1. MAE 280A Linear Dynamic Systems
Robert E Skelton, office hours (help session): 4:00-5:00 TU, 1804 EBU-1
text 1: skelton, dynamic systems control, Wiley 1988 ISBN
text 2: skelton, iwasaki and grigoriadis, a unified algebraic approach to control design, Taylor and Francis 1998 ISBN
prerequisites: linear algebra, differential eqs
homework turned in on every Monday, late homework cannot be accepted (solutions will be posted on web)
hwnotebook = corrected homework solutions, bound in a notebook (due last week of class)
grade=.25exam + .25exam + .3final + .2hwnotebook
read assignment before lecture (come to class with questions in your head)
Homework 1: read chapter 3, text 1. Do exercises 3.2, 3.7, and 3.8

2. MAE280A Syllabus How to get Models of Dynamics
How to get linear Models of Dynamics
How to get solution of linear models
How to measure performance of dynamic system
How to compute performance without solving the ODEs
How to modify performance with control

3. MAE280A Syllabus How to get Models of Dynamics Dynamics
State space models
Linearization

4. Modeling, the Most Difficult part
How should we model a pendulum?
Should we model:
Flexibility of rod?
Bearing dynamics?
Friction?
Aerodynamic disturbances?
Depends on control accuracy required of y
Control accuracy will depend on model, hence,
Modeling and Control Problem not independent
How do we get a model suitable for control design?
An ongoing research topic!

5. How to get Dynamic Models
Particle dynamics
Put model in state form y y mg u x x

6. How to get Dynamic Models
Rigid body dynamics
Linearize about u = 90, ux = Put model in state form y y r u mg u x x

7. What is a Linear System? A linear algebraic system
A linear dynamic system

8. State Space form of Dynamic Models
Nonlinear Models
LTV (Linear Time-Varying) Models
LTI (Linear Time-Invariant) Models
LaPlace Transform of LTI Model

9. State form of Dynamic Models, Discrete
Nonlinear Models
LTV (Linear Time-Varying) Models, Discrete
LTI (Linear Time-Invariant) Models, Discrete
z Transform of LTI Model, Discrete

10. What is a Linear System?
The math model is an abstraction (always erroneous) of the Real System
Are there any Real Systems that are linear?
Yes. Annually compounded interest at the bank.

11. Taylor’s series

12. Nonlinear Systems/Taylor’s Series

13. MAE280A Syllabus How to get Models of Dynamics
How to get linear Models of Dynamics
How to get solution of linear models
Coordinate Transformations
The Liapunov Transformation
The State Transition Matrix
HW2: chapter 4, exercises 4.11, 4.13, 4.14, 4.23, 4.25, 4.28

14. Coordinate Transformations

15. LTI Systems
State: enough IC required to SOLVE the ODE (together with u(t))

16. LTI Solutions

17. MAE 280A Outline Modeling, introduction to state space models
linearization
vectors, inner products, linear independence
Linear algebra problems, matrices, matrix calculus
least squares
Spectral decomposition of matrices: Eigenvalues/eingenvectors
coordinate transformations
solutions of linear ode’s
controllability
pole assignment
observability
state estimation
stability
trackability
optimality
model reduction