Course: 2019/2020

Control Engineering II

(14032)

Students are expected to have completed

Control Engineering I

Competences and skills that will be acquired and learning results. Further information on this link

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: programme

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 s and z planes
3.3 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.
5.5 Structure of a real discrete PID.
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 Dinamic systems.
7.3 Linearization and invariance.
7.4 Linearization process.
7.5 Representations in the state space.
7.6 Equivalences between systems.
7.7 Obtaining the state space model.
7.8 Transformations between representation.
7.9 Obtaining the transfer function from the state space model.
8. Solution of the state space equation.
8.1 Transition matrix.
8.2 Calculation of the transition matrix. Properties.
8.3 Solution of the state space equation in discrete time.
9. State Feedback Control.
9.1 Controllability and observability.
9.2 Complete controlability of the states.
9.3 Complete controlability of the output.
9.4 Complete observability of the states.
9.5 Invariance of the controlability and observability through transformations.
9.6 State feedback control: positioning poles.
9.7 Pole position adjustment in closed loop.
9.8 Gain adjustment.
9.9 Modification of the type of a system.
10. Design of states observers.
10.1 Concept of state observer.
10.2 Conditions for the state observation.
10.3 Full-order state observer.
10.4 Error dynamics in the full-order state observer.
10.5 Design of the feedback gains matrix of the observer.
10.6 Dynamics of the combined system with a full-order observer and a state feedback matrix.
10.7 Minimum-order observer.

Learning activities and methodology

This course is composed of different activities:
1. Lectures. Main concepts (explanation and discussion). Different units in slides with the theoretical concepts.
2. Seminars. Various problems will be proposed for each unit. The solutions will be given after the seminars.
3. Lab sessions. Three 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

- % end-of-term-examination 0
- % of continuous assessment (assigments, laboratory, practicals...) 100

Basic Bibliography

- DeRusso, P.M.; Roy, R.J. and Close, C.M.. State Variables for Engineers. Wiley. 1965
- 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.

Additional Bibliography

- Franklin, G.F; Powell, J.D. y Workman, M.. Digital control of dynamic systems. Addison Wesley. 1998

**More information: **http://roboticslab.uc3m.es/roboticslab/people/ca-monje