### Credits:

3L-0T-0P-0A (9 Credits)

### 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)

### 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