Generation of Linear Models in Standard Forms

In this chapter, several methods are described to assist the designer in rejecting designs that do not provide acceptable closed-loop performance, using models linearized about a steady state. These are generated by expressing the open-loop response of the process outputs, y s, in terms of the variations of the inputs, m 5, and disturbances, 

The procedure for deriving the linear state-space model and the input-output transfer function model in Eq. (21.1) involves the following steps  

Step 1 The nonlinear state and output equations are derived from the material and energy balances that model the process. These are expressed in the form  

Step 2 The state and output equations are solved at a stationary (steady) state that is defined either in terms of the desired state variable values or those of the input variables  

Step 3 The equations are linearized in the vicinity of the desired stationary point by a Taylor series expansion of Eq. (21.2)  

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