Modern Control System

UNIT I: Non-Linear Control System Introduction, some common types of nonlinearlities, comparison of linear and non-linear systems, properties of nonlinear control systems, describing functions, stability analysis using describing functions, limit cycle, Liapunov Stability Analysis Of Linear Systems, Second method of Liapunov with four Stability theorems. UNIT II: State Space Analysis Basics: state no uniqueness, eigen values, its invariance, diagonalization and Jordan canonical form, Caylay- Hamilton theorem, Computation of state transition matrix by a) Inverse Laplace method and b) Caylay Hamilton method, controllability and observability (Time Variant Systems), state equations in CCF, OCF and Diagonal Canonical form, Decompositions of Transfer Functions, Effect of Pole-Zero cancellation in Transfer Function. UNIT III: Control System Design By State Space : Pole placement design, Ackermann’s Formula for Pole Placement, design of full and reduced order state observers, design of Servo system. UNIT IV: Discrete System Control : Introduction, Impulse sampling and Data Hold, Reconstructing Original signals from Sampled signals, The Pulse Transfer Function, Mapping between the s Plane and the z Plane, Dominant characteristic Equation Roots, Stability Analysis using Bilinaer transformation Method and Jury’s stability test. UNIT V: Optimal Control Systems: The Discrete Eular-Lagrange Equation, The Discrete Maximum(Minimum) Priciple, Solution of the Discrete Riccati Equation by a) Recursive Method of solving the Riccati equation b) The Eigenvalue-Eigenvector Method. Text Books: 1) Control Systems Engineering; I.J.Nagrath and M. Gopal; New Age International Publishers, Fourth Edition. 2) Digital Control Systems; Benjamin.C. Kuo; Oxford University Press, Second edition. Reference Books: 1) Modern Control Engineering, Roy Choudhary, PHI. 2) Control System Analysis and Design by K.K. Agrawal. 3) Control Engineering Theory and Practice by M.N. Bandhopadhyay, PHI. 4) Introduction to Control Engg. Model, Analysis and Design by Ajit. K. Mandal, New Age International Publishers.