**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.