A two-layer architecture for economically optimal process control and operation

A two-layer architecture for dynamic real-time optimization (or nonlinear modelpredictive control (NMPC) with an economic objective) is presented, where the solution of the dynamic optimization problem is computed on two time-scales. On the upper layer, a rigorous optimization problem is solved with an economic objective function at a slow time-scale, which captures slow trends in process uncertainties. On the lower layer, a fast neighboring-extremal controller is tracking the trajectory in order to deal with fast disturbances acting on the process. Compared to a single-layer architecture, the two-layer architecture is able to address control systems with complex models leading to high computational load, since the rigorous optimization problem can be solved at a slower rate than the process sampling time. Furthermore, solving a new rigorous optimization problem is not necessary at each sampling time if the process has rather slow dynamics compared to the disturbance dynamics. The two-layer control strategy is illustrated with a simulated case study of an industrial polymerization process.     

On finite-time and infinite-time cost improvement of economic model predictive control for nonlinear systems

A novel two-layer economic model predictive control (EMPC) structure that addresses provable finite-time and infinite-time closed-loop economic performance of nonlinear systems in closed-loop with EMPC is presented. In the upper layer, a Lyapunov-based EMPC (LEMPC) scheme is formulated with performance constraints by taking advantage of an auxiliary Lyapunov-based model predictive control (LMPC) problem solution formulated with a quadratic cost function. The lower layer LEMPC uses a shorter prediction horizon and smaller sampling period than the upper layer LEMPC and involves explicit performance-based constraints computed by the upper layer LEMPC. Thus, the two-layer architecture allows for dividing dynamic optimization and control tasks into two layers for a computationally manageable control scheme at the feedback control (lower) layer. A chemical process example is used to demonstrate the performance and stability properties of the two-layer LEMPC structure.     

基于满意优化的非线性预测控制

对多约束的非线性系统建立T—S模糊模型,采用局部线性化方法在每个采样点对非线性系统进行线性化,从而得到系统的线性化模型。针对传统的优化方法无法直接处理带有一定模糊不确定性的优化问题,该文在广义预测控制滚动优化的机制下把具有模糊边界约束的有限预测时域的优化问题,转化为等价的确定性规划问题,通过模糊规划方法来求解多约束的目标函数,从而用满意优化取代传统的二次型性能指标来求解模糊约束条件的预测控制。仿真结果表明了该方法的有效性。     

Dissolved oxygen control for activated sludge processes

Controllers for dissolved oxygen reference trajectory tracking for activated sludge processes are proposed and investigated. A nonlinear model predictive controller and a direct reference adaptive controller are investigated. Both the nutrient and the phosphorous removal from a wastewater by its biological treatment using an activated sludge technology are considered. An approach to the controller design utilises a structure of the dissolved oxygen dynamics and its two time scales: fast and slow. The predictive controllers offer good tracking performance and robustness. The direct model reference adaptive controller is much simpler to implement. However, it is more difficult to compromise between tracking accuracy and rate of change and magnitudes of the control actions. The controllers are validated by simulation using real data sets and an ASM2d model of the biological reactor.     

Nonlinear model predictive control using deterministic global optimization

This paper presents a Nonlinear Model Predictive Control (NMPC) algorithm utilizing a deterministic global optimization method. Utilizing local techniques on nonlinear nonconvex problems leaves one susceptible to suboptimal solutions at each iteration. In complex problems, local solver reliability is difficult to predict and dependent upon the choice of initial guess. This paper demonstrates the application of a deterministic global solution technique to an example NMPC problem. A terminal state constraint is used in the example case study. In some cases the local solution method becomes infeasible, while the global solution correctly finds the feasible global solution. Increased computational burden is the most significant limitation for global optimization based online control techniques. This paper provides methods for improving the global optimization rates of convergence. This paper also shows that globally optimal NMPC methods can provide benefits over local techniques and can successfully be used for online control.     

Approximation of Model Predictive Control Laws for Polynomial Systems

A fast implementation of a given predictive controller for polynomial systems is introduced by approximating the optimal control law with a piecewise constant function defined over a hyper‐cube partition of the system state space. Such a state‐space partition is computed in order to guarantee stability, an a priori fixed trajectory error as well as input and state constraints fulfilment. The presented approximation procedure is achieved by solving a set of nonconvex polynomial optimization problems, whose approximate solutions are computed by means of semidefinite relaxation techniques for semialgebraic problems.     

Generalized terminal state constraint for model predictive control

A terminal state equality constraint for Model Predictive Control (MPC) laws is investigated, where the terminal state/input pair is not fixed a priori but it is a free variable in the optimization. The approach, named “generalized” terminal state constraint, can be used for both tracking MPC (i.e. when the objective is to track a given steady state) and economic MPC (i.e. when the objective is to minimize a cost function which does not necessarily attains its minimum at a steady state). It is shown that the proposed technique provides, in general, a larger feasibility set with respect to the existing approaches, given the same prediction horizon. Moreover, a new receding horizon strategy is introduced, exploiting the generalized terminal state constraint. Under mild assumptions, the new strategy is guaranteed to converge in finite time, with arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal state constraint, while still enjoying a larger feasibility set. The features of the new technique are illustrated by an inverted pendulum example in both the tracking and the economic contexts.     

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.     

不确定系统的稳定广义预测控制

针对一类有界不确定线性离散被控对象,采用Min-Max优化方法,提出一种新的稳定广义预测控制(MMSGPC)算法.引入内模控制结构,将干扰和不确定性从被控对象中分离出来,并利用局部反环节对其进行补偿;采用Min-Max优化方法,将终端约束条件转化为有界不确定性最差情况时应的线性方程;通过引入矩阵的Moore-Penrose逆,得到了终端约束线性方程的通解,并结合性能指标函数求得了最优控制律.通过仿真实例验证了该方法的稳定效果.     

混合动力汽车模型预测控制策略研究

针对传统混合动力汽车控制方法无法实现实时最优控制的问题,提出了基于简化混合动力汽车系统模型的预测控制智能优化策略.通过将3自由度的系统模型简化为1自由度的系统模型,并采用连续广义最小残量方法求解模型预测控制问题.运用MATLAB/Simulink与GT-POWER联合仿真平台进行仿真,实验结果验证了系统模型简化的有效性,以及所设计的模型预测控制算法大幅度提高混合动力汽车的燃油经济性的能力和实时控制性能.     

Convergence in economic model predictive control with average constraints

In this paper, we thoroughly investigate various aspects of economic model predictive control with average constraints, i.e., constraints on average values of state and input variables. In particular, we first show that a certain time-varying output constraint has to be included into the MPC problem formulation in order to ensure fulfillment of these average constraints. Optimizing a general (possibly economic) performance criterion may result in a non-converging behavior of the corresponding closed-loop system. While such a behavior might be acceptable in some cases, it may be undesirable for other types of applications. Hence as a second contribution, we provide a Lyapunov-like analysis to conclude that indeed asymptotic convergence to the optimal steady-state follows if the system satisfies a certain dissipativity condition. Finally, for the case that this dissipativity property is not satisfied but still a convergent behavior of the closed-loop is required, we examine two different methods how convergence can be enforced within an economic MPC setup by imposing additional average constraints on the system. In the first method, an additional average constraint is defined which results in the system being dissipative, while the second consists of imposing an additional even zero-moment average constraint. We illustrate our results with various examples.     

Predictive control for a class of distributed delay systems using Chebyshev polynomials

In this paper, the model predictive control (MPC) is developed for linear time-varying systems with distributed time delay in state. The Chebyshev operational matrices of product, integration and delay are utilized to transform the solution of distributed delay differential equation to the solution of algebraic equations. The Chebyshev functions are also applied to derive approximate solution of finite horizon optimal control problem involved in MPC. The proposed method is simple and computationally advantageous. Illustrative example demonstrates the validity and applicability of the technique.     

Distributed model predictive control over network information exchange for large-scale systems

A class of large scale systems, which is naturally divided into many smaller interacting subsystems, are usually controlled by a distributed or decentralized control framework. In this paper, a novel distributed model predictive control (MPC) is proposed for improving the performance of entire system. In which each subsystem is controlled by a local MPC and these controllers exchange a reduced set of information with each other by network. The optimization index of each local MPC considers not only the performance of the corresponding subsystem but also that of its neighbours. The proposed architecture guarantees satisfactory performance under strong interactions among subsystems. A stability analysis is presented for the unconstrained distributed MPC and the provided stability results can be employed for tuning the controller. Experiment of the application to accelerated cooling process in a test rig is provided for validating the efficiency of the proposed method.     

Nonlinear multiobjective model-predictive control scheme for wastewater treatment process

A nonlinear multiobjective model-predictive control (NMMPC) scheme, consisting of self-organizing radial basis function (SORBF) neural network prediction and multiobjective gradient optimization, is proposed for wastewater treatment process (WWTP) in this paper. The proposed NMMPC comprises a SORBF neural network identifier and a multiple objectives controller via the multi-gradient method (MGM). The SORBF neural network with concurrent structure and parameter learning is developed as a model identifier for approximating on-line the states of WWTP. Then, this NMMPC optimizes the multiple objectives under different operating functions, where all the objectives are minimized simultaneously. The solution of optimal control is based on the MGM which can shorten the solution time. Moreover, the stability and control performance of the closed-loop control system are well studied. Numerical simulations reveal that the proposed control strategy gives satisfactory tracking and disturbance rejection performance for WWTP. Experimental results show the efficacy of the proposed method.     

A switching robust model predictive control approach for nonlinear systems

This work considers enhancing the stability and improving the economic performance of nonlinear model predictive control in the presence of disturbances or model uncertainties. First, a robust control Lyapunov function (RCLF)-based predictive control strategy is proposed. Second, the approximate dynamic programming (ADP) is employed to further improve regulation performance. Finally, the ADP and RCLF-MPC are combined to provide a switching control scheme, which is illustrated on a CSTR example to show its effectiveness.     

一类非线性系统的次优控制研究

考虑一类关系度不确定且零动态稳定的非线性系统的控制器设计问题．利用预测控制概念,通过选用较为全面的二次型性能指标,对输出进行高阶泰勒级数展开,推导出一种非切换的解析次优控制律,进而得出了在该控制律下闭环系统局部稳定的充分条件．仿真例子验证了该控制算法具有较好的动态性能,与已有的近似线性化方法相比,显示了该控制策略的优越性．     

Nonlinear model predictive control of a magnetic levitation system

The paper presents a fast nonlinear model predictive control (MPC) scheme for a magnetic levitation system. A nonlinear dynamical model of the levitation system is derived that additionally captures the inductor current dynamics of the electromagnet in order to achieve a high MPC performance both for stabilization and fast setpoint changes of the levitating mass. The optimization algorithm underlying the MPC scheme accounts for control constraints and allows for a time and memory efficient computation of the single iteration. The overall control performance of the levitation system as well as the low computational costs of the MPC scheme is shown both in simulations and experiments with a sampling frequency of 700 Hz on a standard dSPACE hardware.     

Nonlinear MPC based on a Volterra series model for greenhouse temperature control using natural ventilation

Suitable environmental conditions are a fundamental issue in greenhouse crop growth and can be achieved by advanced climate control strategies. In different climatic zones, natural ventilation is used to regulate both the greenhouse temperature and humidity. In mild climates, the greatest problem faced by far in greenhouse climate control is cooling, which, for dynamical reasons, leads to natural ventilation as a standard tool. This work addresses the design of a nonlinear model predictive control (NMPC) strategy for greenhouse temperature control using natural ventilation. The NMPC strategy is based on a second-order Volterra series model identified from experimental input/output data of a greenhouse. These models, representing the simple and logical extension of convolution models, can be used to approximate the nonlinear dynamic effect of the ventilation and other environmental conditions on the greenhouse temperature. The developed NMPC is applied to a greenhouse and the control performance of the proposed strategy will be illustrated by means of experimental results.