Design of experiments (DOE)
Economic oriented stochastic optimization in process control using Taguchi’s method
The optimal operating region of complex production systems is situated close to process constraints related to quality or safety requirements. Higher profit can be realized only by assuring a relatively low frequency of violation of these constraints. We defined a Taguchi-type loss function to aggregate these constraints, target values, and desired ranges of product quality. We evaluate this loss function by Monte-Carlo simulation to handle the stochastic nature of the process and apply the gradient-free Mesh Adaptive Direct Search algorithm to optimize the resulted robust cost function. This optimization scheme is applied to determine the optimal set-point values of control loops with respect to pre-determined risk levels, uncertainties and costs of violation of process constraints. The concept is illustrated by a well-known benchmark problem related to the control of a linear dynamical system and the model predictive control of a more complex nonlinear polymerization process. The application examples illustrate that the loss function of Taguchi is an ideal tool to represent performance requirements of control loops and the proposed Monte-Carlo simulation based optimization scheme is effective to find the optimal operating regions of controlled processes.
Additive sequential evolutionary design of experiments
Optimal experiment design supported by evolutionary strategy is an effective tool for iterative and interactive model development and parameter identification tasks.
Central question of the sequential experiment design method is how to select input profile or time series of a system during the iterative model development phase in order to have the system outputs be most informative regarding the model parameters. This problem can be solved by an iterative-sequential method called optimal experiment design (OED) where the applied extremum-searching algorithm has a key role. The original algorithm was further developed in two elements: (i) I have shown that at these steps, applying evolutionary strategy improves efficiency while (ii) collecting previous results in a database (data ware-house) and using their outcome in the current experiment serves as further improvement for the parameter identification process. In this way, model developments and parameter identification can be managed with less energy efforts and higher reliability.
Controller tuning of district heating networks using experiment design techniques
There are various governmental policies aimed at reducing the dependence on fossil fuel for space heating and the reduction in its associated emission of greenhouse gases. DHNs (District heating networks) could provide an efficient method for house and space heating by utilizing residual industrial waste heat. In such systems, heat is proceduced and/or thermally upgraded in a central plant and then distributed to the end users trough a pipeline network. The control strategies of these networks are rather difficult thanks to the non-linearity of the system and the strong interconnection between the controlled variables. That is why a NMPC (non-linear model predictive controller) could be applied to be method for the applied NMPC to fulfill the control goal as soon as possible. The performance of the controller is characterized by an economic cost function based on pre-defined operation ranges. A methodology from the field of experiment design is applied to tune the model predictive controller to reach the best performance. The efficiency of the proposed methology is proven throughout a case study of a simulated NMPC controlled DHN.
