Course Objective 1: Students will be able to comprehend the concept of stability for nonlinear systems.
Learning Outcomes: Students will be able to
- Find the equilibrium points of a nonlinear system.
- Classify the equilibrium points of a second-order nonlinear system (node, saddle, centroid etc.)
- Draw the approximate trajectories of a second-order nonlinear system on the phase plane
Course Objective 2: Students will be able to understand the concepts related to the periodic trajectories observed in nonlinear systems.
Learning Outcomes: Students will
- Know the definition of a limit cycle.
- Apply the basic results on the existence and non-existence of limit cycles to predict or rule out limit cycles.
Course Objective 3: Students will be able to make describing function analysis.
Learning Outcomes: Students will be able to
- Derive the describing functions for common non-linear elements with and without memory (relay, saturation, dead zone, hysteresis, backlash etc.).
- Determine the existence and stability of a limit cycle along with its parameters based on the describing function analysis.
Course Objective 4: Students will be able to comprehend the concept of stability for nonlinear systems.
Learning Outcomes: Students will
- Understand the definition of the stability of equilibrium points in nonlinear systems.
- Make stability analysis for nonlinear systems based on Lyapunov’s indirect method (linearization).
- Make stability analysis for nonlinear systems based on Lyapunov’s direct method.
- Know the distinction between different stability types like local-global stability, asymptotical stability etc.