Lectures: Non-linear phenomena. Mathematical modelling of nonlinear systems, Stationary points, Linearisation around stationary points and trajectories, Phase plane analysis. Stability analysis using Lyapunov methods, circle criterion, small-gain and passivity. Computer tools for simulation and analysis, Effects of saturation, backlash and dead-zones in control loops, Descring functions for analysis of limit cycles, High-gain methods and relay feedback, Optimal control, Nonlinear synthesis and design.
Laboratory exercises: Analysis using the describing function and control design with dead-zone compensation for an air throttle used in car motors; Energy-based design of a swing-up algorithm for an inverted pendulum; Trajectory generation using optimal control for the pendulum-on-a-cart process.