This course develops the fundamentals of feedback control using linear transfer function system models. It covers analysis in time and frequency domains; design in the s-plane (root locus) and in the frequency domain (loop shaping); describing functions for stability of certain non-linear systems; extension to state variable systems and multivariable control with observers; discrete and digital hybrid systems and the use of z-plane design. Assignments include extended design case studies and capstone group projects. Graduate students are expected to complete additional assignments.

Explains bounded input, bounded output stability.

This module compares two methods for solving time-dependent systems, the Backward-Euler method and the Laplace transform.

Upon successful completion of this course, students will be able to:

* Create lumped parameter models (expressed as ODEs) of simple dynamic systems in the electrical and mechanical energy domains
* Make quantitative estimates of model parameters from experimental measurements
* Obtain the time-domain response of linear systems to initial conditions and/or common forcing functions (specifically; impulse, step and ramp input) by both analytical and computational methods
* Obtain the frequency-domain response of linear systems to sinusoidal inputs
* Compensate the transient response of dynamic systems using feedback techniques
* Design, implement and test an active control system to achieve a desired performance measure

Mastery of these topics will be assessed via homework, quizzes/exams, and lab assignments.

Explica las estabilidad de entrada acotada, salida acotada.

Lists the four Fourier transforms and when to use them.

Covers the same material as 18.03 with more emphasis on theory. First order equations, separation, initial value problems. Systems, linear equations, independence of solutions, undetermined coefficients. Singular points and periodic orbits for planar systems. Topics include first order equations, separation, initial value problems, systems, linear equations, independence of solutions, undetermined coefficients, and singular points and periodic orbits for planar systems.

Covers the same material as 18.03 with more emphasis on theory. First order equations, separation, initial value problems. Systems, linear equations, independence of solutions, undetermined coefficients. Singular points and periodic orbits for planar systems.

"This course covers the same material as Differential Equations (18.03) with more emphasis on theory. In addition, it treats mathematical aspects of ordinary differential equations such as existence theorems."

Describes Laplace transforms.

A formal description of the matrix exponential. The definition is given as well as examples of calculating it. The matrix exponential in the frequency domain is given as well through treatment by the Laplace transform.

This module introduces how to use Laplace transform to calculate the matrix exponential.

In this module we extend our matrix algebra tools to cover dynamic processes. Adding capacitance to our nerve fiber model, we allow for change over time and update the Strang Quartet accordingly. We then introduce two possible modes of attack for solving

A first one-semester course on differential equations aimed at engineers.

This module examines the Laplace Transform, an analytical tool that produces exact solutions for small, closed-form, tractable systems. We use the Laplace transform to move toward a solution for the nerve fiber potentials modeled by the dynamic Strang Quartet in the earlier module of the same name.

Explains poles and zeros of transfer functions.

This course introduces dynamic processes and the engineering tasks of process operations and control. Subject covers modeling the static and dynamic behavior of processes; control strategies; design of feedback, feedforward, and other control structures; model-based control; and applications to process equipment.

A table of signals, Laplace transforms, and regions of convergence for several properties.

Explains how to find the region of convergence for continuous-time linear time-invariant systems.