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SYLLABUS
SYLLABUS
MODULE 1
State Space Representation of Systems
Introduction to state space and state model concepts- State equation of linear continuous time systems, matrix representation- features- Examples of electrical circuits and dc servomotors. Phase variable forms of state representation- Diagonal Canonical forms- Similarity transformations to diagonal canonical form.
MODULE 1 VEDIO LINKS : www.youtube.com/watch?v=_7hpN2bS5M8&list=PLU9qGTRXUDklVU3H96rT5VHQ7YWBfVfMR&pp=iAQB
STATE SPACE ANALYSIS PART 1: Advantages of state space analysis
MODULE 2
State Space Analysis (9 hours)
State transition matrix- Properties of state transition matrix- Computation of state transition matrix using Laplace transform and Cayley Hamilton method.
Derivation of transfer functions from state equations.
Solution of time invariant systems: Solution of time response of autonomous systems and forced systems.
State space analysis of Discrete Time control systems: Phase variable form and Diagonal canonical form representations- Pulse transfer function from state matrix- Computation of State Transition Matrix (problems from 2nd order systems only).
MODULE 2 VEDIO LINKS : www.youtube.com/watch?v=Yqtp43GraXw&list=PLU9qGTRXUDkm6YiY2POphkxfl6kj-WJrx&pp=iAQB
MODULE 3
State Feedback Controller Design (6 hours)
Controllability & observability: Kalman’s, Gilbert’s and PBH tests.- Duality principle State feedback controller design: State feed-back design via pole placement technique State observers for LTI systems- types- Design of full order observer.
MODULE 3 VEDIO LINKS : www.youtube.com/watch?v=8OKQoJxV3h4&list=PLU9qGTRXUDkm5rQJPPqK8DfZaAeQcOnvV&pp=iAQB
MODULE 4
Nonlinear Systems (7 hours)
Types and characteristics of nonlinear systems- Jump resonance, Limit cycles and Frequency entrainment
Describing function method: Analysis through harmonic linearization- Determination of describing function of nonlinearities.
Application of describing function for stability analysis of autonomous system with single nonlinearity (relay, dead zone and saturation only).
MODULE 4 VEDIO LINKS : www.youtube.com/watch?v=JJcmo6pnHQQ&list=PLU9qGTRXUDklNoSIT3EyPt0E41lSNI1Y6&pp=iAQB
MODULE 5
Phase Plane and Lyapunov Stability Analysis (8 hours)
Phase plots: Concepts- Singular points – Classification of singular points.Construction of phase trajectories using Isocline method for linear and nonlinear systems. Lyapunov stability analysis: Lyapunov function- Lyapunov methods to stability of nonlinear systems- Lyapunov methods to LTI continuous time systems
MODULE 5 VEDIO LINKS : www.youtube.com/watch?v=uYe70P47moA&list=PLU9qGTRXUDklbgI9hGhBfiAnyQ4YEU_9y&pp=iAQB
Text Books:
1. Nagarath I. J. and Gopal M., Control System Engineering, 5/e, New Age Publishers, 2007
2. Ogata K., Modern Control Engineering, 5/e, Prentice Hall of India, 2010.
3. Gopal M, Modern Control System Theory, 2/e, New Age Publishers, 1984
4. Kuo B.C, Analysis and Synthesis of Sampled Data Systems, Prentice Hall Publications, 2012.
STUDY MATERIALS
STUDY MATERIALS
STATE SPACE NOTES : drive.google.com/file/d/19oR8vmLsBYoTDrF9aKC3vTPriTO1wR1V/view?usp=sharing
DESCRIBING FUNCTION METHOD NOTES: drive.google.com/file/d/1uEXYmJ5j-ENfvifB3_yjwy-yA8n2eZ1T/view?usp=sharing
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DISCLAIMER
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