AND CONTROL OF FLEXIBLE STRUCTURES:
This course introduces the subject of dynamics and control of
flexible structures in both mechanical and aerospace applications.
It is a combination of mathematics, control theory, and dynamics.
The following topics are covered: review of basic mathematical
background (ordinary differential equations, linear algebra),
models of flexible structures in second-order and first-order
forms, frequency response functions, continuous and discrete-time
representation of dynamic systems, work-energy rate principle,
Liapunov stability, observability and controllability, observer
and Kalman filter, state-feedback control, output-feedback control.
DYNAMICS: This course
gives an introduction to vibration analysis of mechanical systems.
The following topics are covered: equations of motion, free response
of single-degree-of-freedom system, forced response under harmonic,
periodic, and non-periodic excitation, transient and steady state
responses, beat phenomenon, matrix approach to the analysis of
multi-degree-of-freedom systems, frequencies, damping factors,
mode shapes, Lagrange's equations, lumped and distributed parameter
systems, discretization methods, vibration absorbers, introduction
to structural control.
- SYSTEM IDENTIFICATION: This course gives an introduction to
system identification theory and its applications to mechanical
and aerospace systems. The following topics are covered: review
of mathematical foundations, discrete-time and continuous-time
models, state-space and input-output models, Markov parameters
and observer Markov parameters, discrete Fourier transform, frequency
response functions, singular value decomposition, least-squares
parameter estimation, minimal realization theory, Observer/Kalman
filter identification (OKID), recursive identification techniques,
and introduction to adaptive estimation and control theory.
- OPTIMAL CONTROL
AND ESTIMATION: This
course gives an introduction to stochastic optimal control theory
and application. The following topics are covered in the course:
mathematical foundations, parametric optimization, conditions
for optimality, linear quadratic regulator (LQR) numerical optimization,
and neighboring-optimal solutions. Least-squares estimates, propagation
of state estimates and uncertainty, and optimal filters and predictors;
optima control in the presence of uncertainty, certainty equivalence
and the linear-quadratic-Gaussian regulator problem (LQG), frequency
domain solutions and robustness of closed-loop control.
CONTROL AND SOFT COMPUTING:
Learning control deals with
the problem of synthesizing an appropriate control input to make
the system produce a desired action by repeated trials without
having to know detailed knowledge of the system under control.
This concept imitates human learning by practice. This course
will study the current theory of learning control and its connection
to repetitive control, adaptive control, and system identification.
Modern topics such as genetic algorithm, fuzzy logic, and neural
networks will also be explored.
- MODERN CONTROL: Introduction
to modern state-space methods for control system design and analysis
with applications to multiple-input multiple-output dynamical
systems, including robotic systems and flexible structures. The
following topics are covered: state-space representation of systems,
continuous-time and discrete-time representations, controllability
and observability, state feedback control, stability, state estimation,
observer design, input-output models, static and dynamic output
feedback control, optimal control design methods, and introduction
to state-space system identification.
- SOLID MECHANICS: After a brief review
of rigid body statics, the
field equations describing the static behavior of deformable
elastic solids are developed. The stress and strain tensors are
introduced and utilized in the development. Exact and approximate
solutions of the field equations are used in the study of common
loading cases, including tension/compression, bending, torsion,
and pressure. In the laboratory component of the course, various
methods of experimental solid mechanics are introduced. Some
of these methods are used in a laboratory project in which the
deformation and stress in an actual load system (wood bridge
project) are determined and compared with theoretical predictions.