Course Unit Page


This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Decent work and economic growth Industry, innovation and infrastructure Sustainable cities

Academic Year 2021/2022

Learning outcomes

The objective of the course is to provide the students with modern guidance and control techniques which are applicable to all flying vehicles without distinction. The course is intended for students in aerospace engineering oriented to both atmospheric and space flight. The focus is on application of multivariable robust optimal control theory for guidance and control of fixed and rotary wing aircrafts and spacecraft. The project of the autopilots currently implemented in commercial (airliner) and general aviation aircraft is proposed jointly with modern guidance and control systems for satellites, space-stations and microsatellite. An appealing feature of the course is the ready and extensive use of MATLAB®/Simulink® codes in the many solved examples illustrating guidance and control design and analysis. Furthermore, at the end of the course, the operation and programming of commercial autopilots are practically taught by using a certified flight simulator.

Course contents

The course can be divided into two parts:

  1. In the first part multivariable synthesis methods are presented. In particular the optimal control theory both for deterministic and stochastic systems. The case of linear time invariant systems with quadratic cost index (Linear Quadratic and LQ Gaussian case) is treated deeply. It is worth observing that also the basic theory of observers and optimal observers (Kalman Filter) is furnished.
Starting from a review of Dynamic Flight notions the classical autopilot design methods are firstly proposed. Afterwards, the design of Stability Augmentation Systems (SAS), Attitude Control Systems (ACS) and Flight Path Control Systems (FPCS) by means of optimal control methods (LQ and LQG) are proposed. Course contents

Part 1

  1. Optimal Control Law. Optimal Control Problem definition, Hamiltonian function, solution of the LQ optimal control problem; solution of the minimum energy and minimum time optimal control problem; design of the cost parameters; Pontryagin maximum principle.
  2. Feedback Optimal Control. Solution of the optimum control problem: Differential Riccati equation and solution existence and uniqueness conditions, optimal feedback gain. Steady state optimal regulator: algebraic Riccati equation, stability of the steady state regular. Set points different from the origin.
  3. Poles assignments. Coordinate change in input, state and output space. Canonical forms and poles assignment for MIMO systems
  4. State observers and dynamic feedback. Identity observer, sub-optimal control problem by means of dynamic feedback
  5. Notes on probability and stochastic process theory
  6. Stochastic Optimal Observer. Optimal state estimate, Kalman Filter, differential Riccati equation and existence and uniqueness conditions.
  7. Stochastic Optimal Regulator. Cost index, LQG regulator.

Part 2

  1. Flight Dynamics overview. Six degree of freedom rigid body model. Military Flying qualities. Longitudinal and lateral-directional dynamics and model in case of coupled dynamics. Linearized models: longitudinal and lateral-directional modes. Dryden turbulence description and wind gust model.
  2. Classical Autopilots. Stability Augmentation Systems (SAS): pitch rate SAS and other longitudinal dynamic SAS lateral-directional SAS: yaw dumper, roll rate dumper, spiral mode stabilization. Attitude Control Systems (ACS): pitch ACS, roll angle ACS, wing leveler, sideslip suppression ACS, turn coordination ACS. Flight Path Control System (FPCS): altitude hold system, speed control system, direction control system, heading control system, VOR-coupled automatic tracking system, ILS localizer coupled control system, ILS glide-path-coupled control system, automatic landing system
  3. Design of Autopilot by means of Optimal Control LQ and LQG methods. Steady state control: determination of the inputs (command surfaces deflection and throttle) corresponding to a given steady state flight condition; determination of the optimal gain satisfying the flight qualities. Methods to arm and engage autopilots. Vertical mode autopilots (case of airbus 319/320/321) : climb rate and airspeed hold, altitude capture and hold, glide slope capture and hold, flare and touchdown. Lateral mode autopilots (case of airbus 319/320/321) : bank angle and sideforce ACS, heading capture and hold, track capture and hold, localizer capture and hold. Gain scheduling methodology. Notes on guidance methods: navigation mode. Notes on the design of an integrated navigation, guidance and control system. Notes on control of missiles. Notes on model based linear and non linear Fault Detection and Isolation methods.
  4. Optimal Control applied to attitude stabilization and orbital control of satellite
  5. Optimal Control applied to trajectory tracking for missile


Part 1

M. Tibaldi. Progetto di Sistemi di Controllo.Pitagora Editrice. Bologna
B.D.O. Anderson, J.B. Moore. Optimal Control: Linear Quadratic Methods. Prentice Hall Information and System Sciences Series

Part 2

Notes of the teacher (downloadableat AMS Campus)

D. McLean. Automatic Flight Control Systems. Prentice Hall Series in Sytems and Control Engineering
A.E. Bryson, Jr. Control of Spacecraft and Aircraft. Princeton University Press.

Teaching methods

Lessons in classroom plus laboratory autopilot design tested on matlab/simulink flight simulator.

Laboratory for flight controller and avionic devices .

Assessment methods


Optional Project regarding an autopilot design or more generally the design of a Navigation, Guidance and Control System in Matlab/Simulink or UNIX/ROS/GAZEBO

Teaching tools

Lessons in classroom plus laboratory autopilot design tested on matlab/simulink flight simulator.

Hangar laboratory with flight controllers and avionics available.

Office hours

See the website of Paolo Castaldi