Piotr Tatjewski

Advanced control and on-line process optimization in multilayer structures §

Abstract The paper demonstrates the place, role and mutual interaction of advanced control algorithms and on-line set-point optimization in process control structures. First, a multilayer control structure resulting from a functional decomposition is briefly presented. The role and selected realizations of advanced control algorithms, in particular mostly applied now model predictive control (MPC) ones, at direct control and supervisory constraint control layers is discussed. Then possible solutions to on-line set-point optimization, depending of disturbance dynamics, are presented: dynamic set-point optimization including involved structures based on temporal decomposition, and steady-state set-point optimization for cases with disturbance dynamics both much slower than and comparable with the process dynamics. For the last case, important in industrial practice, different structures of interaction and even integration of MPC and steady-state optimization are discussed. The topics are illustrated by briefly presented examples, selected from given references.

ITERATIVE OPTIMIZING SET-POINT CONTROL – THE BASIC PRINCIPLE REDESIGNED

Abstract The paper is concerned with on-line process steady-state optimization under uncertainty. In such cases a single process model optimization can yield a set-point far away from the one optimal for the true process. The way to improve the set-point is to apply steady-state feedback, i.e., an iterative optimizing algorithm utilizing new measurements available after every subsequent set-point application. Integrated System Optimization and Parameter Estimation (ISOPE) method yields subsequent set-points converging to the true process optimum, despite uncertainty. It requires, at every iteration, model parameters to be updated under certain additional equality constraint. The aim of the paper is to present how the ISOPE can be redesigned resulting in a new structure without this constraint. Moreover, the parameter estimation itself is then not necessary at every iteration, although possible when reasonable.

Supervisory predictive control and on-line set-point optimization

Supervisory predictive control and on-line set-point optimization The subject of this paper is to discuss selected effective known and novel structures for advanced process control and optimization. The role and techniques of model-based predictive control (MPC) in a supervisory (advanced) control layer are first shortly discussed. The emphasis is put on algorithm efficiency for nonlinear processes and on treating uncertainty in process models, with two solutions presented: the structure of nonlinear prediction and successive linearizations for nonlinear control, and a novel algorithm based on fast model selection to cope with process uncertainty. Issues of cooperation between MPC algorithms and on-line steady-state set-point optimization are next discussed, including integrated approaches. Finally, a recently developed two-purpose supervisory predictive set-point optimizer is discussed, designed to perform simultaneously two goals: economic optimization and constraints handling for the underlying unconstrained direct controllers.

Nonlinear predictive control based on neural multi-models

Nonlinear predictive control based on neural multi-models This paper discusses neural multi-models based on Multi Layer Perceptron (MLP) networks and a computationally efficient nonlinear Model Predictive Control (MPC) algorithm which uses such models. Thanks to the nature of the model it calculates future predictions without using previous predictions. This means that, unlike the classical Nonlinear Auto Regressive with eXternal input (NARX) model, the multi-model is not used recurrently in MPC, and the prediction error is not propagated. In order to avoid nonlinear optimisation, in the discussed suboptimal MPC algorithm the neural multi-model is linearised on-line and, as a result, the future control policy is found by solving of a quadratic programming problem.

An efficient nonlinear predictive control algorithm with neural models and its application to a high-purity distillation process

This paper is concerned with a computationally efficient (suboptimal) nonlinear model-based predictive control (MPC) algorithm and its application to a high-purity high-pressure ethylene-ethane distillation column. A neural model of the process is used on-line to determine the local linearisation and the nonlinear free response. In comparison with general nonlinear MPC technique, which hinges on non-convex optimisation, the presented structure is far more reliable and less computationally demanding because it results in a quadratic programming problem, whereas its closed-loop control performance is similar.

New dual-type decomposition algorithm for nonconvex separable optimization problems

Abstract The aim of the paper is to present a new dual-type decomposition algorithm for large-scale nonconvex optimization problems of general separable structure. After reformulation of the augmented Lagrange function and introduction of auxiliary variables, called approximation points, separable local optimization problems are created. The lower level of the method consists of a few optimization runs of these problems for subsequently improved approximation points, whereas standard updating of Lagrange multipliers constitutes the highest level. Simple rules for adjusting the approximation points and the Lagrange multipliers are given and thoroughly analysed. Applicability conditions and example numerical results indicate that the presented algorithm eliminates, to a great extent, drawbacks of the previous approaches.

Multilayer and integrated structures for predictive control and economic optimisation

Abstract The problem of co-operation of model predictive control (MPC) algorithms with nonlinear economic optimisation is considered. It is important when dynamics of disturbances is comparable with dynamics of the process, thus when application of the classical multilayer approach may be not efficient. Two main approaches are discussed and their features studied. The first one consists in approximate linear, linear-quadratic or piecewise-linear formulations of the target set-point optimisation depending on problem properties. The idea of the second approach consists in integrating the economic optimisation and manipulated variables calculation by MPC algorithm into one optimisation problem. The nonlinear steady-state model used in economic optimisation is approximated on-line. The resulting optimisation problem is then integrated with the MPC optimisation task and a computationally efficient quadratic programming problem is obtained.

Disturbance modeling and state estimation for offset-free predictive control with state-space process models

Abstract Disturbance modeling and design of state estimators for offset-free Model Predictive Control (MPC) with linear state-space process models is considered in the paper for deterministic constant-type external and internal disturbances (modeling errors). The application and importance of constant state disturbance prediction in the state-space MPC controller design is presented. In the case with a measured state, this leads to the control structure without disturbance state observers. In the case with an unmeasured state, a new, simpler MPC controller-observer structure is proposed, with observation of a pure process state only. The structure is not only simpler, but also with less restrictive applicability conditions than the conventional approach with extended process-and-disturbances state estimation. Theoretical analysis of the proposed structure is provided. The design approach is also applied to the case with an augmented state-space model in complete velocity form. The results are illustrated on a 2×2 example process problem.

Optimizing control of uncertain plants with constrained feedback controlled outputs

On-line set-point optimization of technological processes under uncertainty is the subject of the paper for the case with important active constraints on certain process outputs. A miltilayer structure with additional upper layer follow-up constraint controller responsible for keeping the output constraints satisfied both in steady states and during transient processes is considered. The integrated system optimization and parameter estimation (ISOPE) method is investigated, i.e. iterative algorithms using an on-line steady-state feedback, designed to determine optimum operation of the plant in the presence of inaccurate models and disturbance uncertainties. A new formulation of the ISOPE method suitable for the considered structure is derived and discussed, followed by a development of an efficient dual-type algorithm. The algorithms are applied to a case study examplean industrial styrene production unit consisting of a series of distillation columns. Results of simulation runs for cases with and without errors in the feedback information from the process to the optimizer are reported.

Software Implementation of Explicit DMC Algorithm with Improved Dependability

The paper presents an approach to improve the dependability of software implementation of the explicit DMC (Dynamic Matrix Control) Model Predictive Control (MPC) algorithm. The investigated DMC algorithm is implemented for a control system of a rectification column - a process with strong cross-couplings and significant time delays. The control plant has two manipulated inputs and two outputs. The fault sensitivity of the proposed implementation is verified in experiments with a software implemented fault injector. The experimental results prove the efficiency of proposed software improvements.