Moritz Wendt

Brief A probabilistically constrained model predictive controller

We propose a novel control algorithm, probabilistically constrained predictive control, to deal with the uncertainties of system disturbances. The output is to be controlled in the constrained range with a desired probability. Under the assumption of a linear system, the formulated joint probabilistically constrained problem is convex. Thus, it can be solved with a nonlinear programming solver. The probabilities and gradients of the constraints, composed of disturbance sequences with multivariate normal distribution, are computed using an efficient simulation approach. The results of a test problem show the effectiveness of the proposed algorithm.

Robust model predictive control under chance constraints

Abstract We propose a robust control strategy, model predictive control under chance constraints, to deal with multivariable constrained control problems. Both model and disturbance uncertainties are considered and assumed to be correlated multivariate stochastic variables. The output constraints are to be held with a predefined probability in respect of the entire horizon. The problem formulated is a stochastic program under joint probabilistic constraints. Using an efficient sampling method this problem is relaxed to a nonlinear programming problem which can be solved by SQP. Simulation results of a distillation column control show the performances of the proposed strategy

Stochastic Optimization for Operating Chemical Processes under Uncertainty

Mathematical optimization techniques are on their way to becoming a standard tool in chemical process engineering. While such approaches are usually based on deterministic models, uncertainties such as external disturbances play a significant role in many real-life applications. The present article gives an introduction to practical issues of process operation and to basic mathematical concepts required for the explicit treatment of uncertainties by stochastic optimization.

Theoretical and Experimental Studies on Startup Strategies for a Heat-Integrated Distillation Column System

Because of their higher efficiency of energy utilization, heat-integrated column systems have been widely used in the chemical industry. However, the heat integration leads to difficulties in startup of such columns, i.e. a long startup time, and thus considerable costs will result. In this work, a study consisting of modelling, simulation, optimization and experimental verification is carried out to develop optimal operation strategies for heat-integrated columns to reduce the startup time. A pilot two-pressure column system with bubble-cap trays is considered. More than 35% of the startup time can be reduced in comparison to conventional startup procedure. Heuristics for startup operation of such processes are suggested.

Close-Loop Stochastic Dynamic Optimization Under Probabilistic Output-Constraints

In this work, two methods based on a nonlinear MPC scheme are proposed to solve close-loop stochastic dynamic optimization problems assuring both robustness and feasibility with respect to output constraints. The main concept lies in the consideration of unknown and unexpected disturbances in advance. The first one is a novel deterministic approach based on the wait-and-see strategy. The key idea is here to anticipate violation of output hard-constraints, which are strongly affected by instantaneous disturbances, by backing off of their bounds along the moving horizon. The second method is a new stochastic approach to solving nonlinear chance-constrained dynamic optimization problems under uncertainties. The key aspect is the explicit consideration of the stochastic properties of both exogenous and endogenous uncertainties in the problem formulation (here-and-now strategy). The approach considers a nonlinear relation between the uncertain input and the constrained output variables.

A new optimization framework for dynamic systems under uncertainty

Abstract In industrial practice, uncertainties are usually compensated for by using conservative decisions like an over-design of process equipment or an overestimation of operational parameters caused by worst case assumptions of the uncertain parameters, which leads to significant deterioration of the objective function in an optimization problem. In other deterministic optimization approaches, the expected values are used, which most likely leads to violations of the constraints when the decision variables are implemented on site. Thus, several studies on systematic approaches taking these uncertainties into consideration have been made recently. In this work, novel algorithms for nonlinear chance constrained optimization are proposed specially for such stochastic optimization problems where no monotone relation between constrained output and uncertain input variables exists. This is necessary, especially for those processes which involve chemical chain reactions or other complex reaction systems where the decision variables are strongly critical to the question of whether there is a monotony or not.

Robust optimization of a reactive semibatch distillation process under uncertainty

Abstract Deterministic optimization has been the common approach for batch distillation operation in previous studies. Since uncertainties exist, the results obtained by deterministic approaches may cause a high risk of constraint violations. In this work, we propose to use a stochastic optimization approach under chance constraints to address this problem. A new scheme for computing the probabilities and their gradients applicable to large scale nonlinear dynamic processes has been developed and applied to a semibatch reactive distillation process. The kinetic parameters and the tray efficiency are considered to be uncertain. The product purity specifications are to be ensured with chance constraints. The comparison of the stochastic results with the deterministic results is presented to indicate the robustness of the stochastic optimization.

Optimal production planning under uncertain market conditions

Abstract We propose to use a dynamic stochastic optimization approach to address production planning problems under uncertain market conditions. The problem is formulated as a dynamic mixed-integer chance constrained optimization problem which can be relaxed to an equivalent deterministic MILP formulation. Using this approach, a quantitative relationship between profit achievement and risk of constraints violation can be received, through which the sensitive uncertain variables can be identified. An optimal decision with a desirable trade-off can be made for the future purchase, sales and operation.

Optimal Control of a Continuous Distillation Process under Probabilistic Constraints

A continuous distillation process with random inflow rate is considered. The aim is to find a control (feed rate, heat supply, reflux rate) which is optimal with respect to energy consumption and which is robust at the same time with respect to the stochastic level constraints in the feed tank. The solution approach is based on the formulation of probabilistic constraints. An overall model including the dynamics of the distillation process and probabilistic constraints under different assumptions on the randomness of inflow is developed and numerical results are presented.

Improving the Efficiency of Batch Distillation by a New Operation Mode

Abstract Batch distillation processes are well-known for their high degree of flexibility. A feature of batch distillation is that it produces not only the desired products but also off-cuts. Conventionally, off-cuts are recycled to the reboiler of the column for the next batch. In this work, we propose a new operation mode for batch distillation, namely, the off-cuts will be recycled in form of a continuous feed flow into the column. The separation effect is promoted in this way and thus economical benefits can be achieved. Simulation and optimization based on a rigorous model are carried out to study the properties of this operation mode and develop optimal operating policies. Results of applying this mode to two industrial batch columns show significant improvements of operation efficiency in comparison to the conventional recycle strategy.