Objectives

The course is designed as a compulsory course to give the students a broad understanding of vibrations and control of mechanical systems. The course will introduce the students to the concepts of vibrations in single and multi-degree of freedom systems, approximate methods and classical control theory. The course will also include brief discussions on vibrations of continuous systems

Course content

Introduction to modeling of dynamical systems including models for damping. Single Degree of Freedom Systems – Free undamped vibration, Free damped vibration, Forced vibration, Transmissibility, Convolution method and its application to finite-duration shock inputs. Two Degree of Freedom System – Free and forced vibrations, vibration absorber. Multi Degree of Freedom Systems (undamped and proportional damping) – Matrix methods, Modal analysis. Approximate Methods. Vibration of continuous systems (free vibration only). Introduction to controls. Review of Laplace transforms. Transfer function, Block diagrams, Stability – Routh-Hurwitz criterion, Controller performance and types. Steady state errors and constants. Types of feedback control systems – Derivative error compensation, Integral error compensation, Proportional error compensation, Root locus method, Bode plots, Nyquist plots. Modern control/Digital control (time permitting)

Total number of lectures: 40

Lecturewise breakup

1. Introduction – modelling of dynamical systems including models for Damping

2. Vibrations of single degree of freedom systems – Free undamped, free damped, Forced vibration, Transmissibility, Convolution method

3. Two Degree of Freedom System – Free and forced vibration, vibration absorber

4. Multi Degree of Freedom Systems (undamped and proportional damping) – Matrix methods, Modal analysis

5. Approximate methods – Rayleigh-Ritz method : 1 Lecture

6. Vibration of continuous systems (free vibration only): 2 Lectures

7. Introduction to controls, review of Laplace transforms: 2 Lectures

8. Transfer functions and Block diagrams, Overall transfer function, Stability – Routh-Hurwitz criterion

9. Controller performance and types. Steady state errors and constants: 2 Lectures

10. Types of feedback control systems – Derivative error compensation, Integral error compensation, Proportional error compensation. (PID controllers) and relation performance

11. Root locus method. Frequency domain Analysis: Bode plots, Nyquist 5,2 plots. Modern control/ Digital control: 2 Lectures

Recommended books

1. Theory of Vibrations. W. T. Thomson, Prentice Hall

2. Control Systems Engineering. N. S. Nise, John Wiley & Sons

3. Vibration Problems in Engineering. W. Weaver, S. P. Timoshenko and D. H. Young, John Wiley & Sons

4. Mechanical Vibration. J. P. Den Hartog, Dover Publications

5. Feedback Control of Dynamic Systems. G. Franklin, J. D. Powell, and A. Emami-Naeini, Prentice Hall

6. Modern Control Engineering. K. Ogata, Prentice Hall

Any other remarks

There should be follow up courses on vibrations of continuous systems as well Statefeedback /Modern advanced controls

Proposing instructors: Dr. A. Chatterjee, Dr. S. S. Gupta, Dr. P. Wahi, Dr. A. Mimani