0/0/0/2 + 7 E-lectures

This course teaches the elements of handling dynamics in systems encountered in Aerospace Engineering. The student is introduced to the concepts of dynamical systems; inputs, outputs and system boundary and environment. Students learn to connect different system descriptions; state-space models, transfer functions, differential equations and frequency response discriptions. Students learn block diagram descriptions and how to manipulate these. Desirable and undesirable properties of control systems are distinguished, the choice between elementary controller types to match a specific controlled system is discussed. Tuning methods for the controller parameters include the root-locus method, and frequency design methods (Bode and Nyquist). The Nyquist stability criterion is introduced and used to determine closed-loop stability.
The course uses examples commonly found in aerospace engineering, both dynamic models for whole systems (aircraft or satellites) and models for components, such as a landing gear or control surface with a hydraullic servo.

At the end of this course, the student will be able to…

1. Given a schematic of a physical system and desired behavior, design a simple (single-loop) controller.
2. Formulate linear dynamical system models from block diagrams or schematic mechanical system descriptions.
3. Identify dynamical properties across domains time, frequency, transfer function, A-matrix eigenvalues.
4. Evaluate stability of open and closed loop systems (in different domains: time, frequency, poles)
5. Calculate and judge responses to input signals in time and frequency domain.
6. Select appropriate controller from basic types (P, PI, PD, PID, lag-lead, lead-lag) depending on system properties and requirements.
7. Tune controllers with Bode, Nyquist and Root-locus methods (Evans’) with a computer.

All the above tasks will be done using a Computer Aided Control System Design (CACSD) tool, in this case Matlab

Lecturing, complemented by on-line E-learning lectures.

The book to be used in the course is not yet determined. A definitive choice will be announced in July 2010
Reader or additional material on BlackBoard -- to be determined

Computer exam

The course is given as a combination of lectures and on-line exercises (e-learning). In the lectures, new topics are presented. In the e-learning exercises, the students work with a CACSD tool (Matlab), to get hands-on experience with the material presented in the lectures. Be aware that this is not the same as an exercise accompanying a lecture series; there is significantly more interaction. An e-learning lecture can also include calculations whose results are explained and used in the following lecture.

Week arrangement (e-lectures indicated with <e>):

1 - Introduction, open and closed-loop control, input, output, system concepts, control error
2<e> - Matlab skills for control theory, experimenting with a simple control system

3 - Transfer fucntions, mechanical systems
4<e> - Transfer functions in Matlab, combining transfer functions, response calculations, control systems requirements

5 - State-space systems, aircraft equations of motion as state-space
6<e> - State-space in matlab, response calculation with state-space

7 - Transient and steady-state responses, system type, position, velocity, acceleration error, basic controller types
8<e> - Entering more complex models in Matlab. Combining transfer functions, state-space systems and block diagrams.

9 - Root-locus tuning
10<e> - Root-locus tuning in Matlab, using aircraft autopilot modes.

11 - Frequency response, Bode diagram, non-minimum phase systems
12<e> - Exercise in frequency response, using a flexible satellite. Notch filters.

13 - Stability in the frequency domain. Polar plot, Nyquist contour, Nyquist diagram.
14<e> - Combination of root-locus and frequency domain techniques, applied to a model of an unstable rocket.