Consider performing a
AE 308 : Control Theory
Description:
Dynamics and Controls is one of the four major specializations of Aerospace Engineering (others being Aerodynamics, Structures and Propulsion). This is a branch of science (& mathematics) that deals with the response of a physical system for a given input. The main objective of a control system designer is to design a system that could control this response of the system, usually under given design constraints. This design is usually done in three domains - Laplace Domain, State Space Domain and Digital/discrete domain using the differential equations representing the system behaviour.
In this course, we mainly deal with the Laplace Domain. The course includes modelling of a physical system, i.e., representing the system dynamics in the form of differential equations and representing this system in the form of a transfer function. Later, the basic control system design methodologies are introduced to the student. It is good to have a good grip over certain fundamental concepts such as Laplace Transform, partial fractions, complex numbers, etc.
The basic motive of this course can be illustrated by the following example. Here, the objective is to maintain the pendulum rod in the unstable inverted position for which a control system was designed. Check out the video.
http://www.youtube.com/embed/AZhQt7HOSWo
Credits: 6 (3L-0T-0P-6C)
Prerequisites: None
Course Contents:
The following are the main concepts that are covered in this course usually. However, these may vary a bit depending on the availability of time, pace of the instructor, etc.
- System Differential Equation and its representation in the form of a transfer function using Laplace transform
- Response of the system for specific inputs
- Impulse Response
- Step Response
- Response to any time varying input (involves introduction to convolution integral)
- Stability of a system and Routh's Criterion for stability analysis
- Negative Feedback and Positive Feedback stabilization of a system
- Introduction to Proportional control, steady state error constants, system type, tracking control and integral control, lag compensator, transient response improvement and derivative control, lead compensators.Root Locus Concept and stability analysis using root locus
- Frequency Response, Bode plots and Nyquist plots
- Nyquist stability criterion, Phase margin and Gain margin concepts
- Introduction to basic design of control systems using root locus and frequency response concepts
Motivation
This course is very essential for a student who wishes to venture into Dynamics and Controls. . There are several courses in the department (and also outside the department). This course is a pre-requisite for many of the following courses too. There are several other similar courses in Electrical Engineering too which have a similar course name and content.
- AE 695 : State Space Methods for Flight Vehicles
- AE 690 : Control System Design Techniques
- SC 602 : Control of Nonlinear Dynamical Systems
- SC 604 : Optimal Control System
- SC 613 : Multivariable Control Systems
- SC 617 : Adaptive Control Theory
- CL 692 : Digital Control
References
Several standard references are followed for this course. They are mentioned below. However, the first reference among the below mentioned is sufficient for a student to get a fine grip over the basic concepts that are covered in this course.
- Ogata K., Modern Control Engineering
- Norman Nise, Control Systems Engineering
- Franklin, G.F., Powell, J.D., and Emami-Naeini, A., Feedback Control of Dynamic Systems
D’Azzo & Houpis, Linear control system analysis & design
- Stefani et al, Design of feedback control systems
- Nelson, Flight stability and automatic control
External References and Other useful links
http://en.wikipedia.org/wiki/Control_theory and other important links in that page
http://bookboon.com/en/textbooks/chemistry-chemical-engineering/control-engineering-matlab - Using MATLAB for control system design