Linear process model state-space representation

Most design methods for multivariable controllers require a dynamic model of the process in the linear state space representation. Such a model Is given by... 

Hints Use the MATLAB MPC Toolbox, if desired, for this exercise. Two commands are used to produce a linear model of the plant in the representation needed for controller design. First, the dlinmod command obtains a state-space representation (A, B, C, D). To use this command, be sure that the Simuhnk diagram is drawn so that the process manipulated inputs and disturbances correspond to in ports on the top level of the Simulink flow sheet similarly, the outputs must correspond to out ports. Then the ss2mod command produces a model in MPC mod format, specifying inputs that are manipulated variables, measured disturbances, and unmeasured disturbances. The scmpc command simulates control of the hnearized plant with the MPC controller. 

In principle, the time evolution of a particular linear superposition on the molecular base states will reflect a chemical process via the changes shown by the amplitudes. This represents a complete quantum mechanical representation of the chemical processes in Hilbert space. The problem is that the separability cannot be achieved in a complete and exact manner. One way to introduce a model that is able to keep as much as possible of the linear superposition principle is to use generalized electronic diabatic base functions. 

Dynamic models derived from physical principles typically consist of one or more ordinary differential equations (ODEs). In this section, we consider a general class of ODE models referred to as state-space models, that provide a compact and useful representation of dynamic systems. Although we limit our discussion to linear state-space models, nonlinear state-space models are also very useful and provide the theoretical basis for the analysis of nonhnear processes (Henson and Se-borg, 1997 Khalil, 2002). 

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See also in sourсe #XX -- [ ]

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