(5061111-A) Modern Control Theory
Teaching scheme: 3 lectures/week Credits: 3
Exam scheme: Paper- 100 marks
1. State Space analysis of continuous time multivariable systems: State equations for dynamic systems,
State equations using phase, physical and canonical variables, realization of transfer matrices, Minimal
realization, Solution of state equation, concepts of controllability, reachability, observability,
Controllability and Observability tests: Kalman's test matrix, Gilbert's test, Popov-Belevitch-Hautus test,
2. Discrete time control systems: sampling theorem, pulse transfer function, modified Z-transform, stability
3. State space analysis of discrete time multivariable systems: Discretization of State equations for
dynamic systems, State equations using phase, physical and canonical variables, realization of transfer
matrices, Minimal realization, Solution of state equation, stability.
4. State Space and Matrix-Fraction Descriptions of Multivariable systems: State observability,
controllability and matrix-fraction descriptions, Some properties of polynomial matrices, Some basic state
space realization, The Smith-McMillan form of a transfer function matrix, Poles and Zeros of a transfer
function matrix, Matrix-fraction description (MFD) of a transfer function, State space realization from a
transfer function matrix, Internal stability, The generalized Nyquist and inverse Nyquist stability criterion.
5. Controller parameterization: Affine parameterization for stable systems, PID synthesis using Affine
parameterization, Affine parameterization for systems with dead time. Affine parameterization of
multivariable control systems.
1. Chen C. T., ‘Linear Systems: Theory & Design’, (Oxford University Press New York), (1999).
2. Gopal M., ‘Modern Control Systems Theory’, (New Age International New Delhi) (1995).
3. Goodwin , Graebe S F & Salgado M E, ‘Control Systen Design’, (Prentice hall of India, Delhi) (2002).
4. Ogata K., ‘Discrete Time Control Systems’, (Prentice Hall of India, Delhi) (2004).
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