A dynamic programming based approach for explicit model predictive control of hybrid systems

This work presents an algorithm for explicit model predictive control of hybrid systems based on recent developments in constrained dynamic programming and multi-parametric programming. By using the proposed approach, suitable for problems with linear cost function, the original model predictive control formulation is disassembled into a set of smaller problems, which can be efficiently solved using multi-parametric mixed-integer programming algorithms. It is also shown how the methodology is applied in the context of explicit robust model predictive control of hybrid systems, where model uncertainty is taken into account. The proposed developments are demonstrated through a numerical example where the methodology is applied to the optimal control of a piece-wise affine system with linear cost function.     

Iterative learning model predictive control for constrained multivariable control of batch processes

In this paper, we propose a model predictive control (MPC) technique combined with iterative learning control (ILC), called the iterative learning model predictive control (ILMPC), for constrained multivariable control of batch processes. Although the general ILC makes the outputs converge to reference trajectories under model uncertainty, it uses open-loop control within a batch; thus, it cannot reject real-time disturbances. The MPC algorithm shows identical performance for all batches, and it highly depends on model quality because it does not use previous batch information. We integrate the advantages of the two algorithms. The proposed ILMPC formulation is based on general MPC and incorporates an iterative learning function into MPC. Thus, it is easy to handle various issues for which the general MPC is suitable, such as constraints, time-varying systems, disturbances, and stochastic characteristics. Simulation examples are provided to show the effectiveness of the proposed ILMPC.     

A delay‐dependent robust fuzzy MPC approach for nonlinear CSTR

Based on Takagi–Sugeno (T–S) fuzzy models, a robust fuzzy model predictive control (MPC) algorithm is presented for a class of nonlinear time‐delay systems with input constraints. Delay‐dependent sufficient conditions for the robust stability of the closed‐loop system are derived, and the condition for the existence of the fuzzy model predictive controller is formulated in terms of nonlinear matrix inequality via the parallel distributed compensation (PDC) approach. By using a novel matrix transform technique, a receding optimization problem with linear matrix inequality (LMIs) constraints is constructed to design the desired controllers with an on‐line optimal receding horizon guaranteed cost. Finally, an example of continuous stirred tank reactors (CSTR) is given to demonstrate the effectiveness of the proposed results.     

Multivariable model predictive control of a novel rapid pressure swing adsorption system

A multivariable model predictive control (MPC) algorithm is developed for the control and operation of a rapid pressure swing adsorption (RPSA)‐based medical oxygen concentrator. The novelty of the approach is the use of all four step durations in the RPSA cycle as independent manipulated variables in a truly multivariable context. The RPSA has a complex, cyclic, nonlinear multivariable operation that requires feedback control, and MPC provides a suitable framework for controlling such a multivariable system. The multivariable MPC presented here uses a quadratic optimization program with integral action and a linear model identified using subspace system identification techniques. The controller was designed and tested in simulation using a complex, highly coupled, nonlinear RPSA process model. The model was developed with the least restrictive assumptions compared to those reported in the literature, thereby providing a more realistic representation of the underlying physical phenomena. The resulting MPC effectively tracks set points, rejects realistic process disturbances and is shown to outperform conventional PID control. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1234–1245, 2018     

基于自适应模糊神经网络的非线性系统模型预测控制

针对非线性动态系统的控制问题,提出了一种基于自适应模糊神经网络(adaptive fuzzy neural network, AFNN)的模型预测控制(model predictive control, MPC)方法。首先,在离线建模阶段,AFNN采用规则自分裂技术产生初始模糊规则,采用改进的自适应LM学习算法优化网络参数;然后,在实时控制过程,AFNN根据系统输出和预测输出之间的误差调整网络参数,从而为MPC提供一个精确的预测模型;进一步,AFNN-MPC利用带有自适应学习率的梯度下降寻优算法求解优化问题,在线获取非线性控制量,并将其作用到动态系统实施控制。此外,给出了AFNN-MPC的收敛性和稳定性证明,以保证其在实际工程中的成功应用。最后,利用数值仿真和双CSTR过程进行实验验证。结果表明,AFNN-MPC能够取得优越的控制性能。     

Hybrid fuzzy predictive control based on genetic algorithms for the temperature control of a batch reactor

In this paper we describe the design of hybrid fuzzy predictive control based on a genetic algorithm (GA). We also present a simulation test of the proposed algorithm and a comparison with two hybrid predictive control methods: Explicit Enumeration and Branch and Bound (BB). The experiments involved controlling the temperature of a batch reactor by using two on/off input valves and a discrete-position mixing valve. The GA-hybrid predictive control strategy proved to be a suitable method for the control of hybrid systems, giving similar performance to that of typical hybrid predictive control strategies and a significant saving with respect to the computation time.     

An Off-Line Formulation of Tube-Based Robust MPC Using Polyhedral Invariant Sets

In this paper, an off-line formulation of tube-based robust model predictive control (MPC) using polyhedral invariant sets is proposed. A novel feature is the fact that no optimal control problem needs to be solved at each sampling time. Moreover, the proposed tube-based robust MPC algorithm can deal with the linear time-varying (LTV) system with bounded disturbance. The simulation results show that the state at each time step is restricted to lie within a tube whose center is the state of the nominal LTV system that converges to the origin. Finally, the state is kept within a tube whose center is at the origin, so robust stability is guaranteed. Satisfaction of the state and control constraints is guaranteed by employing tighter constraint sets for the nominal LTV system.     

Repetitive model predictive control of a reverse flow reactor

This paper deals with the control of a catalytic reverse flow reactor (RFR) used for methane combustion. The periodic flow reversals effected on the system makes it both continuous and discrete in nature (i.e., a hybrid system). Control of this system is challenging due to the unsteady state behavior of the process along with its mixed discrete and continuous behavior. Although model predictive control (MPC) is proven to be a powerful technique for several processes it becomes less effective in systems such as the RFR where the model prediction errors and the effect of disturbances on the plant output repeat from time to time. In such cases, control can be improved if the repetitive error pattern is exploited. A novel repetitive model predictive control (RMPC) strategy, that combines the basic concepts of iterative learning control (ILC) and repetitive control (RC) along with the concepts of MPC, is proposed for such systems. In the proposed strategy, the state variables of the model are reset periodically along with predictive control action such that the process follows the reference trajectory as closely as possible. The results obtained prove that the RMPC approach provides an excellent performance for the control of the RFR.     

Robust decision making for hybrid process supply chain systems via model predictive control

Model predictive control (MPC) is a promising solution for the effective control of process supply chains. This paper presents an optimization-based decision support tool for supply chain management, by means of a robust MPC strategy. The proposed formulation: (i) captures uncertainty in model parameters and demand by stochastic programming, (ii) accommodates hybrid process systems with decisions governed by logical conditions/rulesets, and (iii) addresses multiple supply chain performance metrics including customer service and economics, within an integrated optimization framework. Two mechanisms for uncertainty propagation are presented – an open-loop approach, and an approximate closed-loop strategy. The performance of the robust MPC framework is analyzed through its application to two process supply chain case studies. The proposed approach is shown to provide a substantial reduction in the occurrence of back orders when compared to a nominal MPC implementation.     

Multi-model predictive control of SCR flue gas denitrification system in coal-fired power plant based on kernel fuzzy c-means clustering and integrated model

A multi-model predictive control strategy based on kernel fuzzy c-means (KFCM) clustering and integrated model is proposed for the complex problem of rapid and accurate control of ammonia injection in selective catalytic reduction (SCR) denitrification systems of coal-fired power plants under a wide range of variable load conditions. First, the SCR data samples are clustered using the KFCM clustering algorithm, and the number of clusters is determined by introducing the Xie-Beni index. Second, the prediction model of the SCR denitrification system is established by an integrated modelling approach, and the sub-learners of the integrated model are the genetic algorithm optimized back propagation (GA-BP) neural network model and the least squares support vector machine (LSSVM) model. Third, a multi-model prediction controller based on the particle swarm optimization (PSO) algorithm and the integrated model is designed and developed. To ensure the stability of the system, a model-switching strategy based on the minimum Euclidean distance is proposed. Finally, simulation verification and industrial field application verification are fulfilled by comparing with proportion integral differential (PID) control and single model predictive control (MPC). The results show that the multi-model predictive control method proposed in this paper can obtain higher control accuracy and better control stability and meet the control requirements for the long-term operation of the SCR denitrification system.     

Off-line model reduction for on-line linear MPC of nonlinear large-scale distributed systems

Model predictive control (MPC) is an efficient method for the controller design of a large number of processes. However, linear MPC is often inappropriate for controlling nonlinear large-scale systems, while non-linear MPC can be computationally costly. The resulting optimization-based procedure can lead to local minima due to the, non-convexities that non-linear systems can exhibit. To overcome the excessive computational cost of MPC application for large-scale nonlinear systems, model reduction methodology in conjunction with efficient system linearizations have been exploited to enable the efficient application of linear MPC for nonlinear distributed parameter systems (DPS). An off-line model reduction technique, the proper orthogonal decomposition (POD) method, combined with a finite element Galerkin projection is first used to extract accurate non-linear low-order models from the large-scale ones. Trajectory Piecewise-Linear (TPWL) methodologies are subsequently developed to construct a piecewise linear representation of the reduced nonlinear model, both in a static and in a dynamic fashion. Linear MPC, based on quadratic programming, can then be efficiently performed on the resulting low-order, piece-wise affine system. Our combined methodology is readily applicable in combination with advanced MPC methodologies such as multi-parametric MPC (MP-MPC) (Pistikopoulos, 2009). The stabilisation of the oscillatory behaviour of a tubular reactor with recycle is used as an illustrative example to demonstrate our methodology.     

A robustly stabilizing fault-tolerant MPC: A performance improvement-based approach

In terms of model predictive control (MPC) performance degradation caused by operational faults, in this article, a robust MPC strategy with active fault tolerance properties is proposed. The proposed strategy incorporates a fault supervision layer into the structure of conventional cost-contracting formulation-based robust MPC for the online update of the nominal controller model in the event of faults. The robust MPC is based on multiplant uncertainty, while the supervisory layer consists of a bank of unknown input observers and a decision-making algorithm. Simulation results in a nonlinear polymerization reactor subject to process faults demonstrate that the proposed approach offers superior performance compared to the conventional strategy.     

基于区间运算的字典序多目标模型预测控制

考虑优化级多目标优化控制问题,提出一种基于区间运算的字典序多目标模型预测控制算法。对约束线性系统,结合字典序列法和滚动优化原理,建立按优先级定义的分层多目标模型预测控制策略。在此基础上,引入区间运算法则,在线求解预测控制量。通过一双容水箱单输入双输出液位控制,仿真验证了该方法的有效性。     

An optimal filter based MPC for systems with arbitrary disturbances

In this study, a linear model predictive control (MPC) approach with optimal filters is proposed for handling unmeasured disturbances with arbitrary statistics. Two types of optimal filters are introduced into the framework of MPC to relax the assumption of integrated white noise model in existing approaches. The introduced filters are globally optimal for linear systems with unmeasured disturbances that have unknown statistics. This enables the proposed MPC to better handle disturbances without access to disturbance statistics. As a result, the effort required for disturbance modeling can be alleviated. The proposed MPC can achieve offset-free control in the presence of asymptotically constant unmeasured disturbances. Simulation results demonstrate that the proposed approach can provide an improved disturbance õrejection performance over conventional approaches when applied to the control of systems with unmeasured disturbances that have arbitrary statistics.     

Multi-rate observer design and optimal control to maximize productivity of an industry-scale fermentation process

Chemical industries focus primarily on profitable operations, resulting in growing attention and advances in the field of digital twins and optimal control algorithms. However, most industries still struggle due to a lack of physical sensors, infrequent measurements, and asynchronous sampling. Thus, in this work, we have designed a multi-rate state observer for state estimation from plant measurements and developed a model predictive controller (MPC) that maximized the profitability of an industry-scale fermentation process (fermenter volume < 378,500 L). Additionally, as the fermentation process is complex due to the use of microorganisms, which cannot be accurately captured using a first-principles model, we utilize a previously developed hybrid model in the proposed MPC formulation. The MPC uses a GAMS-MATLAB framework to determine the optimal input profiles while considering practical process constraints. It is shown using multiple datasets, that the MPC can increase productivity while also decreasing the plant operating cost.     

On improving accuracy of computationally efficient nonlinear predictive control based on neural models

For nonlinear processes the classical model predictive control (MPC) algorithm, in which a linear model is used, usually does not give satisfactory closed-loop performance. In such nonlinear cases a suboptimal MPC strategy is typically used in which the nonlinear model is successively linearised on-line for the current operating point and, thanks to linearisation, the control policy is calculated from a quadratic programming problem. Although the suboptimal MPC algorithm frequently gives good results, for some nonlinear processes it would be beneficial to further improve control accuracy. This paper details a computationally efficient nonlinear MPC algorithm in which a neural model is linearised on-line along the predicted trajectory in an iterative way. The algorithm needs solving on-line only a series of quadratic programming problems. Advantages of the discussed algorithm are demonstrated in the control system of a high-purity ethylene–ethane distillation column for which the classical linear MPC algorithm does not work and the classical suboptimal MPC algorithm is slow. It is shown that the discussed algorithm can give practically the same control accuracy as the algorithm with on-line nonlinear optimisation and, at the same time, the algorithm is significantly less computationally demanding.     

Machine learning-based model predictive control of hybrid dynamical systems

This article presents a machine learning-based model predictive control (MPC) scheme for stabilization of hybrid dynamical systems, for which the evolution of states exhibits both continuous and discrete dynamics described by differential and difference equations, respectively. We first present the development of two recurrent neural networks (RNNs) for approximating continuous- and discrete-time dynamics of hybrid dynamical systems, respectively, and then construct a unified hybrid RNN by integrating the two RNN models to capture both continuous and discrete dynamics. The hybrid RNN is used as the prediction model in Lyapunov-based MPC (RNN-LMPC), under which closed-loop stability of hybrid dynamical systems is established. Finally, two case studies including a bouncing ball example and a chemical process are utilized to illustrate the open- and closed-loop performance of the proposed RNN-LMPC scheme.     

Hybrid convolution model and its application in predictive pH control

This paper presents a new method for synthesising chemical process models that combines prior knowledge and fuzzy models. The hybrid convolution model consists of a fuzzy model based steady-state, and an impulse response model based dynamic part. Prior knowledge enters to the dynamic part as a resident time distribution model of the process. The proposed approach is applied in the modelling and model based control of a highly nonlinear pH process.     

Scheduling of a mixed batch/continuous sugar milling plant using Petri nets

Scheduling of processes in mixed batch/continuous plants, due to their hybrid nature, can become very complex. This paper presents the Timed Hybrid Petri net (THPN) as a suitable tool for modelling and scheduling of hybrid systems. One of the major benefits over traditional methods is a significant reduction in complexity during problem formulation. A sugar milling plant containing both batch and continuous processing units is used to illustrate the application of the proposed scheduling algorithm.