Non-linear control system in advanced control system.pptx

Introduction to non linear system, Phase plane method, Lyapunov function with examples

1. Advance Control System Non-Linear Control System

2. Introduction to Nonlinear Systems

3. Introduction to Nonlinear Systems A nonlinear system is one in which the principle of superposition (linearity) does not hold . This means: Output is not directly proportional to the input. The response depends on magnitude as well as direction of the input. System behavior can change at different operating points. Mathematically, a nonlinear system can be represented as:

4. Type of Nonlinearity Type of Nonlinearity Description Example Saturation Output cannot increase beyond a limit Amplifier saturation Dead zone No output for small input Motor with slack Backlash Hysteresis due to mechanical play Gear systems Relay Sudden switching Thermostat Friction Opposes motion, non-smooth Mechanical drives Multivariable nonlinearity Nonlinear coupling between variables Chemical reactors

5. Few problems based on Lyapunov function