Control Engineering II

Control Engineering II (223 - 14032)
Bachelor in Industrial Electronics and Automation
Semester 2/Spring Semester
2nd Year/Lower Division

STUDENTS ARE EXPECTED TO HAVE COMPLETED:

Control Engineering I

Competences and Skills that will be Acquired and Learning Results:

The main objective of this course is that the students learn the basics concepts to perform computer control of discrete-time systems by two different methods: classic control, and state space. To achieve these objectives, the student must acquire a range of skills and abilities.

At the end of the course, the student will be able to:
1. Obtain the z transform for a given discrete-time sequence and the time sequence corresponding to a function in the z domain. Solve the difference equation of an invariant linear system, obtaining its transfer function in z and the time response.
2. 2. Choose a suitable sampling period. Obtain the transfer function of a continuous system with a zero-order hold and a sampler. Obtain the transfer function of a closed loop digital control system. Determining the output error for different inputs.
3. Determine the stability of an open loop discrete-time system with unitary feedback. Get the location of the roots of a discrete system, and study the system response by the analysis of the root locus.
4. Discretize a continuous controller. Design an adequate controller (P, PD,PI, PID) using the root locus method. Design a discrete regulator by direct synthesis.
5. Get the state space model for a system defined by differential equations. Obtain the transfer function of a discrete-time system from the state space representation. Get a linearized model of a nonlinear system.
6. Get the solution of the state equation for a continuous linear model. Get the discrete-time model from the model solution of the continuous-time representation (transition matrix). Get the solution of the state equation for a discrete-time system. Obtain different representations of a system in the state space using transformation matrices.
7. Determine the controllability (state and output) and the observability of a system.
8. Design control systems in the state space using the pole positioning method (state feedback matrix).
9. Design a full-order observer for a state space system and study its effects. Study the dynamics of the combined system with a full-order observer and a state feedback matrix. Design a minimum-order observer.

In terms of general skills, we will work in different aspects:

a. General overview of the control problem for lineal systems.
b. Ability to design controllers for linear dynamic systems, as well as to analyse the results. In particular, the lab sessions and the seminars will be helpful in this aspect.
c. Ability to work cooperatively in teams, being critical and respectful with the other members of the group.
d. Recognition of the need for continuous learning. Ability to obtain and apply the information required by accessing to the related technical literature of the area in both Spanish and English.
e. Ability to communicate effectively both orally, written, or graphic in both Spanish and English (exercises, debates, labs, etc.).

Description of Contents/Course Description:

The programme is composed of the following parts:
First Part:
1. Z Transform.
1.1 Modelling of a discrete-time system.
1.2 Differences equations.
1.3 Z Transform, inverse and properties.
1.4 Differences equation solution.

2. Obtaining the Transfer Function.
2.1 Hold and Sampler.
2.2 Obtaining the transfer function in the z domain.
2.3 Sampling theorem.

3. Stability analysis.
3.1 Stability analysis in the z plane.
3.2 Jury stability test.
3.3 Root locus in the z plane.
3.4 Analysis of the system response.

4. Discretization of continuous systems.
4.1 Discretization of a continuous system.
4.2 Equivalent discrete transfer function.
4.3 Sampling a transfer function.
4.4 Discretization of an analogic controller.

5. Design of PID Controllers.
5.1 PID controllers in discrete time.
5.2 Discretization of an analogic PID controller.
5.3 Obtaining the sampling time.
5.4 Design of PID controllers by the root locus method

6. Design of controllers by direct synthesis.
6.1 Design of controllers by direct synthesis.
6.2 Restrictions: physically possible and stability.
6.3 Simplicity.

Second Part:
7. Modelling and analysis of systems in the state space.
7.1 Introduction to the state space.
7.2 Linearization.
7.3 Representations in the state space.
7.4 Equivalences between systems.
7.5 Obtaining the state space model.
7.6 Transformations between representation.
7.7 Obtaining the transfer function from the state space model.

8. Solution of the state space equation.
8.1 Transition matrix. Properties.
8.2 Solution of the state space equation in continuous time.
8.3 Discretization.
8.4 Solution of the state space equation in discrete time.

9. State Feedback Control.
9.1 Controllability and observability.
9.2 State feedback control: positioning poles.
9.3 Gain adjustment.
9.4 Modification of the type of a system.

10. Design of Observers.
10.1 Full-order state observer.
10.2 Dynamics of the combined system with a full-order observer and a state feedback matrix.
10.3 Minimum-order observer.

Learning Activities and Methodology:

This course is composed of different activities:

Lectures. Main concepts (explanation and discussion). Different units in slides with the theoretical concepts.
Seminars. Various problems will be proposed for each unit. The solutions will be given after the seminars.
Lab sessions. Different practical cases will be proposed in each lab session. Before the lab session, a problem will be given to be solved before the lab session. A report about the work in the lab must be prepared after the session.

Assessment System:

The score will be formed by a theoretical and a practical part. The grade of the theoretical part is obtained from two partial exams:
* If the student fails one of the partial exams, the corresponding part will be repeated in a recovery exam. The average between the recovery exam (pass or failed) and the passed partial exam is computed. If the score is 5 or greater, the theoretical part is passed.
* If the student fails both partial exams, the whole parts will be repeated in the recovery exam. The theoretical mark will be the score of the recovery exam.
* If the student passes both exams, it is not necessary to do the recovery exam. If the student still wants to do to the recovery exam to improve his/her score, the previous mark will be erased (only the recovery exam counts).

Regarding the practical part, it is also necessary to pass it (5 or greater).

The final score is computed from the theoretical part (80% of the final score) and the practical part (20% of the final score). But it is important to remark that this subject will be passed only if both parts are passed separately.

Basic Bibliography:

Martín, F.. Problemas de Ingeniería de Control para Sistemas Discretos. CopyRed.
Moreno, L.; Garrido, S. y Balaguer, C.. Ingeniería de Control. Ariel.
Ogata, K.. Discrete-Time Control Systems. Prentice Hall.