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# FRTN55 - Automatic Control, Advanced Course

## Official Course syllabus

### General Information

Elective for: B5, C4, D4-ssr, E4-ra, F4, F4-r, I4, I4-pvs, K5, M4, N4, Pi4-ssr
Language of instruction: The course will be given in English

### Aim

The course gives an in-depth treatment of design of linear control systems with limitations. Special attention is given to design trade-offs and fundamental limitations, and how mathematical optimziation can be used as a design tool, both offline and online. The course covers both continuous-time and discrete-time control systems.

### Learning outcomes

Knowledge and understanding
For a passing grade the student must

• be able to translate between, and intelligently select among, different representations for continuous-time and discrete-time systems, in particular transient responses, transfer functions, and state-space descriptions.
• be able to derive properties of interconnected systems from the properties of their subsystems, and to characterize and quantify the role of the different subsystems.
• be able to formulate constraints on input signals and output signals of a control system and to relate these to conditions on the matrices that describe the system.
• be able to analyse how process characteristics put limitations on the control performance that can be achieved.

Competences and skills
For a passing grade the student must

• be able to independently formulate technical specifications based on understanding of the control system should be used and interact with the external environment.
• be able to select control design methods and model structures, and translate specifications into mathematical optimization problems to be solved online or offline.
• draw conclusions from numerical calculations about the correctness of models and specifications, and about the consequences for the interaction between the system and the environment.

Judgement and approach
For a passing grade the student must

• understand relationships and limitations when simplified models are used to describe a complex and dynamic reality
• show ability to teamwork and group collaboration at laboratories.

### Contents

The control design process, stability, sensitivity, robustness, the small-gain theorem, transfer function matrices, non-minimum-phase systems, disturbance models in the time domain and frequency domain, frequency-domain specifications, fundamental limitations and trade-offs, controller structures, the Youla parameterization and internal model control, sampled-data control, linear-quadratic optimization of state feedback and Kalman filter, model-predictive control, controller synthesis using convex optimization.

### Examination details

Assessment: Written exam (5 hours), three laboratory exercises, one hand-in assignment. In case of less than 5 registered students the retake exams may be given in oral form.

Required prior knowledge: FRTF05 Automatic Control, Basic Course, or FRTN25 Automatic Process Control.