A rational deterministic design procedure is presented for a class of distributed parameter multivariable plants described by linear scalar differential equations. The Galerkin projection method is employed to form an approximate finite dimensional plant model. The subsequent solution of a quadratic regulator problem for the finite dimensional model results in a lumped multivariable controller which operates on the inputs and outputs of the actual plant. A deterministic observer is constructed to estimate the model state. Techniques for optimal location of the input zones and output transducers are developed. Two examples are presented.

A model has been derived to predict the steady-state input-output characteristics of vortex amplifiers operating in the incompressible flow regime. The model was correlated with experimental data to affect prediction of the influence of the operating fluid properties and the vortex valve critical dimensions on the valve characteristics. The model has been implemented in a digital computer program which includes procedures for the design of vortex valves with specified flow and pressure turndown ratios and the design of vortex amplifiers with proportional (single-valued) characteristics.

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