Sankaranarayanan Subramanian

Economic multi-stage output nonlinear model predictive control

Nonlinear Model Predictive control is one of the most promising control strategies in the field of advanced control. It can be used to optimize economic cost functions online satisfying all constraints which makes it very appealing in the context of industrial applications. In the last years, several robust NMPC methods have been presented. Among them, multi-stage stochastic NMPC has been proven to provide very promising results and to be computationally feasible by the use of advanced optimization tools. In this paper, we present an extension of the multi-stage approach that takes into account explicitly not only plant-model mismatch but also state estimation error through innovation sampling. We accommodate these errors into the resulting optimization problem by including them in the scenario tree formulation. We use a multiple-model estimation algorithm that fits to the multi-stage approach. The results are illustrated by simulation results of a chemical reactor.

Non-conservative robust Nonlinear Model Predictive Control via scenario decomposition

This work presents an optimization-based scheme for the predictive control of systems under uncertainty using multi-stage stochastic optimization and its efficient solution applying scenario decomposition techniques. The approach presented relies on the application of a robust Nonlinear Model Predictive Control (NMPC) scheme that is based on the description of the evolution of the uncertainty by a scenario tree. Since the size of the resulting optimization problem grows exponentially with the number of uncertainties taken into account and with the prediction horizon (number of stages), we discuss the use of scenario decomposition techniques as a possibility to deal with this problem. The approach is illustrated by simulation results for a nonlinear process that show that the resulting large optimization problem can be solved parallely, faster and with smaller memory requirements than using a monolithic approach.

A non-conservative robust output feedback MPC for constrained linear systems

Model predictive control is an advanced control strategy with a large number of applications. The ability to handle multi-variable problems easily while satisfying input and state constraints make this approach highly appealing. However, when uncertainties are present, a robust scheme is required to ensure stability and satisfaction of constraints. Robustness however should not lead to a drastic deterioration of the performance in the nominal case. One kind of uncertainties that require a robust behavior are disturbances and uncertain model parameters, another uncertain influence comes from measurement errors and state estimation. While most MPC approaches assume that exact state information is available at every time step in the MPC formulation, this is not realistic. Normally not all the states are measured and the measurements are corrupted by noise. Because of the presence of constraints, the separation principle does not hold even in the case of linear systems and hence an output feedback scheme needs to be devised such that the estimation error is accounted for in addition to plant-model mismatch and disturbances. In this work, we propose and demonstrate a non-conservative output feedback scheme within the multi-stage MPC framework for linear time-invariant systems.

Economics optimizing control of a multi-product reactive distillation process under model uncertainty

Abstract By the use of online optimization, the profitability of chemical processes can be enhanced while meeting process-related, environmental and ecological constraints. Two well-known techniques to achieve an economically optimal operation of chemical processes are repetitive stationary optimization (RTO) combined with advanced control and direct economics optimizing control on a receding horizon (also called one-layer approach or dynamic RTO). Direct economics optimizing control can react faster to disturbances and is better suited for the optimization of transients between different products. On the other hand it is computationally demanding and requires sufficiently accurate dynamic models. In this paper, we discuss economics optimizing control of a very complex process, a multi-product transesterification reaction that is realized in a reactive distillation process. The process model, the specification of the economics optimizing controller, the implementation of the dynamic optimization, and the robustification of the controller by a multi-stage approach are discussed using simulation studies.

State estimation using a multi-rate particle filter for a reactive distillation column described by a DAE model

State estimation for systems that exhibit nonlinear dynamics is a challenging task. Various estimation techniques have been proposed and the applicability of the available techniques has been demonstrated for more or less complex cases. Applications to really large process models are still rare. In this paper, we investigate a reactive distillation (RD) process that is modeled by a high-dimensional nonlinear system that is described by differential and algebraic equations (DAE) with more than one hundred states. The process exhibits highly nonlinear dynamics and only a few states are measured. The measurements include both differential and algebraic states and are available at different frequencies. We present a formulation of the multi-rate particle filtering (PF) state estimation method which is specifically designed to handle models that are described by DAE. Compared to existing publications on multirate particle filtering modifications of the algorithm are required for nonlinear DAE models where algebraic state variables are measured. We demonstrate the computational feasibility of the methods for the high order RD process model and compare the performance of the proposed estimator for the single-rate case where all measurements are available at every sampling instance and for the multi-rate case where the outputs are available at different sampling rates. We also investigate the effect of the number of particles on the mean squared estimation error for the single-rate and for the multi-rate sampling case and show that the proposed particle filtering technique can be applied to this complex system with a reasonable number of particles.

A novel tube-based output feedback MPC for constrained linear systems

Model Predictive Control (MPC) is an advanced strategy for the control of multi-variable and constrained dynamical systems. Tube-based MPC is a robust control technique that handles uncertainties present in the model. Since full state information is seldom available in practical systems, the estimation error must also be taken into account in addition to model uncertainties to achieve closed-loop stability and constraint satisfaction despite estimation and model errors. In this paper, we propose a novel strategy for the design of a tube-based output feedback MPC which is independent of the estimation method employed. We formulate a control policy by choosing a candidate estimate that is consistent with the reachable sets of the system under control. The proposed method can be combined with any estimation scheme as long as the assumed error bounds are satisfied. We show that the proposed method is recursively feasible, robustly exponentially stable, and performs better than other available strategies.

Handling structural plant-model mismatch via multi-stage nonlinear model predictive control

In this paper we present an approach to deal with structural uncertainties (structure and dimension of the model are not perfectly known) in the framework of nonlinear model predictive control (NMPC). The presented method is based on robust multi-stage NMPC which represents the uncertainty as a scenario tree with the possibility of recourse, reducing the conservativeness of the approach. In the case of structural mismatch, the unmodeled dynamics can cause a significant difference between the model used for the predictions and the reality, which can cause violations of constraints. We generate a scenario tree to account for the mismatch between the plant and the model by assuming a bound on the effect of the structural mismatch on the model. Thus the proposed scheme will be robust to the structural mismatch present in the model. We demonstrate the advantages of the proposed approach for a nonlinear continuous stirred tank reactor example.