Dynamic Optimization Of Hybrid Parametric System

Confronting increasingly fierce global competitions in process industries,an enterprise has to optimize its overall production activities including scheduling and dynamic optimization.Integrating decision making at different levels becomes of utmost importance to identify economic potentials for increasing the profit margins.Hybrid parametric system is the mathematical model of a continuous process with batch operations,while hybrid parametric dynamic optimization is the mathematical model of integrated optimization of continuous and batch operations.In this work,the hybrid parametric dynamic optimization has been systematically solved from four aspects,i.e dynamic modeling,optimality conditions,numerical algorithms and closed-loop implementation frameworks.The optimization of continuous process is traditionally covered by finding the optimal operation points,which is considered in a steady-state process model and aims to maximize the economic profit during preserving operating constraints.However,the repeatability of batch operations renders the continuous process to behave more like a batch process and batch and continuous operations are optimized separately.In this work,considering the quantitative correlation between amount of added CO promoter and CO combustion dynamic,the completed dynamic mechanism model of a fluid catalytic cracking unit is established.Furthermore,the reasons of necessity for the integrated optimization of continuous and batch operations are explained by the sensitivity analysis.Next,integrated optimization of continuous and batch operations is modeled as the hybrid parametric dynamic optimization.Hybrid parametric system is a special kind of hybrid system,which subsystem is characterized by parameters of model function.The parameters of model function represent the batch operations.The corresponding necessary optimality conditions are established in the form of the hybrid parametric minimum principles,which are proposed and proved in this work.Unlike the hybrid minimum principles,in the virtue of the continuity of parameter space,the hybrid parametric minimum principle only requires a prescribed number of switching times.As the global information is needed for the hybrid parametric dynamic optimization problems,the principle of optimality won't hold in these cases.As most practical problems are too complex to allow for an analytical solution by optimality conditions,the numerical algorithms are inevitable for solving hybrid parametric dynamic optimization problems.Two methods have been proposed in this work.As the batch operations can be parameterized by themselves,the first method is to parameterize continuous and batch operations simultaneously by adaptive control vector parameterization,which can be easily implemented.However,by the hybrid parametric minimum principle,it can be known that the discretization manipulation has already altered the original problem,i.e.they have different solutions described by different optimality conditions.Hence,the solution obtained by parameterization may drift away from the real solution.Moreover,it can't be guaranteed that the optimal solution sequence of batch operations approaches the real optimal solution of batch operations.On the other hand,as an integrated optimization problem,the hybrid parametric dynamic optimization problem can be solved by decomposition algorithm to exploit the decomposable structure of the problems.General Benders decomposition requires the convexity to ensure the rigorous convergence,which is usually lost in real application.The nonconvex sensitivity-based generalized Benders decomposition proposed in this work only requires separable quasi-convexity.By the use of a reformulation strategy(introducing an extra equality constraint and constructing several subproblems),the algorithm handles the nonconvexity by direct manipulations of consistent linear Benders cuts and the check of optimality conditions,which spares the construction of surrogate models,and approximates the feasible region of complicating variables by supporting hyperplanes.By these techniques,it always obtains linear programming master problems and provides sensitivity information about complicating variables.The decomposition algorithm for hybrid parametric dynamic optimization problems can be described as: parameterize continuous operations by control vector parameterization and use the nonconvex sensitivity-based generalized Benders decomposition algorithm with batch operations designated as complicating variables.The numerical optimal solution is of the open-loop form and suboptimal,in order to account for uncertainty,two implementation frameworks are proposed in this work to implement the optimal solution in a closed-form.Both frameworks implement optimal continuous operations as extra PID controllers by tracking the necessary conditions of optimality.The first framework directly implements the numerical optimal batch operations,while the second framework improves the quality of the numerical optimal batch operations by a line search method with the sensitivity information.Comparing to framework 1,framework 2 can obtain an equivalent or better precision solution with relatively coarse discretization.Based on these two frameworks,5 operation modes of fluid catalytic cracking unit are discussed in this work.The result shows that the proposed integrated optimization method substantially improves the overall economic performance during preserving safety,and the economic benefits of integrated optimization mostly come from the optimized continuous operations.At last,the main points of this dissertation are summed up and the potential works are proposed.