Iterative Nonlinear Control of a Semibatch Reactor. Stability Analysis

This paper presents the application of Iterative Nonlinear Model Predictive Control, INMPC, to a semibatch chemical reactor. The proposed control approach is derived from a model-based predictive control formulation which takes advantage of the repetitive nature of batch processes. The proposed controller combines the good qualities of Model Predictive Control (MPC) with the possibility of learning from past batches, that is the base of Iterative Control. It uses a nonlinear model and a quadratic objective function that is optimized in order to obtain the control law. A stability proof with unitary control horizon is given for nonlinear plants that are affine in control and have linear output map. The controller shows capabilities to learn the optimal trajectory after a few iterations, giving a better fit than a linear non-iterative MPC controller. The controller has applications in repetitive disturbance rejection, because they do not modify the model for control purposes. In this application, some experiments with a disturbance in inlet water temperature has been performed, getting good results.Ministerio de Ciencia y Tecnología DPI2004-07444-C04-0

Nonparametric nonlinear model predictive control

Model Predictive Control (MPC) has recently found wide acceptance in industrial applications, but its potential has been much impeded by linear models due to the lack of a similarly accepted nonlinear modeling or databased technique. Aimed at solving this problem, the paper addresses three issues: (i) extending second-order Volterra nonlinear MPC (NMPC) to higher-order for improved prediction and control; (ii) formulating NMPC directly with plant data without needing for parametric modeling, which has hindered the progress of NMPC; and (iii) incorporating an error estimator directly in the formulation and hence eliminating the need for a nonlinear state observer. Following analysis of NMPC objectives and existing solutions, nonparametric NMPC is derived in discrete-time using multidimensional convolution between plant data and Volterra kernel measurements. This approach is validated against the benchmark van de Vusse nonlinear process control problem and is applied to an industrial polymerization process by using Volterra kernels of up to the third order. Results show that the nonparametric approach is very efficient and effective and considerably outperforms existing methods, while retaining the original data-based spirit and characteristics of linear MPC

Model Predictive Regulation

We show how optimal nonlinear regulation can be achieved in a model predictive control fashion

Iterative nonlinear model predictive control of a PH reactor. A comparative analysis

IFAC WORLD CONGRESS (16) (16.2005.PRAGA, REPÚBLICA CHECA)This paper describes the control of a batch pH reactor by a nonlinear predictive controller that improves performance by using data of past batches. The control strategy combines the feedback features of a nonlinear predictive controller with the learning capabilities of run-to-run control. The inclusion of real-time data collected during the on-going batch run in addition to those from the past runs make the control strategy capable not only of eliminating repeated errors but also of responding to new disturbances that occur during the run. The paper uses these ideas to devise an integrated controller that increases the capabilities of Nonlinear Model Predictive Control (NMPC) with batch-wise learning. This controller tries to improve existing strategies by the use of a nonlinear controller devised along the last-run trajectory as well as by the inclusion of filters. A comparison with a similar controller based upon a linear model is performed. Simulation results are presented in order to illustrate performance improvements that can be achieved by the new method over the conventional iterative controllers. Although the controller is designed for discrete-time systems, it can be applied to stable continuous plants after discretization

High-order volterra model predictive control and its application to a nonlinear polymerisation process

Model Predictive Control (MPC) has recently found wide acceptance in the process industry, but the existing design and implementation methods are restricted to linear process models. A chemical process involves, however, severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC), and also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design which relieves practising engineers from the need for first deriving a physical-principles based model. An on-line realisation technique for implementing the NMPC is also developed. The NMPC is then applied to a Mitsubishi Chemicals polymerisation reaction process. The results show that this nonlinear MPC technique is feasible and very effective. It considerably outperforms linear and low-order Volterra model based methods. The advantages of the approach developed lie not only in control performance superior to existing NMPC methods, but also in relieving practising engineers from the need for deriving an analytical model and then converting it to a Volterra model through which the model can only be obtained up to the second order

Towards parallelizable sampling-based Nonlinear Model Predictive Control

This paper proposes a new sampling-based nonlinear model predictive control (MPC) algorithm, with a bound on complexity quadratic in the prediction horizon N and linear in the number of samples. The idea of the proposed algorithm is to use the sequence of predicted inputs from the previous time step as a warm start, and to iteratively update this sequence by changing its elements one by one, starting from the last predicted input and ending with the first predicted input. This strategy, which resembles the dynamic programming principle, allows for parallelization up to a certain level and yields a suboptimal nonlinear MPC algorithm with guaranteed recursive feasibility, stability and improved cost function at every iteration, which is suitable for real-time implementation. The complexity of the algorithm per each time step in the prediction horizon depends only on the horizon, the number of samples and parallel threads, and it is independent of the measured system state. Comparisons with the fmincon nonlinear optimization solver on benchmark examples indicate that as the simulation time progresses, the proposed algorithm converges rapidly to the "optimal" solution, even when using a small number of samples.Comment: 9 pages, 9 pictures, submitted to IFAC World Congress 201

Optimal control of nonlinear systems: a predictive control approach

A new nonlinear predictive control law for a class of multivariable nonlinear systems is presented in this paper. It is shown that the closed-loop dynamics under this nonlinear predictive controller explicitly depend on design parameters (prediction time and control order). The main features of this result are that an explicitly analytical form of the optimal predictive controller is given, on-line optimisation is not required, stability of the closed-loop system is guaranteed, the whole design procedure is transparent to designers and the resultant controller is easy to implement. By establishing the relationship between the design parameters and time-domain transient, it is shown that the design of an optimal generalised predictive controller to achieve desired time-domain specifications for nonlinear systems can be performed by looking up tables. The design procedure is illustrated by designing an autopilot for a missile

Echo State Networks: analysis, training and predictive control

The goal of this paper is to investigate the theoretical properties, the training algorithm, and the predictive control applications of Echo State Networks (ESNs), a particular kind of Recurrent Neural Networks. First, a condition guaranteeing incremetal global asymptotic stability is devised. Then, a modified training algorithm allowing for dimensionality reduction of ESNs is presented. Eventually, a model predictive controller is designed to solve the tracking problem, relying on ESNs as the model of the system. Numerical results concerning the predictive control of a nonlinear process for pH neutralization confirm the effectiveness of the proposed algorithms for the identification, dimensionality reduction, and the control design for ESNs.Comment: 6 pages,5 figures, submitted to European Control Conference (ECC

State-space approach to nonlinear predictive generalized minimum variance control

A Nonlinear Predictive Generalized Minimum Variance (NPGMV) control algorithm is introduced for the control of nonlinear discrete-time multivariable systems. The plant model is represented by the combination of a very general nonlinear operator and also a linear subsystem which can be open-loop unstable and is represented in state-space model form. The multi-step predictive control cost index to be minimised involves both weighted error and control signal costing terms. The solution for the control law is derived in the time-domain using a general operator representation of the process. The controller includes an internal model of the nonlinear process but because of the assumed structure of the system the state observer is only required to be linear. In the asymptotic case, where the plant is linear, the controller reduces to a state-space version of the well known GPC controller