Automatic control systems play an increasingly important role in aerospace engineering, both in view of the higher level of automation expected from flight vehicles and of the recent emergence of unmanned vehicles.

Control systems design problems in aerospace pose significant challenges because of their intrinsically multivariable, nonlinear nature, often associated with large model uncertainty and unstable dynamics. These are the main reasons why advanced methods for analysis and synthesis are frequently adopted in aerospace applications.

In view of the above, the course aims at the following goals: to provide a sound background on modern methods and tools for the stability and performance analysis of linear and nonlinear systems; to cover robust analysis and design of SISO and MIMO linear time-invariant (LTI) feedback control systems; to discuss basic ideas on the linear parameter-varying (LPV) framework for gain-scheduled control systems design; to present classical results on nonlinear analysis; to illustrate the above methods using detailed case studies.

Lectures and exercise sessions will allow students to:

• Master fundamental theoretical results for linear and nonlinear feedback control systems
• Understand modern methods and tools for linear control systems analysis and design
• Formulate and solve advanced control systems design problems

Introduction: Motivation for advanced analysis and design methods; Introductory examples.

Systems theory - stability: Equilibria of nonlinear systems; Lyapunov stability for equilibria of nonlinear systems: definition and examples; Stability for LTI systems: Lyapunov inequalities and equations.

Systems theory - performance: H₂ performance for linear systems; Small gain and passivity theory; H_∞ performance for linear systems. 

Linear SISO feedback systems - robust analysis and design: Uncertainty modelling in SISO systems; Robust stability analysis of SISO feedback systems; Nominal and robust performance analysis; Requirement specification; Robust design: unstructured and structured mixed sensitivity synthesis.

Linear MIMO robust analysis and design: Introduction to MIMO linear systems; Nominal stability and performance in the MIMO case; Robust stability and performance in the MIMO case; MIMO robust design.

Nonlinear analysis methods: Static nonlinearities: circle and Popov criteria; Limit cycles and oscillations: the describing function method; Introduction to nonlinear design: feedback linearisation, backstepping, adaptive control.

Case studies: Attitude control for a small-scale UAV; Attitude control for a full-scale helicopter.

Students are required to know the principles and methods of linear systems theory and SISO linear control systems stability and performance analysis.

The students will be able to choose between an oral exam and a design project which will be presented during the course.

In both cases the evaluation will be also based on the clarity of the presentation.

During the exam the students shall demonstrate that:

• they understand the theoretical fundamentals on linear and nonlinear feedback control systems
• they have acquired modern methods and tools for linear control systems analysis and design
• they have learned how to formulate and solve advanced control systems design problems.