Subject Code:07A80202 L:4 T/P/D:1 Credits:4 Int. Marks:20 Ext. Marks:80 Total Marks:100
UNIT I: STATE SPACE ANALYSIS
State Space Representation, Solution of State Equation, State Transition Matrix, Canonical Forms – Controllable Canonical Form, Observable Canonical Form, Jordan Canonical Form.
UNIT II: CONTROLLABILITY AND OBSERVABILITY
Tests for controllability and observability for continuous time systems – Time varying case, minimum energy control, time invariant case, Principle of Duality, Controllability and observability form Jordan canonical form and other canonical forms.
UNIT III: DESCRIBING FUNCTION ANALYSIS
Introduction to nonlinear systems, Types of nonlinearities, describing functions, describing function analysis of nonlinear control systems.
UNIT IV: PHASE-PLANE ANALYSIS
Introduction to phase-plane analysis, Method of Isoclines for Constructing Trajectories, singular points, phase-plane analysis of nonlinear control systems.
UNIT V: STABILITY ANALYSIS
Stability in the sense of Lyapunov., Lyapunov’s stability and Lypanov’s instability theorems. Direct method of Lypanov for the Linear and Nonlinear continuous time autonomous systems.
UNIT VI: MODAL CONTROL
Effect of state feedback on controllability and observability, Design of State Feedback Control through Pole placement. Full order observer and reduced order observer.
UNIT VII: CALCULUS OF VARIATIONS
Minimization of functionals of single function, Constrained minimization. Minimum principle. Control variable inequality constraints. Control and state variable inequality constraints. Euler Lagrangine Equation.
UNIT VIII: OPTIMAL CONTROL
Formulation of optimal control problem. Minimum time, Minimum energy, minimum fuel problems. State regulator problem. Output regulator problem. Tracking problem, Continuous-Time Linear Regulators.
State Space Representation, Solution of State Equation, State Transition Matrix, Canonical Forms – Controllable Canonical Form, Observable Canonical Form, Jordan Canonical Form.
UNIT II: CONTROLLABILITY AND OBSERVABILITY
Tests for controllability and observability for continuous time systems – Time varying case, minimum energy control, time invariant case, Principle of Duality, Controllability and observability form Jordan canonical form and other canonical forms.
UNIT III: DESCRIBING FUNCTION ANALYSIS
Introduction to nonlinear systems, Types of nonlinearities, describing functions, describing function analysis of nonlinear control systems.
UNIT IV: PHASE-PLANE ANALYSIS
Introduction to phase-plane analysis, Method of Isoclines for Constructing Trajectories, singular points, phase-plane analysis of nonlinear control systems.
UNIT V: STABILITY ANALYSIS
Stability in the sense of Lyapunov., Lyapunov’s stability and Lypanov’s instability theorems. Direct method of Lypanov for the Linear and Nonlinear continuous time autonomous systems.
UNIT VI: MODAL CONTROL
Effect of state feedback on controllability and observability, Design of State Feedback Control through Pole placement. Full order observer and reduced order observer.
UNIT VII: CALCULUS OF VARIATIONS
Minimization of functionals of single function, Constrained minimization. Minimum principle. Control variable inequality constraints. Control and state variable inequality constraints. Euler Lagrangine Equation.
UNIT VIII: OPTIMAL CONTROL
Formulation of optimal control problem. Minimum time, Minimum energy, minimum fuel problems. State regulator problem. Output regulator problem. Tracking problem, Continuous-Time Linear Regulators.
Modern Control System Theory – by M. Gopal, New Age International Publishers, 2nd edition, 1996
Modern Control Engineering – by K. Ogata, Prentice Hall of India, 3rd edition, 1998
Control Systems Engineering by I.J. Nagarath and M.Gopal, New Age International (P) Ltd
Digital Control and State Variable Methods – by M. Gopal, Tata Mc Graw-Hill Companies, 1997.
Systems and Control by Stainslaw H. Zak , Oxford Press, 2003.