| Summary: | Bibliography: leaves 118-123. === This study consists of four clearly defined and interlinked objectives. The first is the development of a method of solving nonlinear optimal control problems. This method is then used to solve the underlying optimal control problems. This method is then used to solve the underlying optimal control problem in a nonliear model predictive control (NMPC) strategy. By way of a case study, and to further understanding of the mechanisms of flotation, a dynamic model of a flotation circuit is developed. This nonlinear dynamic model is then used in the NMPC strategy to simulate the nonlinear predictive control of a flotation cell. An indirect approach is used in the method for solving optimal control problems, applying the Euler-Lagrange equations to transofrm the optimal control problem into a two-point boundary value problem (BVP). Conventionally these problems have been solved using the multiple shooting differential equation solver, or variants of it. In this work the BVP is solved by orthogonal collocation, using the FORTRAN package COLSYS. Stragegies are developed to solve a number of different classes of optimal control problems, including problems with constraints on the control trajectory, and terminal state constraints. An important aspect of this solution method is that it produces a continuous control trajectory over the entire solution horizon. The use of this optimal control problem in the nonlinear model predictive control strategy of Chen and Algöwer (1998) is then shown. This strategy is a quasi-infinite horizon NMPC strategy making use of a stabilising terminal penalty cost and terminal state inequality constraint. Stability is guaranteed if the optimal conrol problem is feasible.
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