A convex approach for NMPC based on second order Volterra series models

In model predictive control (MPC), the input sequence is computed, minimizing a usually quadratic cost function based on the predicted evolution of the system output. In the case of nonlinear MPC (NMPC), the use of nonlinear prediction models frequently leads to non‐convex optimization problems with several minimums. This paper proposes a new NMPC strategy based on second order Volterra series models where the original performance index is approximated by quadratic functions, which represent a lower bound of the original performance index. Convexity of the approximating quadratic cost functions can be achieved easily by a suitable choice of the weighting of the control increments in the performance index. The approximating cost functions can be globally minimized by convex optimization techniques in order to compute the input sequence. The minimization of the performance index is carried out by an iterative optimization procedure, which guarantees convergence to the solution. Furthermore, for a nominal prediction model, asymptotic stability for the proposed NMPC strategy can be shown. In the case of considering an estimation error in the prediction model, input‐to‐state practical stability is assured. The control performance of the NMPC strategy is illustrated by experimental results. Copyright © 2014 John Wiley & Sons, Ltd.     

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.     

State estimation and predictive control of fed-batch cultures of hybridoma cells

Fed-batch cultures of hybridoma cells are commonly used for the production of monoclonal antibodies (MAb). In this study, a simple macroscopic model of the cell culture is used, which is based on the overflow metabolism paradigm. This allows to specify optimal culture conditions, and the natural formulation of a nonlinear model predictive control strategy (NMPC). As not all the component concentrations are available for measurement, system observability is analyzed, and an unscented Kalman filter (UKF) is designed, which provides satisfactory estimates of glucose and glutamine concentrations. Robustness of the NMPC scheme is investigated, as well as the combined UKF+NMPC scheme, through a minimax robust version and the closed-loop system.     

Experimental application of nonlinear model predictive control: temperature control of an industrial semi-batch pilot-plant reactor

This paper describes the application of nonlinear model predictive control (NMPC) to the temperature control of a semi-batch chemical reactor equipped with a multi-fluid heating/cooling system. The strategy of the nonlinear control system is based on a constrained optimisation problem, which is solved repeatedly on-line by a step-wise integration of a nonlinear dynamic model and optimisation strategy. A supervisory control routine has been developed, based on the same nonlinear dynamic model, to handle automatically the fluid changeovers. Both NMPC and supervisory control have been implemented on a PC and applied to a 16 l batch reactor pilot plant. Experiments illustrate the feasibility of such a procedure involving predictive control and supervisory control.     

Nonlinear model predictive control of an internal combustion engine exposed to measured disturbances

This work presents the design procedure of a speed controller for a large, lean burn, natural gas engine in island mode operation. This is a disturbance rejection problem with a measured, large disturbance. The core element is a nonlinear model predictive control (NMPC) algorithm that serves as outer loop controller in a cascaded control structure and generates set-points for low level control loops. The NMPC relies on a control oriented model that includes the physics based equations, assumptions on underlying control loops and constraints given by the control requirements. It is shown how to design the running cost such that the stability of the NMPC without terminal cost and constraints can be guaranteed for the nominal system and for the perturbed system exposed to parametric uncertainties and un-modeled dynamics. The functionality of the control strategy is demonstrated in simulation and by experimental results derived at the engine-testbed.     

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.     

A hybrid model predictive control strategy for nonlinear plant-wide control

A plant-wide control strategy based on integrating linear model predictive control (LMPC) and nonlinear model predictive control (NMPC) is proposed. The hybrid method is applicable to plants that can be decomposed into approximately linear subsystems and highly nonlinear subsystems that interact via mass and energy flows. LMPC is applied to the linear subsystems and NMPC is applied to the nonlinear subsystems. A simple controller coordination strategy that counteracts interaction effects is proposed for the case of one linear subsystem and one nonlinear subsystem. A reactor/separator process with recycle is used to compare the hybrid method to conventional LMPC and NMPC techniques.     

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.     

MIMO系统的多模型预测控制

针对非线性多变量系统提出一种多模型预测控制(MMPC)策略.首先给出一种多模型 辨识方法,利用模糊满意聚类算法将复杂非线性系统划分为若干子系统,并获得多个线性模型, 通过模型变换得出全局系统模型,接着对全局MIMO系统设计MMPC,并进行了系统的性能分 析,最后以pH中和过程为例,通过仿真研究验证了辨识和控制算法的有效性.     

Dual-mode Nonlinear MPC via Terminal Control Laws With Free-parameters

The paper presents a new dual-mode nonlinear model predictive control (NMPC) scheme for continuous-time nonlinear systems subject to constraints on the state and control. The idea of control Lyapunov functions for nonlinear systems is used to compute the terminal regions and terminal control laws with some free-parameters in the dual-mode NMPC framework. The parameters of the terminal controller are selected offline to estimate the terminal region as large as possible; and the parameters are optimized online to gain optimality of the terminal controller with respect to given cost functions. Then a dual-mode NMPC algorithm with varying time-horizon is formulated for the constrained system. Recursive feasibility and closed-loop stability of this NMPC are established. The example of a spring-cart is used to demonstrate the advantages of the presented scheme by comparing to the dual-mode NMPC via the linear quadratic regulator (LQR) method.      

Multirate sliding mode disturbance compensation for model predictive control

In this paper, a novel hierarchical multirate control scheme for nonlinear discrete‐time systems is presented, consisting of a robust nonlinear model predictive controller (NMPC) and a multirate sliding mode disturbance compensator (MSMDC). The proposed MSMDC acts at a faster rate than the NMPC in order to keep the system as close as possible to the nominal trajectory predicted by NMPC despite model uncertainties and external disturbances. The a priori disturbance compensation turns out to be very useful in order to improve the robustness of the NMPC controller. A dynamic input allocation between MSMDC and NMPC allows to maximize the benefits of the proposed scheme that unites the advantages of sliding mode control (strong reduction of matched disturbances, low computational burden) to those of NMPC (optimality, constraints handling). Sufficient conditions required to guarantee input‐to‐state stability and constraints satisfaction by the overall scheme are also provided. Copyright © 2014 John Wiley & Sons, Ltd.     

一类非线性系统非切换解析模型预测控制方法研究

针对关系度不确定非线性系统, 基于模型预测控制理论和切换解析非线性模型预测控制(Nonlinear model predictive control, NMPC) 提出了一种非切换的解析NMPC新方法. 论证了在非切换解析NMPC控制律下, 通过坐标变换可以将闭环系统分别在关系度确定和不确定的两个子空间近似为线性系统, 得出非切换解析NMPC使闭环系统稳定的必要条件. 通过仿真实验验证了非切换解析NMPC可以达到很好的响应特性, 无需切换的特征也扩大了其应用范围.     

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 existing design and implementation methods are restricted to linear process models. A chemical process, however, involves severe nonlinearity which cannot be ignored in practice. This paper aims to solve this nonlinear control problem by extending MPC to accommodate nonlinear models. It develops an analytical framework for nonlinear model predictive control (NMPC). It also offers a third-order Volterra series based nonparametric nonlinear modelling technique for NMPC design, which relieves practising engineers from the need for deriving a physical-principles based model first. An on-line realisation technique for implementing NMPC is then developed and applied to a Mitsubishi Chemicals polymerisation reaction process. 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 developed approach lie not only in control performance superior to existing NMPC methods, but also in eliminating the need for converting an analytical model and then convert it to a Volterra model obtainable only up to the second order.     

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.     

The advanced-step NMPC controller: Optimality, stability and robustness

Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear programming (NLP) sensitivity have reduced on-line computational costs and can lead to significantly improved performance. In this study, we extend this concept through a simple reformulation of the NMPC problem and propose the advanced-step NMPC controller. The main result of this extension is that the proposed controller enjoys the same nominal stability properties of the conventional NMPC controller without computational delay. In addition, we establish further robustness properties in a straightforward manner through input-to-state stability concepts. A case study example is presented to demonstrate the concepts.     

A reduced regularization strategy for economic NMPC

Nonlinear Model Predictive Control (NMPC) enables the incorporation of detailed dynamic process models for nonlinear, multivariable control with constraints. This optimization-based framework also leads to on-line dynamic optimization with performance-based and so-called economic objectives. Nevertheless, economic NMPC (eNMPC) still requires careful formulation of the nonlinear programming (NLP) subproblem to guarantee stability. In this study, we derive a novel reduced regularization eNMPC approach with stability guarantees. Compared with full state regularization, the proposed strategy is less conservative and easier to implement. The resulting eNMPC framework is firstly demonstrated on a nonlinear continuous stirred-tank reactor (CSTR) example and a large-scale double distillation system example. Then the proposed strategy is applied to a challenging nonlinear CO₂ capture model, where bubbling fluidized bed models comprise a solid-sorbent post-combustion carbon capture system. Our results indicate the benefits of this improved eNMPC approach over tracking to the setpoint, and better stability over eNMPC without regularization.     

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.     

Nonlinear MPC for the airflow in a PEM fuel cell using a Volterra series model

The particular industrial interest in fuel cells is based on the possibility to generate clean energy both for stationary and automotive applications. Performance and safety issues of fuel cells are closely related to the control strategy used for the fuel and oxidant supply. In PEM (polymer electrolyte membrane or proton exchange membrane) fuel cells the oxygen excess ratio expresses the proportion between oxygen reacting in the cells and oxygen entering the stack and represents a decisive variable for the mentioned issues. This work is focused on the design of a nonlinear model predictive control (NMPC) strategy manipulating the air flow rate in order to maintain the oxygen excess ratio in a desired value, both for safety and performance reasons. The designed NMPC, based on a second order Volterra series model, was implemented on a commercial fuel cell. The proposed NMPC strategy is validated in experiments and compared to a linear model predictive controller and to the original built-in controller.     

一种双足机器人实时步态规划方法及相关数值算法

针对步行双足机器人实时步态规划问题,提出了一种改进的非线性模型预测控制（NMPC）方法．采用扩展的关节坐标,将单腿支撑相（SSP）和双腿支撑相（DSP）统一表示为一个非线性动力学模型．通过对SSP和DSP的3个阶段设定运动学和动力学虚拟约束,将复杂实时步态规划问题转化为4个以预测时域内控制量二次型为代价函数的NMPC问题．采用直接法将连续优化问题参数化为有限维优化问题,并采用惩罚函数法将状态变量约束转化为代价函数中的惩罚项,从而得到能够用渐进二次规划（SQP）求解的有限维静态优化问题．仿真结果表明,应用该方法对BIP机器人模型进行实时步态规划,实现了包含足部转动的动态步行,且机器人满足稳定性条件,不发生侧滑,从而证明了该方法的有效性和可实现性．     

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.