Maciej Lawrynczuk

Computationally efficient nonlinear predictive control based on neural Wiener models

This paper describes a computationally efficient nonlinear model predictive control (MPC) algorithm based on neural Wiener models and its application. The model contains a linear dynamic part in series with a steady-state nonlinear part which is realised by a neural network. In the presented MPC algorithm the model is linearised on-line, as a result the future control policy is easily calculated from a quadratic programming problem. The algorithm gives control performance similar to that obtained in fully fledged nonlinear MPC, which hinges on non-convex optimisation. In order to demonstrate the accuracy and the computational efficiency of the considered MPC algorithm a polymerisation process is studied.

Online set-point optimisation cooperating with predictive control of a yeast fermentation process: A neural network approach

Abstract Online set-point optimisation which cooperates with model predictive control (MPC) and its application to a yeast fermentation process are described. A computationally efficient multilayer control system structure with adaptive steady-state target optimisation (ASSTO) and a suboptimal MPC algorithm are presented in which two neural models of the process are used. For set-point optimisation, a steady-state neural model is linearised online and the set-point is calculated from a linear programming problem. For MPC, a dynamic neural model is linearised online and the control policy is calculated from a quadratic programming problem. In consequence of linearisation of neural models, the necessity of online nonlinear optimisation is eliminated. Results obtained in the proposed structure are comparable with those achieved in a computationally demanding structure with nonlinear optimisation used for set-point optimisation and MPC.

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.

Training of neural models for predictive control

This paper emphasises the link between neural model training and its role in model predictive control (MPC) algorithms. This role is of fundamental importance since in MPC at each sampling instant a model is used on-line to calculate predictions of future behaviour of the process and an optimal future control policy. Taking into account this particular function of models in MPC, a training algorithm of neural dynamic models is derived. An example identification problem of a methanol-water distillation process is discussed. The prediction accuracy of models obtained using the described algorithm and the classical backpropagation scheme is compared, which yields one-step ahead predictors.

Efficient Model Predictive Control integrated with economic optimisation

This paper is concerned with a computationally efficient model predictive control (MPC) algorithm for control and set-point computation. The underlying idea consists in integrating the economic optimisation task and manipulated variables calculation by the MPC algorithm into one optimisation problem. The comprehensive nonlinear steady-state model of the process used in economic optimisation is approximated on-line taking into account current state of the plant and disturbance estimate or measurement. Linear and linear quadratic approximations are discussed. The resulting economic optimisation (with the approximate model) is then integrated with standard MPC optimisation problem in such a way that a computationally efficient quadratic programming problem is obtained.

ECONOMIC EFFICACY OF MULTILAYER CONSTRAINED PREDICTIVE CONTROL STRUCTURES: AN APPLICATION TO A MIMO NEUTRALISATION REACTOR

Abstract In the MIMO control system it is often sufficient for some of the output variables to be constrained instead of stabilised. Employing a predictive control algorithm, in which constraints can be easily taken into consideration, is natural in such cases. As a result, in comparison with the standard control problem formulation, in which all relevant output variables are stabilised, the obtained problem has more degrees of freedom. They can be used for improving process economic efficiency. It is demonstrated in the paper on the example of a highly nonlinear MIMO control plant. In order to use the aforementioned feature the multilayer structure with different number of manipulated inputs and controlled outputs is investigated.

Effectiveness of PID and DMC control algorithms automatic code generation for microcontrollers: Application to a thermal process

An effective approach to implement control algorithms using code auto-generation is presented. Using MATLAB and C languages as input, an optimised pure C code is generated using a custom transcompiler. The considered solution is focused on microcontrollers from the STM32 family but any other can be used due to flexibility of the presented system. Controller development for a laboratory thermal process is thoroughly described, PID and DMC algorithms are used. Electronic connection between microcontroller and the process is discussed. Results of the experiments are reported.

Jordan neural network for modelling and predictive control of dynamic systems

This paper discusses the possibility of using a Jordan neural network as a model of dynamic systems and it presents a Model Predictive Control (MPC) algorithm in which such a network is used for prediction. The Jordan network is a simple recurrent neural structure in which only one value of the process input signal (from the previous sampling instant) and only one value of the delayed output signal of the model (from the previous sampling instant) are used as the inputs of the network. In order to obtain a computationally simple MPC algorithm, the nonlinear Jordan neural model is repeatedly linearised on-line around an operating point, which leads to a quadratic optimisation problem. Effectiveness of the described MPC algorithm is compared with that of the truly nonlinear MPC scheme with on-line nonlinear optimisation performed at each sampling instant.

Approximate state-space model predictive control

This paper is concerned with a Model Predictive Control (MPC) algorithm for dynamic systems described by nonlinear state-space models. A unique feature of the algorithm is the fact that the current value of the manipulated variable (i.e. the decision variable of MPC) is not calculated from an optimisation problem, but from an analytical linear control law. The coefficients of the control law, due to a nonlinear nature of the process, are time-varying. They are found on-line by an approximator (a neural network is used for this purpose). The approximator is trained off-line in such a way that the resulting MPC algorithm mimics the suboptimal MPC technique with online model linearisation. Thanks to such an approach, successive on-line model linearisation is not successively performed and some other calculations are not necessary. For a polymerisation reactor off-line training of the approximator is described and the approximate algorithm is compared with the classical MPC algorithms with on-line model linearisation.

An Efficient Nonlinear Predictive Control Algorithm with Neural Models Based on Multipoint On-Line Linearisation

This paper describes a computationally efficient (suboptimal) nonlinear Model Predictive Control (MPC) algorithm and its application to a polymerisation reactor. A neural model of the process is used on-line to determine a local linearisation and a nonlinear free trajectory. Multipoint linearisation method is used, for each sampling instant within the prediction horizon one independent linearised model is obtained taking into account the current state of the process and the optimal input and output trajectory found at the previous sampling instant. In comparison with general nonlinear MPC technique, which hinges on nonlinear, usually 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 performance is similar.