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.     

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 Monte-Carlo based model approximation technique for linear model predictive control of nonlinear systems

In this paper we present a model approximation technique based on N-step-ahead affine representations obtained via Monte-Carlo integrations. The approach enables simultaneous linearization and model order reduction of nonlinear systems in the original state space thus allowing the application of linear MPC algorithms to nonlinear systems. The methodology is detailed through its application to benchmark model examples.     

Assessing plant design with regard to MPC performance

Model Predictive Control is ubiquitous in the chemical industry and offers great advantages over traditional controllers. Notwithstanding, new plants are being projected without taking into account how design choices affect the MPC’s ability to deliver better control and optimization. Thus a methodology to determine if a certain design option favours or hinders MPC performance would be desirable. This paper presents the economic MPC optimization index whose intended use is to provide a procedure to compare different designs for a given process, assessing how well they can be controlled and optimised by a zone constrained MPC. The index quantifies the economic benefits available and how well the plant performs under MPC control given the plant’s controllability properties, requirements and restrictions. The index provides a monetization measure of expected control performance.This approach assumes the availability of a linear state-space model valid within the control zone defined by the upper and lower bounds of each controlled and manipulated variable. We have used a model derived from simulation step tests as a practical way to use the method. The impact of model uncertainty on the methodology is discussed. An analysis of the effects of disturbances on the index illustrates how they may reduce profitability by restricting the ability of a MPC to reach dynamic equilibrium near process restrictions, which in turn increases product quality giveaway and costs. A case of study consisting of four alternative designs for a realistically sized crude oil atmospheric distillation plant is provided in order to demonstrate the applicability of the index.     

Lexicographic optimization based MPC: Simulation and experimental study

Multi-variable prioritized control study is carried out using model predictive control (MPC) algorithms. The conventional MPC algorithm implements multi-variable control through one augmented objective function and requires weights adjustment for required performance. In order to implement explicit prioritization in multiple control objectives, we have used lexicographic MPC. To achieve better tracking performance, we have used a new MPC algorithm, by modifying the lexicographic constraint, referred to as MLMPC, where tuning of weights is not required. The effectiveness of MLMPC algorithm is demonstrated on a PMMA reactor for controlling the number average molecular weight and the reactor temperature. We have also verified the benefits of proposed algorithm on an experimental single board heater system (SBHS) for controlling temperature of a thin metal plate. These simulation and experimental studies demonstrate the superiority of the proposed method over conventional MPC and lexicographic MPC. Finally, we have presented generalized mathematical solutions to the optimization problem in MLMPC.     

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.     

An on-line constraint softening strategy to guarantee the feasibility of dynamic controller in double-layered MPC

A double-layered model predictive control(MPC),which is composed of a steady-state target calculation(SSTC) layer and a dynamic control layer,is a prevailing hierarchical structure in industrial process control.Based on the reason analysis of the dynamic controller infeasibility,an on-line constraints softening strategy is given.At first,a series of regions of attraction(ROA)of the dynamic controller is calculated according to the softened constraints;then a minimal ROA containing the current state is chosen and the corresponding softened constraint is adopted by the dynamic controller.Note that,the above measures are performed on-line because the centers of the above ROA are the steady-state targets calculated at each instant.The effectiveness of the presented strategy is illustrat-ed through two examples.     

Recent developments in the control of constrained hybrid systems

We review recently developed schemes for the constrained control of systems integrating logic and continuous dynamics. The control paradigm we focus on is model predictive control (MPC) and its derivatives, with the emphasis on explicit solution. The exposition of the basic theory is supplemented by a number of application case studies showing the effectiveness as well as the limitations of the deployed algorithms. Current and future lines of research are briefly discussed.     

Predictive optimal management method for the control of polygeneration systems

A predictive optimal control system for micro-cogeneration in domestic applications has been developed. This system aims at integrating stochastic inhabitant behavior and meteorological conditions as well as modelling imprecisions, while defining operation strategies that maximize the efficiency of the system taking into account the performances, the storage capacities and the electricity market opportunities.Numerical data of an average single family house has been taken as case study. The predictive optimal controller uses mixed-integer and linear programming where energy conversion and energy services models are defined as a set of linear constraints. Integer variables model the start-up and shut-down operations as well as the load dependent efficiency of the cogeneration unit. The proposed control system has been validated using more complex building and technology models to asses model inaccuracies. Typical demand profiles for stochastic factors have been used.The system is evaluated in the perspective of its usage in Virtual Power Plants applications.     

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.     

Lyapunov‐based MPC with robust moving horizon estimation and its triggered implementation

In this work, we consider moving horizon state estimation (MHE)‐based model predictive control (MPC) of nonlinear systems. Specifically, we consider the Lyapunov‐based MPC (LMPC) developed in (Mhaskar et al., IEEE Trans Autom Control. 2005;50:1670–1680; Syst Control Lett. 2006;55:650–659) and the robust MHE (RMHE) developed in (Liu J, Chem Eng Sci. 2013;93:376–386). First, we focus on the case that the RMHE and the LMPC are evaluated every sampling time. An estimate of the stability region of the output control system is first established; and then sufficient conditions under which the closed‐loop system is guaranteed to be stable are derived. Subsequently, we propose a triggered implementation strategy for the RMHE‐based LMPC to reduce its computational load. The triggering condition is designed based on measurements of the output and its time derivatives. To ensure the closed‐loop stability, the formulations of the RMHE and the LMPC are also modified accordingly to account for the potential open‐loop operation. A chemical process is used to illustrate the proposed approaches. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4273–4286, 2013     

Analytical design of enhanced PID filter controller for integrating and first order unstable processes with time delay

An analytical design for a proportional-integral derivative (PID) controller cascaded with a first order lead/lag filter is proposed for integrating and first order unstable processes with time delay. The design algorithm is based on the internal model control (IMC) criterion, which has a single tuning parameter to adjust the performance and robustness of the controller. A setpoint filter is used to diminish the overshoot in the servo response. In the simulation study, the controllers were tuned to have the same degree of robustness by measuring the maximum sensitivity, Ms, in order to obtain a reasonable comparison. Furthermore, the robustness of the controller was investigated by inserting a perturbation uncertainty in all parameters simultaneously to obtain the worst case model mismatch, and the proposed method showed more robustness against process parameter uncertainty than the other methods. For the selection of the closed-loop time constant, λ, a guideline is also provided over a broad range of time-delay/time-constant ratios. The simulation results obtained for the suggested method were compared with those obtained for other recently published design methods to illustrate the superiority of the proposed method.     

An optimal control-based safety system for cost efficient risk management of chemical processes

The design of conventional safety systems is based on failure likelihood and accident severity, which is normally obtained empirically, leaving the system vulnerable to process nonlinearities. To ensure process safety, control actions are conservative and small deviations from setpoints may lead to shutdown, generating economic losses. In this work, periodic simulations of system behavior against failures is proposed in order to determine the potential risk to which the system is subjected. Depending on this potential, preventive actions can be taken in order to guarantee the system safety and integrity and avoid potential shutdown. These actions are calculated to provoke least possible disturbance in order to reduce impact on product quality, while keeping the process operating. The goal is to increase annual operating time of the plant without compromising safety and product quality. Results show that the proposal is feasible to real time applications and unnecessary shutdowns can be avoided.     

An adaptive neuro-fuzzy sliding mode controller for MIMO systems with disturbance

This paper introduces the mathematical model of ammonia and urea reactors and suggested three methods for designing a special purpose controller. The first proposed method is Adaptive model predictive controller, the second is Adaptive Neural Network Model Predictive Control, and the third is Adaptive neuro-fuzzy sliding mode controller. These methods are applied to a multivariable nonlinear system as an ammonia–urea reactor system. The main target of these controllers is to achieve stabilization of the outlet concentration of ammonia and urea, a stable reaction rate, an increase in the conversion of carbon monoxide(CO) into carbon dioxide(CO_2) to reduce the pollution effect, and an increase in the ammonia and urea productions, keeping the NH_3/CO_2 ratio equal to 3 to reduce the unreacted CO_2 and NH_3, and the two reactors' temperature in the suitable operating ranges due to the change in reactor parameters or external disturbance. Simulation results of the three controllers are compared. Comparative analysis proves the effectiveness of the suggested Adaptive neurofuzzy sliding mode controller than the two other controllers according to external disturbance and the change of parameters. Moreover, the suggested methods when compared with other controllers in the literature show great success in overcoming the external disturbance and the change of parameters.     

基于控制性能比较的非线性不对称系统预测控制

生产过程某些非线性系统常常表现出不对称动态特性,相对于其在工业工程中经常出现的理论研究特别是控制方法研究则十分有限。本文针对基于正反方向上的两个线性模型分别设计PID控制器的缺陷,提出根据正反方向上的线性模型分别设计相应的状态反馈预测控制器。在每一步的控制率计算中,正反方向的控制器分别计算控制作用,并通过比较正反控制器的控制性能指标来确定最终采用的控制作用。通过pH值控制的仿真实验证明其对非线性不对称系统的控制效果明显优于传统的在正反方向分别采用PID控制的控制效果。     

一种提高发酵单位的SVM与RGA相结合的优化控制策略

An optimal control strategy is proposed to improve the fermentation titer, which combines the support vector machine (SVM) with real code genetic algorithm (RGA). A prediction model is established with SVM for penicillin fermentation processes, and it is used in RGA for fitting function. A control pattern is proposed to overcome the coupling problem of fermentation parameters, which describes the overall production condition. Experimental results show that the optimal control strategy improves the penicillin titer of the fermentation process by 22.88%, compared with the routine operation.     

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.     

MPC of distillation column with side reactors for methyl acetate

This paper focuses on the dynamic control of distillation column with side reactors(SRC)for methyl acetate pro-duction.To obtain the optimum integrated structure and steady state simulation,the systematic design approach based on the concept of independent reaction amount is applied to the process of SRC for methyl acetate produc-tion.In addition to the basic control loops,multi-variable model predictive control modular with methyl acetate concentration and temperature of sensitive plate is designed.Then,based on process simulation software Aspen Plus,dynamic simulation of SRC for methyl acetate production is used to verify the effectiveness of the control scheme.