# Advanced Control Systems (Dept Elec - III) (2180913)

Syllabus

Sr. Topics Teaching Hours Module Weightage
1
State Space Analysis of Control Systems
State Variables; State-Space Representation of Electrical and Mechanical and Electromechanical Systems; State Space Representation of Nth Order Linear Differential Equation; Transformation to Phase Variable Canonical Form; Relationship Between State Equations and Transfer Functions; Characteristic Equation; Eigen Values and Eigen Vectors; Transformation to Diagonal Canonical Form; Jordan Canonical Form; Controllability Canonical Form; Observabilty Canonical Form; Decomposition of Transfer Function-Direct, Cascade and Parallel Decomposition; State Diagram; Solution of the Time-Invariant State Equation; State Transition Matrix and its Properties; Transfer Matrix; Transfer Matrix of Closed Loop Systems
14
30 %
2
Controllability and Observability:
Concept of Controllability and Observability; Kalman’s Theorems on Controllability; and Observability, Alternative Tests (Gilbert’s Method) of Controllability and Observability; Principle of Duality; Relationship among Controllability, Observability and Transfer Function.
4
10 %
3
State feedback controller
Design of state feedback controller using pole placement technique, Ackerman’s formula,
4
10 %
4
Liapunov Stability Analysis
Stability of Equilibrium State in the Sense of Liapunov; Graphical Representation of Stability; Asymptotic Stability and Instability; Sign-Definiteness of Scalar Function; Second Method of Liapunov; Stability Analysis of Linear Systems; Krasovski’s Theorem; Liapunov Function Based on Variable Gradient Method
4
10 %
5
Describing Function Analysis of Nonlinear Control System :
Introduction to Nonlinear Systems, Describing Functions for Common Types of Nonlinearities, Describing Function Analysis, Stability and Limit Cycles
10
20 %
6
Phase Plane Analysis :
Analytical Methods for constructing Trajectories, Graphical Methods for constructing Trajectories; Isocline Method; Delta Method; Pell’s Method; Lienard’s Method; Classification of Singular Points; Limit Cycles; Phase-Place Analysis of Linear control system; Phase-plane Analysis of Non-linear control system. Minimum Time Trajectory; Optimum Switching Curve.
6
30 %