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.     

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。     

AUTOMATICALLY CONFIGURING RADIAL BASIS FUNCTION NEURAL NETWORKS FOR NONLINEAR INTERNAL MODEL CONTROL

A nonlinear internal model control (NIMC) strategy based on automatically configuring radial basis function networks (RBFN) is proposed for single-input single-output (SISO) systems of relative degree greater than unity. The automatic configuration and training of the RBFN is carried out employing hierarchically-self-organizing-learning algorithm, which eliminates a predefined network structure, with closed-loop input-output data generated for a series of setpoint changes using PI controller. Simulation studies with automatically configuring RBFN for isothermal polymerization reactor control demonstrate the superior performance of the proposed control strategy with automatically configuring RBFN over PI control for setpoint tracking as well as disturbance rejection.     

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.     

Input/output linearization with a two-degree-of-freedom scheme for uncertain nonlinear processes

This work presents a new method to control processes with unmeasured input disturbance and random noise parametric uncertainty. The developed method takes advantage of a two-degree-of-freedom control structure in which setpoint regulation and load disturbance rejection are integrated in the controller synthesis. Input/output linearization is selected to provide the setpoint tracking ability. For disturbance rejection, the high-gain technique is used to compensate for the effect of the uncertainty. The control performance of the method is evaluated through numerical simulation of continuous stirred tank reactors with uncertainty. The simulation results show that both unmeasured disturbance and parametric uncertainty can be effectively compensated for by the proposed control method.     

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.     

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.     

积分和不稳定时滞对象的改进内模控制

针对化工过程中一阶积分和不稳定时滞对象,基于内模控制提出了两自由度控制方案。首先根据鲁棒控制理论H2最优性能指标设计设定值跟踪控制器,然后采用期望闭环补灵敏度函数确定扰动抑制控制器。设定值跟踪控制器和扰动抑制控制器可通过性能参数独立调节而无需再取折衷,同时保证系统具有较好的鲁棒稳定性。最后通过仿真实例验证了该控制方案的有效性。     

A time scale-bridging approach for integrating production scheduling and process control

In this paper, we propose a novel framework for integrating scheduling and nonlinear control of continuous processes. We introduce the time scale-bridging model (SBM) as an explicit, low-order representation of the closed-loop input–output dynamics of the process. The SBM then represents the process dynamics in a scheduling framework geared towards calculating the optimal time-varying setpoint vector for the process control system. The proposed framework accounts for process dynamics at the scheduling stage, while maintaining closed-loop stability and disturbance rejection properties via feedback control during the production cycle. Using two case studies, a CSTR and a polymerization reactor, we show that SBM-based scheduling has significant computational advantages compared to existing integrated scheduling and control formulations. Moreover, we show that the economic performance of our framework is comparable to that of existing approaches when a perfect process model is available, with the added benefit of superior robustness to plant-model mismatch.     

Active disturbance rejection generalized predictive control for a high purity distillation column process with time delay

High purity distillation processes have been widely used in the chemical industry. These processes have unique characteristics including higher order, nonlinearity, strong coupling, and time delay. In order to overcome these control issues, an active disturbance rejection generalized predictive control strategy is designed for the distillation column with time delay. The strategy combines the structures of both active disturbance rejection control and generalized predictive control. A delayed designed extended state observer can estimate the model uncertainty and external disturbance, and a non‐incremental generalized predictive control is proposed to deal with the integrators with time delay. Therefore, it rejects disturbances well and has the capability of overcoming time delay. The computation load is also less than the generalized predictive control. In the simulation experiments, the proposed strategy is compared with robust control and model predictive control. The results illustrate that the proposed control strategy has improved robustness performance in dealing with model uncertainties, various disturbances, and time delay.     

NMPC of an industrial crystallization process using model-based observers

This paper illustrates the benefits of a nonlinear model-based predictive control (NMPC) approach applied to an industrial crystallization process. This relevant approach proposes a setpoint tracking of the crystal mass. The controlled variable, unavailable, is obtained using an extended Luenberger observer. A neural network model is used as internal model to predict process outputs. An optimization problem is solved to compute future control actions taking into account real-time control objectives. The performances of this strategy are demonstrated via simulation in cases of setpoint tracking and disturbance rejection. The results reveal a significant improvement in terms of robustness and energy efficiency.     

流化床反应器中气相丙烯聚合反应的动力学和预测控制(英文)

A two-phase dynamic model, describing gas phase propylene polymerization in a fluidized bed reactor, was used to explore the dynamic behavior and process control of the polypropylene production rate and reactor temperature. The open loop analysis revealed the nonlinear behavior of the polypropylene fluidized bed reactor, jus- tifying the use of an advanced control algorithm for efficient control of the process variables. In this case, a central- ized model predictive control （MPC） technique was implemented to control the polypropylene production rate and reactor temperature by manipulating the catalyst feed rate and cooling water flow rate respectively. The corre- sponding MPC controller was able to track changes in the setpoint smoothly for the reactor temperature and pro- duction rate while the setpoint tracking of the conventional proportional-integral （PI） controller was oscillatory with overshoots and obvious interaction between the reactor temperature and production rate loops. The MPC was able to produce controller moves which not only were well within the specified input constraints for both control vari- ables, but also non-aggressive and sufficiently smooth for practical implementations. Furthermore, the closed loop dynamic simulations indicated that the speed of rejecting the process disturbances for the MPC controller were also acceotable for both controlled variables.     

DISTURBANCE COMPENSATION FOR NONLINEAR PROCESSES

This paper focuses on the feedback linearization of nonlinear processes with external measurable and immeasurable disturbances. The proposed disturbance compensator, based on a set of the adjustable parameters, is used as a technique to robustify the cancellation of nonlinear terms under a suitable tuning framework. The bound for the adjustable parameters is given to ensure the stability of the closed-loop system. The proposed methodology is applied to the composition control of a CSTR, such that the output regulation and system robustness are achieved. Computer simulation shows results in satisfactory control.     

废水处理过程的抗扰控制研究

厌氧消化废水处理过程中,动态变化的进水组分、组分浓度,组分间耦合等各种不确定因素,使得简单的闭环控制无法获得理想的污水处理效果。为使污水处理出水水质达标,对污水处理过程模型依赖小、对各种变化（扰动）因素鲁棒性强、动态响应好的控制方法可满足工程要求。为此,设计一种能够主动估计并消除扰动的抗扰控制方法,有效估计并补偿污水处理过程中存在的各种不确定因素,以获得期望的污水处理效果。数值仿真结果表明,抗扰控制具有较好的抗干扰能力,能够满足控制要求,是一种可行的污水处理控制方案。     

A model predictive formulation for control of open-loop unstable cascade systems

Cascade control is commonly used in the operation of chemical processes to reject disturbances that have a rapid effect on a secondary measured state, before the primary measured variable is affected. In this paper, we develop a state estimation-based model predictive control approach that has the same general philosophy of cascade control (taking advantage of secondary measurements to aid disturbance rejection), with the additional advantage of the constraint handling capability of model predictive control (MPC). State estimation is achieved by using a Kalman filter and appending modeled disturbances as augmented states to the original system model. The example application is an open-loop unstable jacketed exothermic chemical reactor, where the jacket temperature is used as a secondary measurement in order to infer disturbances in jacket feed temperature and/or reactor feed flow rate. The MPC-based cascade strategy yields significantly better performance than classical cascade control when operating close to constraints on the jacket flow rate.     

Bounded robust control of constrained multivariable nonlinear processes

This work focuses on control of multi-input multi-output (MIMO) nonlinear processes with uncertain dynamics and actuator constraints. A Lyapunov-based nonlinear controller design approach that accounts explicitly and simultaneously for process nonlinearities, plant-model mismatch, and input constraints, is proposed. Under the assumption that all process states are accessible for measurement, the approach leads to the explicit synthesis of bounded robust multivariable nonlinear state feedback controllers with well-characterized stability and performance properties. The controllers enforce stability and robust asymptotic reference-input tracking in the constrained uncertain closed-loop system and provide, at the same time, an explicit characterization of the region of guaranteed closed-loop stability. When full state measurements are not available, a combination of the state feedback controllers with high-gain state observes and appropriate saturation filters, is employed to synthesize bounded robust multivariable output feedback controllers that require only measurements of the outputs for practical implementation. The resulting output feedback design is shown to inherit the same closed-loop stability and performance properties of the state feedback controllers and, in addition, recover the closed-loop stability region obtained under state feedback, provided that the observer gain is sufficiently large. The developed state and output feedback controllers are applied successfully to non-isothermal chemical reactor examples with uncertainty, input constraints, and incomplete state measurements. Finally, we conclude the paper with a discussion that attempts to put in perspective the proposed Lyapunov-based control approach with respect to the nonlinear model predictive control (MPC) approach and discuss the implications of our results for the practical implementation of MPC, in control of uncertain nonlinear processes with input constraints.     

Development of batch proportional-integral-derivative controller

Previous batch control methods, such as iterative learning control (ILC) or run-to-run (R2R) control, can significantly improve the control performance of the batch process. However, to guarantee the expected good control performance, a fairly accurate process model is required for these controllers. Also, the implementation is numerically complicated so that it is difficult to be applied to real manufacturing processes. To overcome these problems, a new batch proportional-integral-derivative (PID) control method is proposed, which borrows the concept of the conventional PID control method. Simulation studies confirm that the proposed method shows acceptable performance in tracking a setpoint trajectory, rejecting disturbances, and robustness to noises and variation of process dynamics. The application to the commercial batch process of a single crystal grower verifies that the proposed method can significantly contribute to improving the control performances of real batch processes.     

Control System Design for a Single Feed ETBE Reactive Distillation Column

Reactive distillation (RD) is advantageous for the Ethyl Tert‐Butyl Ether (ETBE) synthesis. The steady state model of an ETBE reactive distillation column created using the simulator HYSYS is analyzed to synthesize effective control structures. Since the column exhibits input multiplicity with the dual process objectives of ETBE RD (isobutene conversion and ETBE purity), inferential variables are selected. A control structure that organizes a sensitive tray temperature in the stripping section using the reboiler duty and maintains the temperature difference of reactive trays using the reflux flow, is found to be most suitable. A decentralized PI controller and constrained Model Predictive Controller (MPC) are implemented, and performances are compared for set point tracking and disturbance rejection. MPC control algorithms are implemented in MATLAB and interfaced with HYSYS. Constrained MPC (CMPC) is found to be effective for load disturbance rejection, which frequently occurs in the single feed configuration.     

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.