Course Content:

Introduction to modeling of dynamical systems. Single Degree of Freedom Systems – Free undamped vibration, Free damped vibration, Forced vibration, Transmissibility, Convolution method, Mechanisms of damping. Two Degree of Freedom System (undamped vibration only) – 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. Block diagrams. Root locus method. Stability – Routh-Hurwith criterion, Nyquist plots. Bode plots. Controller performance and types. Steady state errors and constants. Types of feedback control systems – Derivative error compensation, Integral error compensation, Proportional error compensation. Modern control. Digital control.

Lecturewise Breakup

I. Introduction – modelling of dynamical systems: (1 Lecture)

II. Vibrations of single degree of freedom systems – Free undamped, Free damped, Forced vibration, Transmissibility, Convolution method, Mechanisms of damping: (9 Lectures)

III. Two Degree of Freedom System (undamped vibration only) – Free and forced vibration, vibration absorber: (5 Lectures)

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

V. Approximate methods – Raleigh method: (2 Lectures)

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

VII. Introduction to controls: (1 Lecture)

VIII. Review of Laplace transforms: (2 Lectures)

IX. Block diagrams: (1 Lecture)

X. Root locus method: (2 Lectures)

XI. Stability – Routh-Hurwith criterion, Nyquist plots: (3 Lectures)

XII. Bode plots: (2 Lectures)

XIII. Controller performance and types: (1 Lecture)

XIV. Steady state errors and constants: (1 Lecture)

XV. Types of feedback control systems – Derivative error compensation, Integral error compensation, Proportional error compensation: (2 Lectures)

XVI. Modern control: (1 Lecture)

XVII. Digital control: (1 Lecture)

Laboratory sessions:

I(A). Study of a Beat Phenomenon of a Coupled Pendulum.

I(B). Determination of Effective Radius of Gyration of an Irregular Body through Torsional Oscillation of Trifilar Suspensi.

II. Determination of Natural Frequencies of Beams under Simply Supported and Cantilever Boundary Conditions.

III. Study of Dynamic Vibration Absorber.

IV. DC Motor Speed Control with Various Sensors.

V(A). Measurement of Linear Displacement by Potentiometer.

V(B). Speed Torque Characteristics of DC Servomotor.

VI. Balancing of Ball and Beam System through PID Control.

Demonstration (Active Vibration Control)

References

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.