Integrated Two-Time-Scale Scheme for Real-Time Optimisation of Batch Processes (original) (raw)

Dynamic Optimisation of Batch Processes by Integrated Two-Time-Scale Scheme

2010

The theory of neighbouring-extremal control has been developed over the last 4-5 decades to avoid the costly reoptimisation of dynamic systems, primarily in applications with fast nonlinear dynamics. Perhaps the biggest drawback with this approach, when applied to chemical processes, is its poor performance in the presence of large parametric and structural model mismatch. On the other hand, model predictive control (MPC) and run-to-run optimisation are more resistant to model mismatch, but require time-consuming on-line reoptimisation that restricts their applications to slow dynamic systems. This paper proposes to combine both approaches in order to mitigate their deficiencies, thereby leading to an integrated two-timescale scheme with enhanced performance and tractability for dynamic real-time optimization. This scheme is demonstrated by two batch reactor examples.

A Novel Real-Time Methodology for the Simultaneous Dynamic Optimization and Optimal Control of Batch Processes

Computer Aided Chemical Engineering, 2014

A novel threefold optimization algorithm is proposed to simultaneously solve the nonlinear model predictive control and dynamic real-time optimization for batch processes while optimizing the batch operation time. Object-oriented programming and parallel computing are exploited to make the algorithm effective to handle industrial cases. A well-known literature case is selected to validate the algorithm.

Combined on-line and run-to-run optimization of batch processes with terminal constraints

2004

This paper describes the optimization of batch processes in the presence of uncertainty and constraints. The optimal solution consists of keeping certain path and terminal constraints active and driving the sensitivities to zero. The case where the terminal constraints have a larger bearing on the cost than the sensitivities is considered, for which a two-time-scale methodology is proposed. The problem of meeting the active terminal constraints is addressed on-line using trajectory tracking, whilst pushing the sensitivities to zero is implemented on a run-to-run basis. The paper also discusses the run-to-run improvement of trajectory tracking via iterative learning control. The proposed methodology is illustrated in simulation on a batch distillation system.

On-line optimization of batch processes with nonlinear manipulated input

Chemical Engineering Science, 1996

The classical approach to end-point optimization of batch processes leads to a two-point boundary value problem. The numerical solution of this two-point boundary value problem provides the time profile of the manipulated input which has to be implemented in an open-loop fashion. However, due to batch-to-batch variations in the system parameters and initial conditions (which is a typical characteristic of many commercial batch processes), the implementation of this open-loop profile can lead to suboptimal performance. Thus it is desirable to have afeedback which provides the optimal input profile. In a previous paper, we had synthesized optimal state feedback laws for the case where the state model is a linear function of the manipulated input. In this paper, optimal state feedback laws for end-point optimization of dynamic ____.

Optimal operation of batch processes via the tracking of active constraints

ISA Transactions, 2003

This paper presents a new measurement-based optimization framework for batch processes, whereby optimal operation is achieved via the tracking of active constraints. It is shown that, under mild assumptions and to a first-order approximation, tracking the necessary conditions of optimality is equivalent to tracking active constraints (both during the batch and at the end of the batch). Thus, the optimal input trajectories can be adjusted using measurements without the use of a model of the process. When only batchend measurements are available, the proposed method leads itself to an efficient batch-to-batch optimization scheme. The approach is illustrated via the simulation of a semi-batch reactor under uncertainty.

Performance analysis of on-line batch optimization systems

Computers & Chemical Engineering, 1997

In this paper, the on-line optimization of batch reactors under parametric uncertainty is considered. A method is presented that estimates the likely economic performance of the on-line optimizer. The nmthod of t)rthogonal collocation is employed to convert the differential algebraic optimization problem (DAOP) of the dynamic optinfization into a nonlinear t)rogram (NLP) and determine the nominal optimum. Based on the resulting NLP, the optimization steps are approximated by neighbouring extremal problems and the average deviation from tile true process optimum is determined dependent on the measurement error and the parametric uncertainty. A back off from the active path and endpoint constraints is determined at each optimization step which ensures the feasible operation of the process. The method of the average deviation from optimum is developed for time optimal problems. The theory is demonstrated on an example.

Dynamic optimization in the batch chemical industry

2002

Dynamic optimization of batch processes has attracted more attention in recent years since, in the face of growing competition, it is a natural choice for reducing production costs, improving product quality, and meeting safety requirements and environmental regulations. Since the models currently available in industry are poor and carry a large amount of uncertainty, standard model-based optimization techniques are by and large ineffective, and the optimization methods need to rely more on measurements.

A feedback-based implementation scheme for batch process optimization

Journal of Process Control, 2000

The terminal-cost optimization of a control -affine nonlinear system leads to a discontinuous solution that can be characterized in a piecewise manner. To implement such an optimal trajectory despite disturbances and parametric uncertainty, a cascade optimization scheme is proposed in this paper, where optimal reference signals are tracked. Optimality is achieved by the appropriate definition of reference signals (input bounds, state constraints, or switching functions) to track in various sub-intervals. Furthermore, conservatism is introduced into the optimization problem to ensure satisfaction of path constraints in the presence of uncertainty. Finally, the proposed cascade optimization scheme is illustrated on a simulation of a fed-batch penicillin fermentation plant.

Measurement-based optimization of batch and repetitive processes using an integrated two-layer architecture

Journal of Process Control, 2013

This paper is concerned with optimal control of batch and repetitive processes in the presence of uncertainty. An integrated two-layer optimization strategy is proposed, whereby within-run corrections are performed using a neighboring-extremal update strategy and run-to-run corrections are based on a constraint-adaptation scheme. The latter is appealing since a feasible operating strategy is guaranteed upon convergence, and its combination with neighboring-extremal updates improves the reactivity and convergence speed. Moreover, these two layers are consistent in that they share the same objective function. The proposed optimization scheme is declined into two versions, namely an indirect version based on the Pontryagin maximum principle and a direct version that applies a control parameterization and nonlinear programming techniques. Although less rigorous, the latter approach can deal with singular extremals and path constraints as well as handle active-set changes more conveniently. Two case studies are considered. The indirect approach is demonstrated for a level-control problem in an experimental two-tank system, whereas the direct approach is illustrated in numerical simulation on a fed-batch reactor for acetoacetylation of pyrrole. The results confirm that faster adaptation is possible with the proposed integrated two-layer scheme compared to either constraint adaptation or neighboring-extremal update alone.