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## University of Mumbai Semester 8 (BE Fourth Year) Non-linear Control System Revised Syllabus

University of Mumbai Semester 8 (BE Fourth Year) Non-linear Control System and their Unit wise marks distribution

### Units and Topics

# | Unit/Topic | Marks |
---|---|---|

100 | Characteristics of Nonlinear Systems | - |

200 | Phase Plane Analysis | - |

300 | Describing Function Analysis of Nonlinear Systems | - |

400 | Stability of Systems | - |

500 | Passivity | - |

600 | Frequency Domain Analysis of Feedback System | - |

Total | - |

## Syllabus

100 Characteristics of Nonlinear Systems

- Characteristics of nonlinear systems, multiple equilibria, limit cycle, jump phenemona, method of analysis, clasisification of nonlinearities, Common Physical Nonlinearities.

200 Phase Plane Analysis

- Phase Plane Method, phase portraits, Analytical Methods for the Construction of Phase Trajectories, Graphical Method of Construction of Phase Trajectory, Qualitative behavior of Linear systems, phase plane analysis of nonlinear systems, Multiple equilibria, existence of limit cycles, Linearization techniques.

300 Describing Function Analysis of Nonlinear Systems

- Introduction, Basic Definition of Describing Function, Basis of Describing Function Analysis, Describing Function for Typical Nonlinearities (saturation, dead zone, relay, backlash, hysteresis) , Closed Loop Stability Using Describing Function, Stability of the Limit Cycles, Relative Stability from Describing Function.

400 Stability of Systems

- Concept of stability, Stability analysis of autonomous and nonautonomous systems. LaSalle Invariance Principle, stability in the sense of Lyapunov and absolute stability. Zero - input and BIBO stability.
- Second (or direct) method of Lyapunov stability theory for continuous and discrete time systems.

500 Passivity

- Power and energy of passive systems, Definitins, passivity and small gain, Passivity of linear time invariant systems, strictly positive real functions .

600 Frequency Domain Analysis of Feedback System

- Circle, popov criteria, Popov's stability criterion, generalized circle criterion.

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