Explicit output-feedback nonlinear predictive control based on black-box models

Nonlinear model predictive control (NMPC) algorithms are based on various nonlinear models. A number of on-line optimization approaches for output-feedback NMPC based on various black-box models can be found in the literature. However, NMPC involving on-line optimization is computationally very demanding. On the other hand, an explicit solution to the NMPC problem would allow efficient on-line computations as well as verifiability of the implementation. This paper applies an approximate multi-parametric nonlinear programming approach to explicitly solve output-feedback NMPC problems for constrained nonlinear systems described by black-box models. In particular, neural network models are used and the optimal regulation problem is considered. A dual-mode control strategy is employed in order to achieve an offset-free closed-loop response in the presence of bounded disturbances and/or model errors. The approach is applied to design an explicit NMPC for regulation of a pH maintaining system. The verification of the NMPC controller performance is based on simulation experiments.     

A parameter-adaptive control technique

Control of linear stochastic systems with unknown parameters is accomplished by means of an approximate solution of the associated functional equation of dynamic programming. The approximation is based on repeated linearizations of a quadratic weighting matrix appearing in the optimal cost function for the control process. This procedure leads to an adaptive control system which is linear in an expanded vector of state estimates with feedback gains which are explicit functions of a posteriori parameter probabilities. The performance of this controller is illustrated with a simple example.     

Handling uncertainty in economic nonlinear model predictive control: A comparative case study

In the last years, the use of an economic cost function for model predictive control (MPC) has been widely discussed in the literature. The main motivation for this choice is that often the real goal of control is to maximize the profit or the efficiency of a certain system, rather than tracking a predefined set-point as done in the typical MPC approaches, which can be even counter-productive. Since the economic optimal operation of a system resulting from the application of an economic model predictive control approach drives the system to the constraints, the explicit consideration of the uncertainties becomes crucial in order to avoid constraint violations. Although robust MPC has been studied during the past years, little attention has yet been devoted to this topic in the context of economic nonlinear model predictive control, especially when analyzing the performance of the different MPC approaches. In this work, we present the use of multi-stage scenario-based nonlinear model predictive control as a promising strategy to deal with uncertainties in the context of economic NMPC. We make a comparison based on simulations of the advantages of the proposed approach with an open-loop NMPC controller in which no feedback is introduced in the prediction and with an NMPC controller which optimizes over affine control policies. The approach is efficiently implemented using CasADi, which makes it possible to achieve real-time computations for an industrial batch polymerization reactor model provided by BASF SE. Finally, a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty. Simulations results show that a closed-loop approach for robust NMPC increases the performance and that enforcing low variability under uncertainty of the controlled system might result in a big performance loss.     

Theoretical analysis of unconstrained nonlinear model predictive control

Model predictive control (MPC) is a well-established controller design strategy for linear process models. Because many chemical and biological processes exhibit significant nonlinear behaviour, several MPC techniques based on nonlinear process models have recently been proposed. The most significant difference between these techniques is the computational approach used to solve the nonlinear model predictive control (NMPC) optimization problem. Consequently, analysis of NMPC techniques is often connected to the computational approach employed. In this paper, a theoretical analysis of unconstrained NMPC is presented that is independent of the computational approach. A nonlinear discrete-time, state-space model is used to predict the effects of future inputs on future process outputs. It is shown that model inverse, pole-placement, and steady-state controllers can be obtained by suitable selection of the control and prediction horizons. Moreover, the NMPC optimization problem can be modified to yield nonlinear internal model control (NIMC). The computational requirements of NIMC are considerably less than NMPC, but the NIMC approach is currently restricted to nonlinear models with well-defined and stable inverses. The NIMC controller is shown to provide superior servo and regulatory performance to a linear IMC controller for a continuous stirred tank reactor.     

Computation, approximation and stability of explicit feedback min-max nonlinear model predictive control

This paper presents an approximate multi-parametric Nonlinear Programming (mp-NLP) approach to explicit solution of feedback min-max NMPC problems for constrained nonlinear systems in the presence of bounded disturbances and/or parameter uncertainties. It is based on an orthogonal search tree structure of the state space partition and consists in constructing a piecewise nonlinear (PWNL) approximation to the optimal sequence of feedback control policies. Conditions guaranteeing the robust stability of the closed-loop system in terms of a finite l₂-gain are derived.     

Economics-based NMPC strategies for the operation and control of a continuous catalytic distillation process

Process profitability is an yes or no criterion for the successful long-term operation of industrial processes. This article describes the use of dynamic online economic process optimization to improve the performance of chemical processes. Different model-predictive control techniques have progressively been applied to coupled multivariable control problems and in many cases, especially in the petrochemical industry, the reference values are adjusted infrequently by stationary optimization based upon a rigorous nonlinear stationary plant model (real-time optimization, RTO). In between these optimizations, however, the process may be operated suboptimally due to the presence of disturbances. Nonlinear dynamic model-based optimization has been proposed recently to combine optimal operation and feedback control. In this paper, a model of the complex dynamics of a pilot-scale continuous catalytic distillation process is used to explore the potential benefits of online economics optimizing control strategies. We compare the direct economic optimization scheme with a compromise scheme, the economics-oriented tracking controller. The outcome of this work indicates that by using direct economics optimizing NMPC the plant economics can be handled better while guaranteeing the product specifications which are formulated as explicit constraints.     

Nonlinear model predictive control of fed-batch fermentations using dynamic flux balance models

Fed-batch fermentation is an important production technology in the biochemical industry. Using fed-batch Saccharomyces cerevisiae fermentation as a prototypical example, we developed a general methodology for nonlinear model predictive control of fed-batch bioreactors described by dynamic flux balance models. The control objective was to maximize ethanol production at a fixed final batch time by adjusting the glucose feeding rate and the aerobic–anaerobic switching time. Effectiveness of the closed-loop implementation was evaluated by comparing the relative performance of NMPC and the open-loop optimal controller. NMPC was able to compensate for structural errors in the intracellular model and parametric errors in the substrate uptake kinetics and cellular energetics by increasing ethanol production between 8.0% and 14.7% compared with the open-loop operating policy. Minimal degradation in NMPC performance was observed when the biomass, glucose, and ethanol concentration and liquid volume measurements were corrupted with Gaussian white noise. NMPC based on the dynamic flux balance model was shown to improve ethanol production compared to the same NMPC formulation based on a simpler unstructured model. To our knowledge, this study represents the first attempt to utilize a dynamic flux balance model within a nonlinear model-based control scheme.     

Real-time economic nonlinear model predictive control for wind turbine control

Nonlinear model predictive control (NMPC) is a strong candidate to handle the control challenges emerging in the modern wind energy industry. Recent research suggested that wind turbine (WT) control based on economic NMPC (ENMPC) can improve the closed-loop performance and simplify the task of controller design when compared to a classical NMPC approach. This paper establishes a formal relationship between the ENMPC controller and the classic NMPC approach, and compares empirically their closed-loop nominal behaviour and performance. The robustness of the performance is assessed for an inaccurate modelling of the tower fore-aft main frequency. Additionally, though a perfect wind preview is assumed here, the effect of having a limited horizon of preview of the wind speed via the LIght Detection And Ranging (LIDAR) sensor is investigated. Finally, this paper provides new algorithmic solutions for deploying ENMPC for WT control, and report improved computational times.     

基于T-S模糊模型的非线性预测控制策略

提出了一种新的基于T-S模糊模型的非线性预测控制策略. T-S模糊模型用于描述对象的非线性动态特性, 通过将模糊模型的输出反馈回来作为模型输入, 从而构成了模糊多步预报器. 由于T-S模糊模型每条规则的结论部分是一个线性模型, 因此整个模糊模型可以看作一个线性时变系统, 从而将模糊预测控制器中的非线性优化问题转化为一个线性二次寻优问题, 以方便求解. pH中和过程的仿真结果表明其性能优于传统的动态矩阵控制器.     

Design of observer based nonlinear model predictive controller for a continuous stirred tank reactor

Model predictive control (MPC) schemes are now widely used in process industries for the control of key unit operations. Linear model predictive control (LMPC) schemes which make use of linear dynamic model for prediction, limit their applicability to a narrow range of operation (or) to systems which exhibit mildly nonlinear dynamics.

In this paper, a nonlinear observer based model predictive controller (NMPC) for nonlinear system has been proposed. An approach to design NMPC based on fuzzy Kalman filter (FKF) and augmented state fuzzy Kalman filter (ASFKF) has been presented. The efficacy of the proposed NMPC schemes have been demonstrated by conducting simulation studies on the continuous stirred tank reactor (CSTR). The analysis of the extensive dynamic simulation studies revealed that, the NMPC schemes formulated produces satisfactory performance for both servo and regulatory problems. Simulation results also include an inferential control case, where the reactor concentration is not measured but estimated from temperature measurement and used in the NMPC based on FKF and ASFKF formulations.     

A method for carbon oxide concentration evaluation in high-temperature combustion processes

A method for evaluating carbon oxide concentration in high-temperature combustion processes is presented. The paper offers an optimizing control problem for fuel combustion process using a stabilizing regulatory controller, which affects the fuel/air ratio with respect to carbon oxide concentration in the firebox. In this connection, an approach is offered to solving this problem subject to the correction factor compensating for the error of carbon oxide concentration measurement.     

First principle modeling and predictive control of a continuous biodiesel plant

Typically, the large-scale production of biodiesel involves continuous operation plants. Also, the final biodiesel product has to comply with specifications imposed by standards of quality in order to be marketable. These quality constraints must be satisfied during the production at the minimum possible operating cost, in order to make the process economically viable. In this context, a nonlinear model predictive controller (NMPC) is applied to control the oil transesterification section of a continuous biodiesel plant. The controller determines the optimal profiles of the process variables using a nonlinear mechanistic model of the whole transesterification section. The model describes the dynamics of the composition and temperature of the liquid mixture in the reactors and in the decanters, as well as of the decanters interface level. The capability of the proposed NMPC strategy to improve the process economic performance and to enforce the final biodiesel specifications is demonstrated by simulation.     

基于状态-动作图测地高斯基的策略迭代强化学习

在策略迭代强化学习中,基函数构造是影响动作值函数逼近精度的一个重要因素.为了给动作值函数逼近提供合适的基函数,提出一种基于状态-动作图测地高斯基的策略迭代强化学习方法.首先,根据离策略方法建立马尔可夫决策过程的状态-动作图论描述;然后,在状态-动作图上定义测地高斯核函数,利用基于近似线性相关的核稀疏方法自动选择测地高斯...     

A separation theorem for stochastic control problems with point-process observations

The exact solution is derived for a stochastic optimal control problem involving a linear stochastic plant, quadratic costs, and nonlinear, nongaussian observations. The observations are in the form of a point process in which each point has both a temporal and a spatial coordinate. The state of the stochastic plant influences the intensity of the observed time-space point process. The solution to this dual control problem can be realized with a separated estimator-controller in which the estimator is nonlinear, mean-square optimal, and finite dimensional, and the controller is the certainty equivalent linear controller. Motivation for the stochastic optimal control problem studied here is given in terms of position sensing and tracking for quantum-limited optical communication problems.     

Unscented Kalman filter based nonlinear model predictive control of a LDPE autoclave reactor

This paper presents a multivariable nonlinear model predictive control (NMPC) scheme for the regulation of a low-density polyethylene (LDPE) autoclave reactor. A detailed mechanistic process model developed previously was used to describe the dynamics of the LDPE reactor and the properties of the polymer product. Closed-loop simulations are used to demonstrate the disturbance rejection and tracking performance of the NMPC algorithm for control of reactor temperature and weight-averaged molecular weight (WAMW). In addition, the effect of parametric uncertainty in the kinetic rate constants of the LDPE reactor model on closed-loop performance is discussed. The unscented Kalman filtering (UKF) algorithm is employed to estimate plant states and disturbances. All control simulations were performed under conditions of noisy process measurements and structural plant–model mismatch. Where appropriate, the performance of the NMPC algorithm is contrasted with that of linear model predictive control (LMPC). It is shown that for this application the closed-loop performance of the UKF based NMPC scheme is very good and is superior to that of the linear predictive controller.     

Advanced step nonlinear model predictive control for air separation units

Cryogenic air separation units constitute an integral part of many industrial processes and next generation power plants. These units are characterized by fluctuating operating conditions to respond to changing product demands. The dynamics of these transitions are highly nonlinear and energy-intensive. Consequently, nonlinear model predictive control (NMPC) based on rigorous dynamic models is essential for high performance in these applications. Currently, the implementation of NMPC controllers is limited by the computational complexity of the associated on-line optimization problems. In this work, we make use of the so-called advanced step NMPC controller to overcome these limitations. We demonstrate that this sensitivity-based strategy reduces the on-line computational time to just a single CPU second, while incorporating a highly detailed dynamic air separation unit model. Finally, we demonstrate that the controller can handle nonlinear dynamics over a wide range of operating conditions.     

具有条件马尔科夫结构的离散随机系统最优控制

基于Bellman随机非线性动态规划法, 提出了具有条件马尔科夫跳变结构的离散随机系统的最优控制方法, 应用随机变结构系统的性质对最优控制算法进行了简化处理, 并将后验概率密度函数用条件高斯函数来逼近, 针对一类具有条件马尔科夫跳变结构的线性离散随机系统, 给出了其逼近最优控制算法.     

Nonlinear system identification for predictive control using continuous time recurrent neural networks and automatic differentiation

In this paper, a continuous time recurrent neural network (CTRNN) is developed to be used in nonlinear model predictive control (NMPC) context. The neural network represented in a general nonlinear state-space form is used to predict the future dynamic behavior of the nonlinear process in real time. An efficient training algorithm for the proposed network is developed using automatic differentiation (AD) techniques. By automatically generating Taylor coefficients, the algorithm not only solves the differentiation equations of the network but also produces the sensitivity for the training problem. The same approach is also used to solve the online optimization problem in the predictive controller. The proposed neural network and the nonlinear predictive controller were tested on an evaporation case study. A good model fitting for the nonlinear plant is obtained using the new method. A comparison with other approaches shows that the new algorithm can considerably reduce network training time and improve solution accuracy. The CTRNN trained is used as an internal model in a predictive controller and results in good performance under different operating conditions.     

A general NMPC framework for a diesel engine air path

This paper presents the formulation of a parameterised nonlinear model predictive control (NMPC) scheme to be applied on a diesel engine air path. The most important feature of the proposed controller is that it uses no structural properties of the system model. Therefore, the proposed NMPC scheme can be applied to any nonlinear system, leading to a general framework for a diesel engine air path. Moreover, the computational burden is substantially reduced due to an optimisation problem of low dimension obtained by means of the parameterised approach. Simulation results and an experimental validation are presented in order to emphasise the controller's efficiency and the real-time implementability.