Mathematical models of Physical systems, Performance specification, Root locus analysisand design, frequency domain analysis and design Sampled data control systems – Introduction to con trol systems , Sampli ng process; Sampleand Hold circuit; Types of signals ; Mathematical operation on discrete time signals; Z-transform; Properties of Z-transforms; Inverse Z-transform; Solving the differential equations using Z-transform; and its Applications.
State space analysis- concepts of states; State space formulation; State model of linear system; State diagram and signal flow graph; State-space representation using physical variables-Electrical systems and mechanical translational system; State-space model of Mechanical translational systems and Rotational system
Stability, Controllability and Observability- Linear discrete-time systems(LDS); Transferfunction of LDS systems; Stability analysis of sampled data control systems using Jury’s stability test, Bilinear transformation and Root locus technique; Similarity transformation; Eigen values and Eigen vectors; Canonical form of state model; Controllability test and Observability test using Gilbert’s method of testing, Kalman’stest and Duality property.
Nonlinear systems- Introduction to Nonlinear systems; common physical nonlinearities;Describing function; Derivation of describing function of dead-zone and saturation nonlinearity; Derivation of describing function of saturation nonlinearity; Derivation of describing function of dead-zone nonlinearity; Derivation of describing function of relay with dead-zone and hysteresis
Derivation of describing function of Backlash nonlinearity; Describing function analysis of nonlinear systems using polar plot and Nichols plot ; Phase plane and phase trajectories; Singular points; Stability analysis of nonlinear systems using phase trajectories ; Construction of phase trajectories by- analytical method, Isocline method, delta method; Jump response; Liapunov’s stability criterion; Popov’s stability criterion