Mattia Vallerio

Multi-objective Optimal Control of Chemical Processes using ACADO Toolkit

Abstract Many practical chemical engineering problems involve the determination of optimal trajectories given multiple and conflicting objectives. These conflicting objectives typically give rise to a set of Pareto optimal solutions. To enhance real-time decision making efficient approaches are required for determining the Pareto set in a fast and accurate way. Hereto, the current paper illustrates the use of the freely available toolkit ACADO Multi-Objective ( www.acadotoolkit.org ) on several chemical examples. The rationale behind ACADO Multi-Objective is the integration of direct optimal control methods with scalarisation-based multi-objective methods enabling the exploitation of fast deterministic gradient-based optimisation routines.

Tuning of NMPC controllers via multi-objective optimisation

Abstract Nonlinear Model Predictive Control (NMPC) is a powerful technique that can be used to control many industrial processes. Different and often conflicting control objectives, e.g., reference tracking, disturbance rejection and minimum control effort, are typically present. Most often these objectives are translated into a single weighted sum (WS) objective function. This approach is widespread because it is easy to use and understand. However, selecting an appropriate set of weights for the objective function is often non-trivial and is mainly done by trial and error. The current study proposes a systematic procedure for tuning Nonlinear MPC based on multi-objective optimisation methods. Advanced methods allow an efficient solution of the multi-objective problem providing a systematic overview of the controller behaviour. Moreover, through analytic relations it is possible to link a solution obtained with these novel methods to a set of weights for a weighted sum objective function. Applying this set of weights causes the WS to generate the same solution as obtained with the advanced method. Hence, an appropriate controller can be selected based on the alternatives generated by the advanced method, while the corresponding weights for a WS can be derived for implementing the controller in practice. The procedure is successfully tested on two benchmark applications: the Van de Vusse reactor and the Tennessee Eastman plant.

An interactive decision-support system for multi-objective optimization of nonlinear dynamic processes with uncertainty

We develop an interactive decision support system for dynamic process optimization.The system considers multiple and conflicting objectives to increase sustainability.Operational risk due to parametric uncertainty is included as additional objective.Optimal trade-off solutions and operating policies are interactively visualized.The system is illustrated for the optimal operation of a chemical reactor. The manufacturing industry is faced with the challenge to constantly improve its processes, e.g., due to lower profit margins, more strict environmental policies and increased societal awareness. These three aspects are considered as the pillars of sustainable development and typically give rise to multiple and conflicting objectives. Hence, any decision made will require trade-offs to be evaluated and compromises to be made. To support decision making an interactive multi-objective framework is presented to optimize dynamic processes based on mathematical models. The framework includes a numerically efficient strategy to account for parametric uncertainty in the models and it allows to directly minimize the operational risks arising from this uncertainty. Hence, for the first time expert knowledge on the trade-offs between traditional objective functions and operational risks is readily and interactively available for the practitioners in the field of dynamic systems. The introduced interactive framework for multi-objective dynamic optimization under uncertainty is successfully tested for a three and five-objective fed-batch reactor case study with uncertain feed temperature and heat transfer parameters.

Model predictive control of a CVD reactor for production of polysilicon rods

Production of polysilicon plays a key role in the development of hi-tech and renewable energy industry. Massive production is obtained by chemical vapor deposition (CVD) in semi-batch reactors, traditionally called Siemens reactors, where silicon rods are grown. Following recent increase in market demand for polysilicon, a fine process control on industrial processes for improving production yield and reducing energy consumption is required. In this work, a technique for a real-time model-based predictive control applied to a laboratory-scale Siemens reactor is presented; a lumped model is used for describing the CVD process. Discussion is based on numerical results.

Symmetric algorithmic differentiation based exact Hessian SQP method and software for Economic MPC

Economic Model Predictive Control (EMPC) is an advanced receding horizon based control technique which optimizes an economic objective subject to potentially nonlinear dynamic equations as well as control and state constraints. The main contribution of this paper is an algorithmic differentiation (AD) based real-time EMPC algorithm including a software implementation in ACADO Code Generation. The scheme is based on a novel memory efficient, symmetric AD approach for real-time propagation of second order derivatives. This is used inside a tailored multiple-shooting based SQP method, which employs a mirrored version of the exact Hessian. The performance of the proposed auto-generated EMPC algorithm is demonstrated for the optimal control of a nonlinear biochemical reactor benchmark case-study. A speedup of a factor more than 2 can be shown in the CPU time for integration and Hessian computation of this example.

Multi-objective and robust optimal control of a CVD reactor for polysilicon production

Abstract Traditionally, high-grade poly silicon is produced in the so-called “Siemens” reactor. The process is based on the Chemical Vapor Deposition (CVD) of silicon from a gaseous mixture of silanes and hydrogen on silicon rods. To obtain the crystal growth on the rod surface high temperatures are needed. The rods are heated internally by the Joule effect, i.e., an electrical current induces heating due to the electrical resistance of the silicon material. The Joule effect allows for a tight temperature control but, it also makes this process extremely energy intensive. In this work an existing model is improved by accounting for the reflectivity of the wall and the radiative absorption of the bulk. Additionally, the uncertainty on the thermal conductivity parameter of the silicon rods is taken into account. Hence, a robust optimal control problem is formulated and solved based on the evaluation of Lyapunov equations. Finally, the trade-off among productivity and energy cost is studied via a multi-objective (MO) scalarization method.

Interactive NBI and (E)NNC methods for the progressive exploration of the criteria space in multi-objective optimization and optimal control

Abstract A wide range of problems arising from real world applications present multiple and conflicting objectives to be simultaneously optimized. However, this multi-objective nature is too often neglected. Multi-objective optimization proved to be a powerful tool to correctly describe the trade-offs among conflicting objectives in a set of optimal solutions known as the Pareto set. This paper introduces an interactive method to solve multi-objective problems based on geometric considerations. The method returns a wider Pareto set, at a negligible computational cost, when compared to existing methods. The interactivity also allows the decision-maker to explore only relevant parts of the Pareto set. The extreme solutions yield insightful considerations on the generation of the scalarization parameters for the Normal Boundary Intersection and the Enhanced Normalized Normal Constraints methods. The proposed method is applied to: (i) three scalar multi-objective problems and (ii) the multi-objective optimal control of a tubular and a fed-batch reactor.

SolACE: An Open Source Package for Nolinear Model Predictive Control and State Estimation for (Bio)Chemical Processes

Abstract In spite of the wide spread use of Nonlinear Model Predictive Control (NMPC) in large chemical companies, the small and medium enterprises (SMEs) remain oblivious of its potential mostly due to the large investment costs and in-house expertise required. This paper presents an open source python based simulation environment - SolACE, which can aid SMEs in realizing the full potential of the advanced control techniques. The syntax to introduce the controller and plant models is straightforward, enabling even non-experts to easily formulate the control (and estimation) problems. With the developed package, SMEs can consider the implementation of NMPC on their processes without any overlaying costs or large technical know-how. From a research perspective, the current package can be used as a building block to develop toolkits for advanced control strategies like robust or economic NMPC. It also provides researchers a way to test various models in an NMPC framework without the hustle of having to write the discretization and optimization routines themselves.

Towards nonlinear model predictive control with integrated experiment design

Nonlinear model predictive control (NMPC) has become an important tool in the control and optimization of nonlinear systems in a variety of engineering applications. A requirement for a well-performing NMPC implementation is obtaining and maintaining an appropriate mathematical model of the considered system. For linear dynamic systems, developments have been made to incorporate information content objectives in closed loop, i.e., to solve the dual control problem. However, formulations for nonlinear dynamic systems remain scarce. In this paper we extend the formulation for the integration of experiment design of linear dynamic systems to nonlinear dynamic systems resulting in a NMPC formulation with integrated experiment design (iED-NMPC). This results for nonlinear systems in the presence of a nonlinear matrix inequality. We propose to reformulate this nonlinear matrix inequality using Sylvesters criterion. The suggested approach allows us to replace the nonlinear matrix inequality by additional nonlinear constraints. The resulting formulation can subsequently be implemented in existing NMPC software packages.

Approximate robust optimal control of nonlinear dynamic systems under process noise

Dynamic optimization techniques for nonlinear systems can provide the process industry with sustainable and efficient operating regimes. However, these regimes often lie close to the operating limits. It is therefore critical that these model based operating conditions are robust with respect to process noise, i.e, unmodeled time-varying random disturbances. Besides the effect of uncertainty in the satisfaction of constraints, also the effect of uncertainty on the objective function should be considered. Including uncertainty in an optimization problem typically leads to numerically challenging semi-infinite optimization problems. In this paper several computationally tractable methods are exploited to approximately solve robust optimal control problems. The presented approaches have the advantage that they allow the use of fast deterministic gradient based optimization techniques. The first method is based on a linearization approach while the second method exploits the unscented transformation to construct an estimate of the uncertainty propagation. Both methods yield an approximation of the variance-covariance matrix of the critical constraints and of the objective function. These variance-covariance matrices are employed in the optimization routine to obtain more robust control actions. The illustrative case study concerns a jacketed tubular reactor.