NON LINEAR SYSTEM AND LINEARIZATION - MODERN CONTROL SYSTEM - ELECTRICAL CONTROLLING ENGINEERING

1. Describe the process of linearization by small signal analysis.

2. Linearize following non-linear equation with equilibrium state x0=0

                     

                             𝑥̇=𝑥2 𝑥̇2=𝜇(1−𝑥2)𝑥2−𝑥1 𝜇>0

     Also check its stability

3. The state equation of a nonlinear system are given below. Determine all points of equilibrium and investigate the stability in the neighbourhood of these points

                                            𝑥1̇=𝑥2 𝑥̇2=−𝑥12−𝑥22−2𝑥1−2𝑥2

4. Derive the describing function of following

    a. Ideal relay

    b. Practical relay

    c. Combination of dead zone and saturation

    d. Backlash

5. How stability is decided by describing function method?

6. Determine stability of following system by describing function method. The describing function of nonlinearity is given by