Design and analysis of multivariable predictive control applied to an oil-water-gas separator: A polynomial approach

This dissertation uses a polynomial-operator technique to study stability and performance of unconstrained multivariable predictive control. A simple and direct way to determine stability of the closed-loop system is developed.; It is shown that to guarantee stability of the closed-loop two transfer matrices must be stable. These are represented as fraction descriptions, a ratio of “numerator” and “denominator” polynomial matrices from which the poles can be determined. Because both transfer matrices possess the same denominator matrix the position of the roots of its determinant give sufficient conditions for stability of the closed-loop. Furthermore it is shown that if a coprime fraction description is done for the process transfer matrix then it is necessary and sufficient to check if the roots of the determinant of the denominator matrix lie inside the unit circle. This technique avoids the inversion of transfer matrices which is a numerically difficult task allowing the tuning of multivariable systems with many inputs and outputs.; Performance is also studied and it is proven that the system has zero offset response to step changes in the reference, a property known to be valid for the single-input single-output case. For systems with an equal number of inputs and outputs the “inversion of the plant” is also proven. In this case the weights on the input are zero and the solution to the optimization problem results in a controller that inverts the plant and the output matches the reference.; The use of a multivariable predictive control for an oil-water-gas separator is studied. The nonlinear model of the plant is linearized around a steady state and different predictive controllers are designed for it. The controller responds positively to changes in the parameters and performance objectives are pursued. Results show agreement with the simulations done for the linear model, it is concluded that predictive control is a successful control strategy for oil-water-gas separators.; This method becomes an important tool for the analysis of predictive controllers, allowing the study of the effect of tuning parameters on the behavior of the system when the constraints are removed.