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Course Co-ordinated by IIT Bombay
Prof. S.D. Agashe
IIT Bombay


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Mathematics 3 (Web Course)


Introduction to control problem

Industrial Control examples. Transfer function models of mechanical, electrical, thermal and hydraulic systems. System with dead-time. System response. Control hardware and their models: potentiometers, synchros, LVDT, dc and ac servomotors, tachogenerators, electro hydraulic valves, hydraulic servomotors, electropeumatic valves, pneumatic actuators. Closed-loop systems. Block diagram and signal flow graph analysis, transfer function.

Basic characteristics of feedback control systems

Stability, steady-state accuracy, transient accuracy, disturbance rejection, insensitivity and robustness. Basic modes of feedback control: proportional, integral and derivative. Feed-forward and multi-loop control configurations, stability concept, relative stability, Routh stability criterion.

Time response of second-order systems, steady-state errors and error constants. Performance specifications in time-domain. Root locus method of design. Lead and lag compensation.

Frequency-response analysis

Relationship between time & frequency response, Polar plots, Bode’s plot, stability in frequency domain, Nyquist plots. Nyquist stability criterion. Performance specifications in frequency-domain. Frequency-domain methods of design, Compensation & their realization in time & frequency domain. Lead and Lag compensation.

Op-amp based and digital implementation of compensators. Tuning of process controllers. State variable formulation and solution.

State variable Analysis

Concepts of state, state variable, state model, state models for linear continuous time functions, diagonalization of transfer function, solution of state equations, concept of controllability & observability.

Introduction to Optimal control & Nonlinear control

Optimal Control problem, Regulator problem, Output regulator, treking problem.
Nonlinear system – Basic concept & analysis.

Suggested Text Books & References

• Gopal. M., “Control Systems: Principles and Design”, Tata McGraw-Hill, 1997.
• Kuo, B.C., “Automatic Control System”, Prentice Hall, sixth edition, 1993.
• Ogata, K., “Modern Control Engineering”, Prentice Hall, second edition, 1991.
• Nagrath & Gopal, “Modern Control Engineering”, New Ages International.

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