ADVANCED CONTOL SYSTEMS
ADVANCED CONTROL SYSTEMS (PEEC5414)
Module‐I : (15 Hours) Discrete ‐ Time Control Systems :
Introduction: Discrete Time Control Systems and Continuous Time Control Systems, Sampling
Digital Control Systems: Sample and Hold, Analog to digital conversion, Digital to analog conversion.
The Z‐transform: Discrete‐Time Signals, The Z‐transform, Z‐transform of Elementary functions,
Important properties and Theorms of the Z‐transform. The inverse Ztransform, Z‐Transform method
for solving Difference Equations.
Z‐Plane Analysis of Discrete Time Control Systems: Impulse sampling & Data Hold, Reconstruction
of Original signals from sampled signals: Sampling theorm, folding, aliasing. Pulse Transfer function:
Starred Laplace Transform of the signal involving Both ordinary and starred Laplace Transforms;
General procedures for obtaining pulse Transfer functions, Pulse Transfer function of open loop and
closed loop systems.
Mapping between the s‐plane and the z‐plane, Stability analysis of closed loop systems in the z‐
plane: Stability analysis by use of the Bilinear Transformation and Routh stability critgion, Jury
stability. Test. Book No. 1: 1.1; 1.2; 1.4; 2.1; 2.2; 2.3; 2.4; 2.5; 2.6; 3.2; 3.4; 3.5; 4.2; 4.3.
Module ‐II : (15 Hours) State Variable Analysis & Design:
Introduction: Concepts of State, State Variables and State Model (of continuous time systems):
State Model of Linear Systems, State Model for Single‐Input‐Single‐Output Linear Systems,
Linearization of the State Equation. State Models for Linear Continuous – Time Systems: State‐
Space Representation Using Physical Variables, State – space Representation Using Phase Variables,
Phase variable formulations for transfer function with poles and zeros, State – space Representation
using Canonical Variables, Derivation of Transfer Function for State Model. Diagonalization:
Eigenvalues and Eigenvectors, Generalized Eigenvectors.
Solution of State Equations: Properties of the State Transition Matrix, Computation of State
Transition Matrix, Computation by Techniques Based on the Cayley‐Hamilton Theorem, Sylvester’s
Expansion theorm. Concepts of Controllability and Observability: Controllability, Observability,
Effect of Pole‐zero Cancellation in Transfer Function. Pole Placement by State Feedback, Observer
Systems. State Variables and Linear Discrete – Time Systems: State Models from Linear Difference
Equations/z‐transfer Functions, Solution of State Equations (Discrete Case), An Efficient Method of
Discretization and Solution, Linear Transformation of State Vector (Discrete‐Time Case), Derivation
of z‐Transfer Function from Discrete‐Time State Model. Book No. 2: 12.1 to 12.9.
Module ‐III : (12 Hours) Nonlinear Systems :
Introduction : Behaviour of Non linear Systems, Investigation of nonlinear systems.
Common Physical Non Linearities: Saturation, Friction, Backlash, Relay, Multivariable Nonlinearity.
The Phase Plane Method: Basic Concepts, Singular Points: Nodal Point, Saddle Point, Focus Point,
Centre or Vortex Point, Stability of Non Linear Systems: Limit Cycles, Construction of Phase