The students to join this subject must have passed Control Engineering I.

By the end of this subject, students will be able to have: 1. A systematic understanding of the key aspects and concepts of the design of discrete controllers through their analysis in the time (state space) and frequency (transfer function) domains. 2. Coherent knowledge of their branch of engineering including some at the forefront of the branch in control engineering. 3. The ability to apply their knowledge and understanding of control engineering to identify, formulate and solve engineering problems using established methods for the time and frequency analysis of discrete control systems. 4. The ability to apply their knowledge and understanding to develop and realise designs of discrete controllers to meet defined and specified requirements. 5. An understanding of design methodologies for discrete controllers, and an ability to use them. 6. Workshop and laboratory skills to implement discrete controllers in real platforms. 7. The ability to select and use appropriate equipment, tools and methods for the design and implementation of discrete controllers. 8. The ability to combine theory and practice to solve problems related to the design and implementation of discrete controllers. 9. An understanding of applicable techniques and methods in control engineering, and of their limitations.

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.

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 in total). Three practical cases (groups of 2-3 students) will be proposed in each lab session. Before the lab session, a problem will be given to be solved before that session. A report about the work in the lab must be prepared after the session.