Disturbance rejection of ball mill grinding circuits using DOB and MPC

Ball mill grinding circuit is essentially a multivariable system with couplings, time delays and strong disturbances. Many advanced control schemes, including model predictive control (MPC), adaptive control, neuro-control, robust control, optimal control, etc., have been reported in the field of grinding process. However, these control schemes including the MPC scheme usually cannot achieve satisfying effects in the presence of strong disturbances. In this paper, disturbance observer (DOB), which is widely used in motion control applications, is introduced to estimate the disturbances in grinding circuit. A compound control scheme, consisting of a feedforward compensation part based on DOB and a feedback regulation part based on MPC (DOB-MPC), is thus developed. A rigorous analysis of disturbance rejection performance is given with the considerations of both model mismatches and external disturbances. Simulation results demonstrate that when controlling the ball mill grinding circuit, the DOB-MPC method possesses a better performance in disturbance rejection than that of the MPC method.     

Disturbance rejection of dead-time processes using disturbance observer and model predictive control

This article mainly focuses on disturbance rejection of dead-time processes by integrating a modified disturbance observer (MDOB) with a model predictive controller (MPC). The effect caused by model mismatches is regarded as a part of the lumped disturbances. This means that the disturbances considered here include not only external disturbances, but also internal disturbances caused by model mismatches. Control structure of the proposed method includes two parts which can be designed separately. The MPC which acts as a prefilter, is employed to generate appropriate control actions such that a desired setpoint tracking response is achieved. The MDOB is employed to estimate the disturbances of the closed-loop system, and the estimation is used for feedforward compensation design to reject disturbances. Rigorous analysis of setpoint tracking and disturbance rejection properties of the closed-loop system are given in the presence of both model mismatches and external disturbances. The proposed scheme is applied to control the temperature of a simplified jacketed stirred tank heater (JSTH). Simulation results demonstrate that the proposed method possesses a better disturbance rejection performance than those of the MDOB-PI, MPC and PI methods in controlling such dead-time processes.     

Model predictive control of an industrial pyrolysis gasoline hydrogenation reactor

This study focuses on the implementation of a nonlinear model predictive control (MPC) algorithm for controlling an industrial fixed-bed reactor where hydrogenations of raw pyrolysis gasoline occur. An orthogonal collocation method is employed to approximate the original reactor model consisting of a set of partial differential equations. The approximate model obtained is used in the synthesis of a MPC controller to control the temperature rising across a catalyst bed within the reactor. In the MPC algorithm, a sequential optimization approach is used to solve an open-loop optimal control problem. Feedback information is incorporated in the MPC to compensate for modeling error and unmeasured disturbances. The control studies are demonstrated in cases of set point tracking and disturbance rejection.     

基于改进DOB的矿物研磨过程最优运行先进反馈控制(英文)

Advanced feedback control for optimal operation of mineral grinding process is usually based on the model predictive control (MPC) dynamic optimization. Since the MPC does not handle disturbances directly by controller design, it cannot achieve satisfactory effects in controlling complex grinding processes in the presence of strong disturbances and large uncertainties. In this paper, an improved disturbance observer (DOB) based MPC advanced feedback control is proposed to control the multivariable grinding operation. The improved DOB is based on the optimal achievable H 2 performance and can deal with disturbance observation for the nonminimum-phase delay systems. In this DOB-MPC advanced feedback control, the higher-level optimizer computes the optimal operation points by maximize the profit function and passes them to the MPC level. The MPC acts as a presetting controller and is employed to generate proper pre-setpoint for the lower-level basic feedback control system. The DOB acts as a compensator and improves the operation performance by dynamically compensating the setpoints for the basic control system according to the observed various disturbances and plant uncertainties. Several simulations are performed to demonstrate the proposed control method for grinding process operation.     

Hybrid fuzzy model-based predictive control of temperature in a batch reactor

Processes in industry, such as batch reactors, often demonstrate a hybrid and non-linear nature. Model predictive control (MPC) is one of the approaches that can be successfully employed in such cases. However, due to the complexity of these processes, obtaining a suitable model is often a difficult task. In this paper a hybrid fuzzy modelling approach with a compact formulation is introduced. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for the hybrid fuzzy modelling purposes is presented. An efficient method for identifying the hybrid fuzzy model is also proposed.

A MPC algorithm suitable for systems with discrete inputs is treated. The benefits of the MPC algorithm employing the proposed hybrid fuzzy model are verified on a batch-reactor simulation example: a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model was made. We established that the latter approach clearly outperforms the approach where a linear model is used.     

一种扰动自适应的鲁棒预测控制算法

针对实际生产中扰动的时变性,提出了一种扰动自适应的鲁棒预测控制（RAMPC）算法以提高扰动抑制性能。采用时间序列（ARMA）模型在线辨识系统的不可测扰动,通过基于多次迭代思想的递推辨识算法（multi-iteration pseudo-linear regression,MIPLR）来保证在线辨识的质量和收敛速度。考虑到数据与辨识模型的不确定性,改用min-max形式描述MPC算法的控制作用优化命题,并将在线辨识过程中的误差数据引入min-max命题,使在线辨识与控制作用鲁棒优化求解紧密结合起来,提高算法鲁棒性。进一步将此min-max问题转换为一个等效的非线性min问题,并采用多步线性化方法实现快速求解,解决了传统min-max方法在线计算负荷高的问题。仿真结果表明了该算法的有效性。     

基于加权偏离度统计方法的预测控制性能评估算法

针对带区域约束条件的预测控制系统性能评估问题,在考虑过程输出变量约束类型的基础上,提出了基于加权偏离度统计方法的控制性能评估算法。该方法依据控制要求的不同,将输出变量分为质量变量和约束变量,并结合工程经验合理选择变量的权重。基于系统闭环运行数据和约束设置,通过计算变量的加权偏离度得到控制系统的性能评估指标,从而为预测控制器的参数调整和性能提升提供了决策依据。系统仿真实例和工程应用证明了该评估算法对区域预测控制系统性能评估的有效性。     

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.     

受扰双线性系统的近似最优扰动抑制方法

研究具有外界持续扰动作用下双线性系统的最优控制问题.关于二次型性能指标给出了一种设计最优扰动抑制控制律的逐次逼近方法.利用该算法可将在扰动作用下双线性系统的最优控制问题转化为求解一组线性非齐次两点边值序列问题.通过迭代序列得到的最优扰动抑制控制律由解析的线性前馈-反馈项和序列极限形式的非线性补偿项组成.通过截取非线性补偿序列的有限项,可以得到近似最优扰动抑制控制律.仿真结果表明,该方法抑制外部持续扰动的鲁棒性优于经典反馈最优控制.     

基于结构逼近式神经网络的间歇反应器优化控制

利用结构逼近式混合神经网络（SAHNN）建立了一类典型放热液相二级平行间歇反应的数学模型。基于主产物浓度和反应温度的递归神经网络（RNN）模型,使用混合PSO-SQP算法求解该间歇反应主产物产率最大化问题,进而得到反应温度优化曲线。鉴于反应温度实时可测,提出扩展的EISE指标,该指标把实时计算的模型误差引入控制策略,为基于模型的控制增加了反馈通道,增强了控制方法的鲁棒性和抗干扰性能。利用 原理对所提出的一步超前预测控制做了稳定性分析,证明了算法的正确性。研究的结果充分证明了基于SAHNN混合神经网络模型的优化控制策略的有效性。     

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.     

Performance assessment of MIMO control systems with time-variant disturbance dynamics

In this paper, we consider performance assessment problem for multivariable control systems subject to piecewise constant time varying disturbance dynamics. The problem is motivated by the observation that most industrial controllers are linear time invariant (LTI) but the process, particularly the disturbance dynamics, can be time varying. We consider a class of disturbance dynamics that can be modelled by piecewise linear disturbance models, namely piecewise linear time varying (LTV) disturbance dynamics. The problem is formulated as searching for a multi-input multi-output (MIMO) benchmark control that is LTI but optimal in regulating the LTV disturbances. The single-input single-output (SISO) case has been previously solved by minimizing the variance of a most representative disturbance or by the minimization of the sum of the weighted variances of all but one of major disturbances, while satisfying a structured regulatory performance requirement for the major disturbance. In this paper, the previous results are extended to MIMO systems. The counterparts of the two SISO benchmarks are defined as the regular linear time varying disturbances (LTVDs) benchmark and the weighted LTVD benchmark for MIMO control systems, respectively. In addition, a new yet more practical LTVD benchmark, the generalized LTVD benchmark, is also proposed, which minimizes the maximum total variance among all different disturbance dynamics. These three LTVD benchmarks are compared by simulation and industrial application examples. The results show that the weighted and generalized LTVD benchmarks can always lead to better trade-offs on the total output variances.     

ROBUST NONLINEAR PREDICTIVE CONTROL USING A DISTURBANCE ESTIMATOR

A robust nonlinear predictive control strategy using a disturbance estimator is presented. The disturbance estimator is comprised of two parts: one is the disturbance model parameter adaptation and the other is future disturbance prediction. A linear discrete model is proposed as a disturbance model which is formulated by using process inputs and available process measurements. The recursive least square (RLS) method with exponential forgetting is used to determine the uncertain disturbance model parameters and for the future disturbance prediction, future disturbances projected by the future process inputs are used. Two illustrative examples: a jacketed CSTR as a SISO system: an adiabatic CSTR as a MIMO system, and experimental results of the distillation column control are presented. The results indicate that a substantial improvement in nonlinear predictive control performance is possible using the disturbance estimator.     

Application of state estimation based NMPC to an unstable nonlinear process

Model predictive control (MPC) has become very popular both in process industry and academia due to its effectiveness in dealing with nonlinear, multivariable and/or hard-constrained plants.Although linear MPC can be applied for controlling nonlinear processes by obtaining a linearized model of the plant, this is only valid in a limited region. Therefore, a substantial improvement can be achieved by using the whole knowledge of the process dynamics, specially in the presence of marked nonlinearities. This effect can be strong if the process to control is open-loop unstable.The purpose of this paper is to introduce a nonlinear model predictive controller (NMPC) based on nonlinear state estimation, in order to exploit the knowledge of the nonlinear dynamics and to avoid modeling simplifications or linearization.A state-space formulation is proposed to achieve the control objective. To update the optimization involved in NMPC strategy, state estimation based on the measured outputs is proposed.As a particular application, we consider an open-loop unstable jacketed exothermic chemical reactor. This CSTR is widely recognized as a difficult problem for the purpose of control. In order to achieve the control goal, a NMPController coupled with a state observer are designed. The observer is also used to estimate some unmeasured disturbances. Finally, computer simulations are developed for showing the performance of both the nonlinear observer and the control strategy.     

An experimental evaluation of Kalman filtering

The effectiveness of the stationary form of the discrete Kalman filter for state estimation in noisy process systems was demonstrated by simulated and experimental tests on a pilot plant evaporator. The filter was incorporated into a multivariable, computer control system and resulted in good control despite process and/or measurement noise levels of 10%. The results were significantly better than those obtained when the Kalman filter was omitted or replaced by conventional exponential filters. In this application the standard Kalman filter was reasonably insensitive to incorrect estimates of initial conditions or noise statistics and to errors in model parameters. The filter estimates were sensitive to unmeasured process disturbances. However this sensitivity could be reduced by treating the noise covariance matrices R and Q as design parameters rather than noise statistics and selecting values which result in increased weighting of the process measurements relative to the calculated model states.     

Simultaneous process synthesis and control design under uncertainty: A worst‐case performance approach

A new methodology that includes process synthesis and control structure decisions for the optimal process and control design of dynamic systems under uncertainty is presented. The method integrates dynamic flexibility and dynamic feasibility in a single optimization formulation, thus, reducing the costs to assess the optimal design. A robust stability test is also included in the proposed method to ensure that the optimal design is stable in the presence of magnitude‐bounded perturbations. Since disturbances are treated as stochastic time‐discrete unmeasured inputs, the optimal process synthesis and control design specified by this method remains feasible and stable in the presence of the most critical realizations in the disturbances. The proposed methodology has been applied to simultaneously design and control a system of CSTRs and a ternary distillation column. A study on the computational costs associated with this method is presented and compared to that required by a dynamic optimization‐based scheme. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2497–2514, 2013     

基于扰动观测器的模型预测控制在磨矿分级过程中的应用

磨矿分级过程（GCP）是冶金选矿行业的关键流程,其产品粒度指标必须严格控制,以保证精矿产品品位和金属回收率。GCP本质上是一个多变量强耦合过程,具有时滞和逆向特性,且存在强扰动。扰动的存在造成系统控制性能变差,甚至不稳定。以两输入两输出GCP为研究对象,提出了一种基于扰动观测器（DOB）的模型预测控制（MPC）复合控制方案DOB-MPC。仿真研究表明DOB-MPC不仅可以有效抑制GCP的外部扰动,而且可以抑制由模型失配和变量之间的耦合而导致的内部扰动;在获得良好的解耦控制能力的同时,取得了满意的抗扰动性能。     

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.     

基于二次型性能指标的不确定混沌系统最优控制器设计

研究具有不确定性并带有扰动的混沌控制系统。首先基于成熟线性理论中的二次型最优控制理论将扰动非线性的混沌系统模型转换为无扰动的等价线性系统模型,然后给出了针对伪线性系统的基于二次型性能指标的最优控制器设计方法。对Liu混沌系统的参数不确定性的仿真结果表明：控制品质有了较大的改善和提高。     

Nonlinear model predictive control based on support vector machine and genetic algorithm

This paper presents a nonlinear model predictive control (NMPC) approach based on support vector machine (SVM) and genetic algorithm (GA) for multiple-input multiple-output (MIMO) nonlinear systems. Individual SVM is used to approximate each output of the controlled plant. Then the model is used in MPC control scheme to predict the outputs of the controlled plant. The optimal control sequence is calculated using GA with elite preserve strategy. Simulation results of a typical MIMO nonlinear system show that this method has a good ability of set points tracking and disturbance rejection.