Introduction to Linear, Time-Invariant, Dynamic Systems for Students of Engineering

Reviewed by Eric Gilbertson, Associate Teaching Professor, Seattle University on 4/12/24

Comprehensiveness rating: 4 see less

The text covers most topics that I cover in a senior-level dynamic systems class, as well as some topics from my senior-level controls class. This looks to be a good potential alternative to the current book I’m using (which is not open access). If it also covered electromechanical systems (DC motors) and liquid level systems, then it would be a perfect match for my class.

Content Accuracy rating: 5

All material I reviewed is accurate with no obvious errors.

Relevance/Longevity rating: 5

The topics of modeling dynamic systems are relevant to today’s engineering problems and will remain relevant for a long time. The text covers the fundamentals of modeling and controlling mechanical and electrical systems and these principles can be applied to complicated systems for current engineering problems.

Clarity rating: 5

Derivations of relevant formulas are easy to follow with good figures and adequate explanation of steps. Descriptions are written in a way that is easy to follow.

Consistency rating: 5

Chapters are all in the same format and consistent equation and figure formatting is used so the text looks very professional.

Modularity rating: 5

Concepts are well-organized into modular chapters that could be taught in a different order if desired, or some chapters could be skipped if desired.

Organization/Structure/Flow rating: 4

The text is well-organized like a standard textbook, with appropriate chapter length and topics and homework problems at the end of each chapter. I cover the topics in a different order when I teach the class, but that is not a major problem.

Interface rating: 5

The pdf of the book provides an easy interface to use. It might be nice if the index had clickable hyperlinks to appropriate sections of the main text, but that’s not a big deal.

Grammatical Errors rating: 5

All text is free from grammatical errors.

Cultural Relevance rating: 5

The examples in the text were not culturally biased or insensitive.

Comments

I like how the book includes Matlab code that the students could copy and paste from the pdf version of the book into their own matlab file. I use Matlab in my current dynamic systems class so this book would be well suited for that class.

Reviewed by Cuneyt Yalcin, Visiting Lecturer, James Madison University on 10/29/23

Comprehensiveness rating: 5 see less

The text covers areas and ideas of the subjects in acceptable level and provides an effective index and/or glossary.

Content Accuracy rating: 5

Content is accurate and unbiased.

Relevance/Longevity rating: 5

The content is relevant to many areas that utilize Linear Time-Invariant Systems and can serve as an excellent reference for deriving related equations.

Clarity rating: 5

The text is written in lucid, accessible prose, and provides adequate context for any jargon/technical terminology used.

Consistency rating: 5

The text is internally consistent in terms of terminology and framework.

Modularity rating: 4

The text is developed in a very theoretical manner. For undergraduate level, however, it needs example problems.

Organization/Structure/Flow rating: 5

The topics in the text are presented in a logical, clear fashion.

Interface rating: 5

The text is generally free of significant interface issues, but there are some minor points that can be addressed. Examples of these include:
• In Chapter 17, the Nyquist plots are missing the representation of the lines at infinite distance, making it difficult to explain the plots to students.
• Equation 5-6 is missing a negative sign in front of the inductance constant.

Grammatical Errors rating: 5

The text contains no grammatical errors.

Cultural Relevance rating: 5

The text is not culturally insensitive or offensive.

Comments

This textbook covers Linear Time-Invariant (LTI) systems, which form the foundation of many engineering courses, including System Dynamics, basic Classical Control Theory, Structural Vibration, and even more math-oriented courses on Laplace and Fourier Transformations. The book covers solutions to differential equations and Laplace-based solutions for 1st, 2nd, and 4th-order system time responses. Studying the content equips the reader with skills to analyze the time behavior of higher-order systems. Similarly, it thoroughly covers the frequency responses of 1st and 2nd-order systems, and the techniques introduced can be extrapolated for higher-order systems. The book also includes significant content about introductory Control Theory. However, it lacks coverage of the state-space representation, and there is no discussion of discrete systems. Also, it does not adequately cover Multi-Input-Multi-Output systems. Nevertheless, Laplace transform methods and related frequency domain approaches are explained deeply and extensively in a clear and concise manner.

The book also uses MATLAB as a calculation tool and provides examples of code to help solve or plot specific equations. However, it does not incorporate more advanced commands used for system analysis and control, and the utilization of the software is not systematically ordered in the book. Although the book cannot be used as a MATLAB learning tool, the index includes some of the MATLAB commands utilized throughout the book.

The organization of the chapters and subtitles is concise and can be covered in typical class periods. The chapters develop the topics step by step and meticulously, showing all the derivations. However, there is limited commentary on the meaning of the developed concepts through derivation. While the topics build on each other and involve a good amount of exercises using previous findings to develop new derivations, the content lacks practical applications and utilizations of the developed concepts. There are no practical examples within the text for students to grasp the concepts, and procedures on how to approach a system analysis or control problem are rare or absent within chapters. An instructor can add these, but this time the length of the lecture topics should be rearranged and planned from scratch. In my opinion, the text can be closely followed for a graduate-level course or used as a valuable reference book for derivations covered in class. An effective approach might involve assigning the derivations of equations or concepts as reading assignments and creating homework assignments or online quizzes based on them.

Reviewed by Robert Williams, Professor, Ohio University on 2/1/18

Comprehensiveness rating: 5 see less

This on-line textbook is a challenging combination of system dynamics and responses, mechanical vibrations, mechanical and electrical systems, rigid body dynamics, and feedback control. Covered are free and forced, undamped and damped responses, in both the frequency and time domain.

The textbook focuses on linear time-invariant (LTI) systems, with time- and Laplace-solutions of the governing ordinary differential equations (ODEs). First-, second-, and fourth-order systems are included and considered. The time constant is presented for first-order LTI systems, and natural frequency, damping ratio, and resonance are presented for second-order LTI systems. Translational and rotational systems mechanical systems are included, with inertial, spring, and damping elements. Electrical circuit LTI systems with resistors, capacitors, inductors, and operational amplifiers are also presented. MATLAB software is applied as a tool and for examples throughout the book. Some examples and applications specific to Aerospace Engineering are presented throughout. System identification from experimental data and homework problems with real and simulated data are featured.

Content Accuracy rating: 5

See 11.

Relevance/Longevity rating: 5

See 11.

Clarity rating: 4

See 11.

Consistency rating: 4

See 11.

Modularity rating: 4

See 11.

Organization/Structure/Flow rating: 5

See 11.

Interface rating: 5

Very good.

Grammatical Errors rating: 5

Correct.

Cultural Relevance rating: 3

NA

Comments

This on-line textbook is a challenging combination of system dynamics and responses, mechanical vibrations, mechanical and electrical systems, rigid body dynamics, and feedback control. Covered are free and forced, undamped and damped responses, in both the frequency and time domain.

The textbook focuses on linear time-invariant (LTI) systems, with time- and Laplace-solutions of the governing ordinary differential equations (ODEs). First-, second-, and fourth-order systems are included and considered. The time constant is presented for first-order LTI systems, and natural frequency, damping ratio, and resonance are presented for second-order LTI systems. Translational and rotational systems mechanical systems are included, with inertial, spring, and damping elements. Electrical circuit LTI systems with resistors, capacitors, inductors, and operational amplifiers are also presented. MATLAB software is applied as a tool and for examples throughout the book. Some examples and applications specific to Aerospace Engineering are presented throughout. System identification from experimental data and homework problems with real and simulated data are featured.

The stated prerequisites are: 1. The student should be, at minimum, a junior in an accredited four-year engineering curriculum; and 2. The student should have already completed standard first courses in engineering dynamics and differential equations. Other desired, but not strictly necessary, stated prerequisites are a course in basic electrical circuits, a course in basic computer programming, familiarity with MATLAB commands, knowledge of matrix notation and matrix arithmetic operations (basic course in linear algebra), and knowledge of Laplace transforms.

Here are some limitations of the book, as identified by the author. The bond graph approach is not presented, but author says this book prepares the student to tackle that subject. No state-space representation nor solutions nor control are presented, even for the fourth-order systems. The author stated that his textbook as grown into too much material for a three-hour semester course – so an instructor must pick and choose topics rather than try to present it all.

On my shelf I have at least four separate textbooks each covering one of these topics in depth (system dynamics and responses, mechanical vibrations, mechanical and electrical systems, rigid body dynamics, and feedback control). At 439 pages, the current book is long, but short in terms of complete coverage for each of these related but distinct subjects. In my opinion, the math level is beyond standard engineering juniors, and seems to be written more for electrical, mechanical, and aerospace engineering graduate students.

The sections that I read in detail are comprehensive, accurate, error-free and unbiased, clear to read, consistent in notation, modular in the sense that portions can be used easily from the whole, the organization is logical, and it is free of grammatical errors. Overall, I believe this on-line textbook is very strong and should be seriously considered for adoption by instructors of courses in linear systems dynamics and related topics. This textbook is a serious contender, with long-range potential in longevity and topics coverage, that could support at least four related, required courses in linear systems dynamics at my university.