Module 4: Multivariable Systems, Eigenvalues, Eigenvectors and Similarity Transformations

Lectures

Folder description

Please click the folder link above to access the Module 4 instructional content. Module 4 contains three video lectures that present the following topics:

Characteristic Equation for Multivariable Transfer Functions (4A)
Eigenvalues and Eigenvectors (4B)
Similarity Transformations (4C)

Technical

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Module at a Glance ObjectivesHow to Complete This Module:

Cell description

Objectives

By the end of this module, you will be able to:

Compute / ascertain the characteristic equation for multivariable systems.
Compute / determine the multivariable transfer function, given a state-space plan description.
Determine the eigenvalues of a dynamic state-space system.
Compute the eigenvectors and generalized eigenvectors of a dynamic state-space system.
Apply similarity transformation techniques to transform the structure of a general state-space system from one form to another (e.g., to control canonical form, observer canonical form or diagonal canonical form).

How to Complete This Module:

View Lecture 4A (“Characteristic Equation for Multivariable Transfer Functions”).
View Lecture 4B (“Eigenvalues and Eigenvectors”).
View Lecture 4C (“Similarity Transformations”).
Complete the assigned reading: Chapter 8, Sections 8.9-8.10 in the 10th Edition of the textbook (Chapter 10, Sections 10.7-10.9 in the 9th Edition).
Complete the Module 4 Practice Assignment.
Take part in the Module 4 Discussion.

Technical

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Readings

Cell description

To access EReserves readings, click the Readings title above or EReserves on the course menu.

This week's reading assignment includes the following:

Golnaraghi, Farid, and Benjamin C. Kuo. Automatic Control Systems (10th Edition).
- Chapter 8, Sections 8.9-8.10
- (Or, Chapter 10, sections 10.7-10.9 in the 9th Ed. of the textbook.)

Technical

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Module 4 Practice Assignment

Cell description

Instructions: Download and print the Module 4 Practice Assignment PDF, complete by hand, and then scan and upload your final document to the Blackboard course site. Please ensure that your scan is of readable quality and oriented in the proper direction for reading. All final submittals are to be in PDF format.

Submit your file using the following naming structure: Lastname_Firstname_M4Assignment (example: Palumbo_Neil_M4Assignment).

Technical

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Module 4 Discussion

Cell description

Students should respond to the following prompt and respond to at least two classmate’s post as well.

In module 4, we discussed the concept of similarity transformation of a state-space system representation, and introduced a number of structural representations including control canonical and diagonal canonical forms. Therefore, is it safe to say that the states and related system structure are not unique? What about the transfer function form of a dynamic system? Is it unique? Why or why not? Justify your answers with specifics. If you are still having difficulty with a topic/concept, please elaborate so that I and/or your classmates can assist you.

Technical

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Module 4 Discussion Assignment Solution

Cell description

The states and related state space system structure are not necessarily unique as they are dependent on the designer's selection. The transfer function form of a dynamic system is unique because it represents the input-output characteristics of a system, independent of the choice of states or structure of the plant matrices.

(To be released on the first day of Module 5.)

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Module 4 Practice Assignment Solutions

Cell description

Click on the link below to review the Practice Assignment Solutions.

(To be released on the first day of Module 5.)

Technical

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