Performance of Third-order Nonlinear Control Systems
This thesis investigates a method of predicting the step response of control systems described by third-order nonlinear differential equations. The nonlinearities are specified mainly as being smooth and not a function of the derivatives of the dependent variable. The method is based on the construction of a root excursion plot, which is the locus, in a root vs. dependent-variable plane, of the roots of a nonlinear characteristic equation. Various possible shapes of third-order root excursion plots are examined, and the step response of the system is related to each particular shape. In particular, it is possible to predict the exact value of system gain or step amplitude which will yield the fastest possible no-overshoot response. Advantages of the method are mainly that the number and location of the nonlinearities are not limited. The prediction of the response is not restricted to a small range immediately around an equilibrium point. That is, for the cases in which the method does apply, if the system is stable over an extended range, the point of the fastest no-overshoot response within that range can be predicted very accurately. Presently, there are no other methods available which will yield response information of this type. A possible extension of the method to higher-order nonlinear systems is demonstrated by several fourth-order examples. (Author).
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