Reduced order modeling & controller design for mass transfer in a grain storage system |
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Authors: | Paramita Guha Sunita Mishra |
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Affiliation: | Agrionics Division, Central Scientific Instruments Organisation, Chandigarh 160030, India |
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Abstract: | This paper considers the problem of simulating the humidity distributions of a grain storage system. The distributions are described by partial differential equations (PDE). It is quite difficult to obtain the humidity profiles from the PDE model. Hence, a discretization method is applied to obtain an equivalent ordinary differential equation model. However, after applying the discretization technique, the cost of solving the system increases as the size increases to a few thousands. It may be noted that after discretization, the degree of freedom of the system remain the same while the order increases. The large dynamic model is reduced using a proper orthogonal decomposition based technique and an equivalent model but of much reduced size is obtained. A controller based on optimal control theory is designed to obtain an input such that the output humidity reaches a desired profile and also its stability is analyzed. Numerical results are presented to show the validity of the reduced model and possible further extensions are identified. |
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Keywords: | Grain storage system finite element method modeling reduced order modeling proper orthogonal decomposition optimal control Lyapunov stability criteria |
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