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C) x2 + ve, x1 > 2, one has xo1 = x2, xo 2 = - 5/2, a parabola in the phase plane. Similarly for x2 negative, (d) x2 - ve, x1 < - 2, one has xo1 = x2, xo 2 = 5/2, a parabola in the phase plane. (e) x2 - ve, - 2 # x1 # 2, one has xo1 = x2, xo 2 + x1 - 1/2 = 0, a circle in the phase plane. (f) x2 - ve, x1 > 2, one has xo1 = x2, xo 2 = - 3/2, a parabola in the phase plane. 34 An Introduction to Nonlinearity in Control Systems The Phase Plane Method Because all the phase plane trajectories are described by simple mathematical expressions, it is straightforward to calculate specific phase plane trajectories.

Thaler, GJ & Pastel, MP 1962, Analysis and Design of Nonlinear Feedback Control Systems, McGraw Hill, New York. Van der Pol, B 1934, Nonlinear theory of electric oscillations. Proc. IRE, Vol 22, pp 1051-1086. West, JC. 1960, Analytical Techniques for Nonlinear Control Systems, EUP, London. c. system possessing torque limitation. Proc. IEE, Vol 101, pp 156-165. 1 Introduction The describing function, which will be abbreviated DF, method was developed simultaneously in several countries during the 1940s.

K! 22) can be solved to obtain a and γ. 497. 10. 11 is considered. 12. 5 enters the loop at the nonlinearity output. 5. This is due to the integrator in the loop, the input of which must have an average value of zero in the steady state.

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