Linearized model accurate near steady state

Thus the simulations show that the linear model is quite accurate for conditions near the steady state. Of course, losses in accuracy are greater, the... 

The autoregulating Windkessel was found to accurately reproduce the experimental flow step response of both vascular beds and the systemic circulation. The model further provided the steady-state pressure-flow autoregulation curve, in linearized form. The impedance spectrum was predicted to differ from that of the three element Windkessel for frequencies below the heart rate. For frequencies near zero, the impedance approached the slope of the pressure-flow autoregulation curve, as opposed to peripheral... 

Prominent examples include the exponential dependence of reaction rate on temperature (considered in Chapter 2), the nonlinear behavior of pH with flow rate of acid or base, and the asymmetric responses of distillate and bottoms compositions in a distillation column to changes in feed flow. Classical process control theory has been developed for linear processes, and its use, therefore, is restricted to linear approximations of the actual nonlinear processes. A linear approximation of a nonlinear steady-state model is most accurate near the point of linearization. The same is true for dynamic process models. Large changes in operating conditions for a nonlinear process cannot be approximated satisfactorily by linear expressions. 

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