State Space Models

The design of model-based controllers requires a state space representation of the process model. As the population balance is a first-order nonlinear partial differential equation, a transformation must be used to get such a form.

Using the definitions of the moments of the distribution, the population balance can be transformed into a set of moment equations (eqn [14]):

For a continuously operated system with no impurities, a constant V, a size-independent growth rate, no agglomeration, nucleation at zero size, one crystal-free inlet stream, and a nonclassified product stream,

The first four moment equations, together with the kinetic relation (eqns [10] and [11]) and the mass, energy and component balances, form a closed set which describes the crystallization process. Unfortunately, the description will not be very realistic because of the large simplifications which form the basis of this description.

Other methods have been used to obtain a state space model. First of all the method of lines is applied to solve the population balance yielding a state space representation. For controller design this high order nonlinear model was first linearized and then further reduced. As an alternative a black box model was derived using system identification techniques.

Solar Panel Basics

Solar Panel Basics

Global warming is a huge problem which will significantly affect every country in the world. Many people all over the world are trying to do whatever they can to help combat the effects of global warming. One of the ways that people can fight global warming is to reduce their dependence on non-renewable energy sources like oil and petroleum based products.

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