible to the real implementation. We also solved some doubts about midterm exam 1.

– You can find next the recording of the videoconference and the materials generated during it.

- Recording of the videoconference.Â Â Part 1.Â Â Part 2.
- Lesson 3.1.Â Example 3.Â Â Â Wording.Â Â Â Solution

Finally, as I told, you’ll find here an example ofÂ Midterm Exam 1.

**Lecture 11: 29th April, 2020. ONLINE LESSON.**

Part 1:

–Â Practical session:

Part 2:

–Â WeÂ studied lesson 3.2 (design of state observers) and we did a complete example.

– You can find next the recording of the videoconference and the materials generated during it.

- Recording of the videoconference.
- Lesson 3.2 with annotations.
- Lesson 3.2. Complete example (controlling a system through observed state feedback.Â Â Â Wording.Â Â Â Solution

Please remind that you can do the final exercises of the subject (available on the blog), which can add up to 1 additional point to your final mark (continuous evaluation). You can solve these three exercises either individually or in teams up to 3 students. The deadline is June 3.

**Lecture 12: 6th May, 2020. ONLINE LESSON.**

Part 1:

–Â Practical session:

Part 2:

– We completed the final example of lesson 3.2, analyzing the possibility of cancelling zeros that have influence on the dynamic response.

– We did exercise 10 of lesson 3.1. (controlling a system which is not controllable and not observable).

– WeÂ studied lesson 3.3 (design of control systems to track a reference).

You can find next the recording of the videoconference and the materials generated during it.

- Recording of the videoconference.
- Contents of the last sessions.
- Lesson 3.2. Complete example.Â Â Â Wording.Â Â Â SolutionÂ (includes zero cancellation)
- Lesson 3.1, exercise 10.Â Â Wording(a)Â Â Wording(b)Â Â Â Solution.
- Lesson 3.3 with annotations.
- Lesson 3.3. Final example.Â Â Wording.Â We will solve this example next day.

**Lecture 13: 13th May, 2020. ONLINE LESSON.**

Part 1:

– WeÂ did the final example of lesson 3.3,Â (design of an integral controller, state feedback and observer).

– WeÂ introduced the control of MIMO systems.

1. First we studied that there are different possibilities to share the energy of the inputs between the state variables. Each possibility leads to a specific CCF of the original system.

2. We started to solve an example about how to set the dynamics of a MIMO system by using a continuous-time controller (state feedback).

You can find next the recording of the videoconference and the materials generated during it.

- Recording of the videoconference.
- Lesson 3.3. Solution to the final example.
- MIMO Systems.Â Â CCF of the original system.Â Â Example 1.

Part 2:

–Â Practical session:

**Lecture 14: 20th May, 2020. ONLINE LESSON.**

Part 1:

– We continued the study of MIMO systems:

1.Â We finished example 1: Design of the state feedback. In it, we studied that there are different possibilities to build the matrix A of the controlled system in CCF. It is recommendable to develop and check some of them, and retain the solution with the most balanced control inputs.

2. WeÂ did example 2: Design ofÂ a MIMO observer.

3. We did example 3: Simultaneous design of the state feedback and the integral controller in a MIMO system.

You can find next the recording of the videoconference and the materials generated during it.

- Recording of the videoconference.
- MIMO Systems.Â Â Example 1 (complete).Â Â Â Example 2.Â Â Â Example 3.

Finally, as I told, you’ll find here an example ofÂ Midterm Exam 2.

Part 2:

–Â Practical session:

**Â END OF THE CONTENTS OF THE SUBJECTÂ **