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The flotation industrial process is a strong nonlinear and coupling multivariable cascade process with a structure of device and operational layers. To address its operational control problem, this article describes nonlinear dynamic characteristics and disturbances in both device and operational layers as the previous sample unmodeled dynamics and its change rate and proposes a compensation-signal-based dual-rate operational feedback adaptive decoupling control approach. First, a device layer controller consisting of a controller-driven model, a proportional–integral controller, an unmodeled dynamics compensator (UDC), and an unmodeled dynamics change rate compensator (UDCRC) is designed. Then, the device layer closed-loop system and the operational layer system are unified in the same time scale, and hence, a controlled plant model is obtained. A system identification algorithm is proposed to obtain the parameters of this model. With these parameters, an operational layer controller consisting of a controller-driven model, a proportional–integral–derivative controller, a feedback decoupling controller, an UDC, and an UDCRC is designed. Finally, convergence proofs of the proposed identification algorithm and the closed-loop system stability analysis are given, and emulation experiments in a hardware-in-the-loop system are used to verify the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

The automatic control of blast furnace (BF) ironmaking process has always been an important yet arduous task in metallurgic engineering and automation. In this article, a novel Kalman filter-based robust model-free adaptive predictive control (MFAPC) method is proposed for the direct data-driven control of molten iron quality in BF ironmaking. First, a compact-form dynamic linearization-based extended MFAPC method for multivariable molten iron quality control is proposed by generalizing the existing single-variable MFAPC method to multivariable systems. Based on it, a Kalman filter-based robust MFAPC is further proposed considering the problems of data loss and measurement noise in quality detection. Specifically, the robust mechanism in the robust MFAPC combines a novel dynamic linearization method with a concept termed Pseudo-Jacobian matrix to predict the missing data during data loss. After that, a Kalman filter is constructed based on a prediction model to filter the measurement noise. The stability of the proposed control method is analyzed, and various data experiments using actual industrial data are performed to verify the effectiveness of the proposed methods. Note to Practitioners—The extremely complicated dynamics of blast furnace ironmaking process make the model-based controllers difficult to realize in practice. In this article, a novel robust model-free adaptive predictive control method is proposed for direct data-driven control of multivariate molten iron quality in the ironmaking process. This method directly uses the process input and output data to design the multivariable quality controller online by the compact-form dynamic linearization technology and the internal multilayer prediction mechanism, thus avoids the drawback of model-based controllers in troublesome process modeling. Moreover, the proposed method can effectively avoid the influence of data loss and measurement noise on the controller performance with the designed Kalman filter-based robust mechanism. The superiority and practicability of the proposed method are verified using various experiments against actual industrial data. [ABSTRACT FROM AUTHOR]

The electricity demand of the fused magnesia smelting process (FMSP) is defined as the average electric power consumption over a fixed period of time, which is used to monitor the electricity cost in the FMSP. In this article, we develop a dynamic model of the electricity demand based on the closed-loop control system of the smelting current in the FMSP. The electricity demand prediction model combines an identifiable linear model with an unknown nonlinear dynamic system, which takes advantage of system identification. To predict the unknown nonlinear dynamic system, an adaptive deep learning prediction approach is proposed based on a multilayer long short-term memory. The real data in the FMSP is used to verify the effectiveness of the proposed electricity demand forecasting method. [ABSTRACT FROM AUTHOR]

This article investigates the use of a mesoscale kinetic model to cooperate with the operational optimal control of bauxite ore grinding process. In this article, we propose a new modeling framework where a discretized distributed parameter macroscale model and a mesoscale kinetic model are combined to predict the grinding product particle size. The mesoscale kinetic method does not need an explicit model of the process because it describes the process as a stochastic process. However, the high computational demand has prevented the kinetic model from using an online setting. τ-leap method. The proposed model is validated using experimental data. Finally, a solution of the bauxite ore grinding operational optimal control is proposed and the cooperation of the predictive model with other modular is demonstrated. [ABSTRACT FROM AUTHOR]

The hematite regrinding process is a multivariable nonlinear industrial process with variant dynamic characteristic. When there are high-frequency disturbances on the pulp density and flowrate caused by the one-stage grinding and separation system, the dynamic characteristics of the hematite regrinding process becomes time variant. In this article, considering the fact that the regrinding system mostly works near its operating point, the dynamic characteristics of the regrinding system can be described as a combination of a deterministic linear model and an unknown high-order nonlinearity. Based on this description, a hydrocyclone feeding pressure (HFP) inner-loop proportional integral (PI) control system is proposed, and a dynamic model of the sump level (SL) outer-loop is established. The unknown change of the high-order nonlinearity is described by the previous sampled high-order nonlinearity and its change rate. A PI feedforward controller is then designed to compensate the previous sampled high-order nonlinearity based on a one-step optimal feedforward control law design approach. A one-step optimal regulate law based adaptive compensator is designed by using the tracking error and the exactly calculated value of the previous sampled high-order nonlinearity and its change rate. With the proposed PI feedforward controller and the adaptive compensator, a signal compensation based adaptive level outer-loop PI controller and an adaptive cascade control structure are proposed. Finally, the performance analysis and the industrial application demonstrate that, when the unknown high-frequency disturbances and the unknown change on the model parameters are in presence, the proposed algorithm can maintain the HFP, the hydrocyclone feeding density, and the SL in the desired ranges during the entire operation. [ABSTRACT FROM AUTHOR]

In order to improve the pulp quality and to reduce the energy consumption, the fiber length distribution (FLD) is generally employed as one of the important technological indexes in the refining process. Considering that the traditional mean and variance of fiber length are unable to adequately characterize the non-Gaussian distribution properties, this paper proposes a novel geometric analysis based double closed-loop iterative learning control (ILC) method for probability density function (PDF) shaping of output FLD in the refining process. Primarily, a radial basis function (RBF) neural network with Gaussian-type is utilized to approximate the square root PDF in the inner loop, where the RBF basis function parameters (center and width) are tuned between any two adjacent batches by using an ILC law, and the subspace identification method can be applied to establish the state-space model of weight vector. Then, for the sake of accelerating the convergence rate of the closed-loop system, a geometric analysis based ILC method is adopted in the outer loop. Finally, both simulation and experiments demonstrate the effectiveness and practicability of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper studies the two-timescales operational optimal control problem for the flotation industrial process with unknown operational model in the presence of setpoint constraints on the device layer. A novel dual-rate data-driven algorithm based on lifting technology and reinforcement learning (RL) is proposed. First, a dual-rate flotation process model including the device layer and the operational models is formulated. Then, a proportional integral (PI) controller for device layer is designed, by using lifting technology, a unified timescale controlled plant model with partially unknown dynamics is established. Based on such a model, an online learning algorithm using neural network is presented so that the operational indices, namely concentrate and tail grades, can be kept in the target range while maintaining the setpoints of the device layer within the specified bounds. At last, emulation experiments in a hardware-in-the-loop system are used to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Operation performance of mineral grinding processes is measured by the grinding product particle size and the circulating load, as two of the most crucial operational indices that measure the product quality and operation efficiency, respectively. In this paper, a data-driven method is proposed for the operational control design of mineral grinding processes with input constraints. A reference governor is introduced to take into account the input constraints and the infeasible setpoint issue. The reference governor generates feasible setpoints that keep control inputs within allowed regions. The lookup table embedded in the reference governor mapping steady-state outputs to inputs provides feasible setpoints for output regulation and baseline for inputs. An ad hoc optimization guarantees that the input constraints are not violated, with the priority of regulating the grinding product particle size if regulation of both indices is not feasible. Since the dynamic model of the controlled plant is complicated because of the strongly nonlinear and intricately coupled nature of ball mills and hydrocyclones, a novel policy iteration algorithm is proposed for optimal regulator design without system modeling. Simulation results comparing performances of a mineral grinding process with and without the reference governor show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Rougher flotation, composed of unit processes operating at a fast time scale and economic performance measurements known as operational indices measured at a slower time scale, is very basic and the first concentration stage for flotation plants. Optimizing operational process for rougher flotation circuits is extremely important due to high economic profit arising from the optimality of operational indices. This paper presents a novel off-policy Q-learning method to learn the optimal solution to rougher flotation operational processes without the knowledge of dynamics of unit processes and operational indices. To this end, first, the optimal operational control for dual-rate rougher flotation processes is formulated. Second, H∞ tracking control problem is developed to optimally prescribe the set-points for the rougher flotation processes. Then, a zero-sum game off-policy Q-learning algorithm is proposed to find the optimal set-points by using measured data. Finally, simulation experiments are employed to show the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper studies the operational optimal control problem for the industrial flotation process, a key component in the mineral processing concentrator line. A new model-free data-driven method is developed here for real-time solution of this problem. A novel formulation is given for the optimal selection of the process control inputs that guarantees optimal tracking of the operational indices while maintaining the inputs within specified bounds. Proper tracking of prescribed operational indices, namely concentrate grade and tail grade, is essential in the proper economic operation of the flotation process. The difficulty in establishing an accurate mathematic model is overcome, and optimal controls are learned online in real time, using a novel form of reinforcement learning we call interleaved learning for online computation of the operational optimal control solution. Simulation experiments are provided to verify the effectiveness of the proposed interleaved learning method and to show that it performs significantly better than standard policy iteration and value iteration. [ABSTRACT FROM PUBLISHER]

The pulp neutralization process is a complex industrial process with strong nonlinearity and time-varying dynamics. In general, this kind of process is hardly controlled by using traditional control techniques such as the proportional-integral-derivative (PID) controller. To resolve this problem, a novel PID control scheme is proposed by integrating a data-driven compensation of unmodeled dynamics and a multistep ahead of optimal control strategy. Essential difference from the classical PID controller lies in the use of unmodeled dynamics, the measured data from the pulp neutralization process is used directly for building the nonlinear PID controller, which plays an important role in control system design. Based on multistep ahead prediction optimal control theory, the controller parameters can be obtained through optimizing a cost function. Some theoretical results on the stability and convergence of the closed-loop system are established. To demonstrate the effectiveness of the proposed control techniques, a simulation model and a cobalt nickel hydroxide pulp neutralization process are employed. Simulations were carried out using data extracted from an actual pulp neutralization process, followed by some industrial experiments. Results from both simulations and experiments indicate that our proposed controller can effectively control the pH value of the pulp neutralization process with promising control performance. [ABSTRACT FROM AUTHOR]

The mixed separation thickening process (MSTP) of hematite beneficiation is a strong nonlinear cascade process with frequency of slurry pump as input, underflow slurry flow-rate (USF) as inner-loop output, and underflow slurry density (USD) as outer-loop output. The model parameters such as settling velocity of slurry particles and slurry height are unknown and nonlinear. Moreover, these model parameters vary from flotation middling, sewage, and magnetic separation slurry. In this paper, the unknown change of the above dynamic characteristics are described by the previous sample unmodeled dynamics and its change rate. A novel adaptive controller using compensation signal based approach is developed. Inner-loop closed-loop control system equation and lifting technology are adopted to develop dual rate adaptive control method. Two compensation signals are constructed and added onto the linear proportional-integral (PI) controller. Such two compensation signals aim at eliminating the effects of the previous sample unmodeled dynamics and tracking error, respectively. The stability and convergence analysis is given and a simulation experiment on hardware-in-the-loop simulation system of MSTP based on industrial data is carried out, where it shows that the USD, USF, and its changing rate can be controlled well inside their targeted ranges when the system is subjected to unknown variations of its parameters. [ABSTRACT FROM AUTHOR]

Industrial flow lines are composed of unit processes operating on a fast time scale and performance measurements known as operational indices measured at a slower time scale. This paper presents a model-free optimal solution to a class of two time-scale industrial processes using off-policy reinforcement learning (RL). First, the lower-layer unit process control loop with a fast sampling period and the upper-layer operational index dynamics at a slow time scale are modeled. Second, a general optimal operational control problem is formulated to optimally prescribe the set-points for the unit industrial process. Then, a zero-sum game off-policy RL algorithm is developed to find the optimal set-points by using data measured in real-time. Finally, a simulation experiment is employed for an industrial flotation process to show the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

The heat exchanging process is a strong nonlinear and cascade industrial unit, which is effected by the large random disturbances in the steam pressure, the outdoor temperature, and the water discharged by users. To solve this problem, in this paper, a PI controller with unmodeled dynamic compensation is combined with a dual-rate control, and a dynamic model of the supply water temperature in the outer loop with linear model and unknown higher order nonlinear is established by introducing the dynamics of the closed-loop control system for the steam flow-rate with a lifting method. This is then used in designing a one-step optimal PI control algorithm with unmodeled dynamics compensation. Second, a data-driven dual-rate control method is proposed for the control of water temperature and steam flow-rate. The stability and convergence of the proposed algorithm is analyzed. Finally, both, a contrast simulated experiment with the interval intelligent cascade control algorithm and an industrial application are included to demonstrate that the proposed method can control water temperature and steam flow-rate with large random disturbances within the target range of values for process requirements. [ABSTRACT FROM AUTHOR]

In this study, a data‐driven optimisation solution for operational index control for a class of industrial processes is presented. First, the operational index control problem is formulated as an optimal tracking control problem. Then, an augmented system composed of the device loop dynamics and operational indices dynamics is constructed on two different time scales. Since, finding mathematical model of the operational indices dynamics is difficult, in contrast to most existing operational optimisation and control methods that use a mathematical model of the operational indices dynamics, a reinforcement learning algorithm based on actor‐critic structure is employed to provide a data‐driven optimisation control method to select optimal process setpoints so that the operational indices can track desired values. This solution does not require complete knowledge of the industrial process dynamics. Moreover, complicated system identification of the dynamics of the operational indices is not required. The effectiveness of the proposed method is demonstrated by experimental results that are carried out on a hardware‐in‐the‐loop emulation system for a mineral grinding process. [ABSTRACT FROM AUTHOR]

In this paper, the performance-based control design problem for double-layer networked industrial processes is investigated. At the device layer, the prescribed performance functions are first given to describe the output tracking performance, and then by using backstepping technique, new adaptive fuzzy controllers are designed to guarantee the tracking performance under the effects of input dead-zone and the constraint of prescribed tracking performance functions. At operation layer, by considering the stochastic disturbance, actual index value, target index value, and index prediction simultaneously, an adaptive inverse optimal controller in discrete-time form is designed to optimize the overall performance and stabilize the overall nonlinear system. Finally, a simulation example of continuous stirred tank reactor system is presented to show the effectiveness of the proposed control method. [ABSTRACT FROM PUBLISHER]

This paper provides a method for automatically selecting optimal operational indices for unit processes in an industrial plant using measured data and without knowing dynamical models of the unit process. A dynamic multiobjective optimization problem is defined to find operational indices that lead to plant-wide production indices close to their target values. A case-based reasoning (CBR) technique is also employed, which uses the stored experience of a human expert to determine appropriate operational indices for given target production indices. The solutions of the optimization problem and CBR technique are combined to form baseline operational indices. The dynamic models of the production indices, however, are time varying and affected by disturbances and online corrections of these baseline operational indices are required. To this end, reinforcement learning (RL) is used to provide a data-driven optimization technique to compensate for disturbances and model approximation errors and variations. The data-driven RL approach is used in two different time scales. The samples of the predicted production indices are used at a fast sampling rate, i.e., at each sample time, and the samples of actual production indices are used at a slower sampling rate, i.e., after each operational run, to correct the baseline operational indices. The effectiveness of this automated decision procedure has been demonstrated by successful implementation of the proposed approach on a large mineral processing plant in Gansu Province, China. [ABSTRACT FROM PUBLISHER]

Grinding particle size (GPS) of a hematite grinding process (HGP) is characteristic of sensitivity to disturbances of ore hardness and size distribution, difficulty in establishing a mathematic model, and absence of measurement, which make the existing operational optimization and control approaches difficult to be applied. This leads to that it is always difficult to obtain a proper ore feed rate and water flow rate during process operation, and consequently, overload fault often occurs. To tackle this problem, based on characteristic analysis of GPS, a GPS prediction algorithm is first developed using an improved neural network (NN), and a data-driven optimization control approach for safety operation of HGP is proposed. The proposed method adopts a two-layer structure, the higher-level operational feedback control, and lower-level basic loop control. The operational feedback control consists of a cascade NN-based loop setpoint optimizer and an overload diagnosis and self-healing controller. The main advantage of the proposed method is that it requires only the available operating data, without knowing the process dynamics. Experiments have been carried out in a self-developed hardware-in-the-loop experiment system with actual data, demonstrating that the proposed method cannot only keep the HGP operation from mill overload fault but also achieve the optimization control with respect to the quadratic performance index of GPS deviation. [ABSTRACT FROM PUBLISHER]

In cement raw meal calcination process, it is very difficult to guarantee the calciner temperature be controlled within its targeted range and the outlet temperature of preheater C5 (i.e., the no. 5 preheater) be less than the maximum value, because of varying boundary conditions and the flow of raw meal. Conventional control could often lead to operational failure, such as C5 feeding tube clogged. To solve this problem, an intelligence-based temperature switching control strategy has been proposed. The control strategy consists of a fuzzy controller based on T-S, an abnormal condition controller, and a switching mechanism based on rule reasoning with a feedforward compensation. Practical application to a raw meal calcination process has shown that this control strategy can ensure that the calciner temperature is within its targeted range and the outlet temperature of the preheater C5 is less than the maximum value, even when the boundary conditions vary frequently. Moreover, it has been observed that the proposed control strategy can avoid the faulty operating condition and effectively increase the decomposition ratio of the raw meal. [ABSTRACT FROM PUBLISHER]

In the smelting process of fused magnesium furnaces (FMFs), frequent changes in the raw material granule size and impurity constituent will cause the arc resistance between the lower end of the electrode and the surface of the molten pool to vary, and thus, the smelting currents fluctuate. Consequently, abnormal conditions, which can arise if the setpoints of electrode currents are not properly adjusted on time, will causethe performance to deteriorate or even the overall operation to stall. Through analysis of the characteristics of different operating conditions, this paper presents a data-driven abnormal condition identification and self-healing control system. The proposed system extracts the identification rules according to the current tracking error, as well as the rate and duration of the current fluctuations, and identifies the abnormal conditions based on rule-based reasoning. The self-healing control is developed using case-based reasoning to correct the current setpoints based on the identification results. The outputs of the control loop track the corrected setpoints, thereby forcing the process to recover from the abnormal conditions. The proposed method and the developed control system have been applied to a real FMF, and substantial improvement is achieved with many benefits provided to the factory. The implementation results show that occurrence of abnormal conditions has been reduced by more than 50%, and the product quality has been increased by more than 2%. [ABSTRACT FROM PUBLISHER]

The whole production line of hematite ore processing is composed of raw ore processing, shaft furnace roasting, grindings, and magnetic separation production phases. Their automation systems consist of the process control part and the operational optimization system. The target of the optimal operational control is to optimize the concerned operational indices, namely, the intermediate product quality, efficiency, and consumptions. The dynamics between the operational indices and the global production indices (i.e., the total concentration grade, metal recovery rate, production rate, beneficiation ratio, and costs) with month, day, and hour time scales changes in line with the variations of production conditions, composition of raw ore together with capability of equipment. These indices are difficult to measure online and as a result it is difficult to model accurately. Moreover, there are characteristics in terms of both interconnections and conflictions among these indices. This leads to isolated operation of individual automation systems for these processes and the optimization of global production indices for whole production line cannot be realized. This paper presents a novel problem description for the integrated optimization of the automation systems of mineral processing. For this purpose, the analysis is made on the difficulty of using the existing optimization methods-based decision making methods to obtain the integrated optimization of the automation systems. The integrated optimization strategy for the automation systems of mineral processes is proposed using our previously established target value optimization of global production indices , two time scales decomposition approach and target value optimization of operational indices. The proposed strategy aims at realizing the optimization of global production indices. Using real data from a mineral processing plant on hematite beneficiation process, relevant simulations, and real industrial experiments have been carried out. The obtained experimental results show the efficiency and effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper introduces the development and implementation of a ball mill grinding circuit simulator, NEUSimMill. Compared to the existing simulators in this field which focus on process flowsheeting, NEUSimMill is designed to be used for the test and verification of grinding process control system including advanced control system such as integrated control. The simulator implements the dynamic ball mill grinding model which formulates the dynamic responses of the process variables and the product particle size distribution to disturbances and control behaviors as well. First principles models have been used in conjunction with heuristic inference tools such as fuzzy logic and artificial neural networks: giving rise to a hybrid intelligent model which is valid across a large operating range. The model building in the simulator adopts a novel modular-based approach which is made possible by the dynamic sequential solving approach. The simulator can be initiated with connection to a real controller to track the plant state and display in real-time the effect of various changes on the simulated plant. The simulation model and its implementation is verified and validated through a case of application to the design, development, and deployment of optimal setting control system. [ABSTRACT FROM AUTHOR]

This paper investigates the setpoints compensation for a class of complex industrial processes. Plants at the device layer are controlled by the local regulation controllers, and a multirate output feedback control approach for setpoints compensation is proposed such that the local plants can reach the dynamically changed setpoints and the given economic objective can also be tracked via certain economic performance index (EPI). First, a sampled-data multivariable output feedback proportional integral (PI) controller is designed to regulate the performance of local plants. Second, the outputs and control inputs of the local plants at the device layer are sampled at operation layer sampling time to form the EPI. Thus, the multirate problem is solved by a lifting method. Third, the static setpoints are generated by real-time optimization and the dynamic setpoints are calculated by the compensator according to the error between the EPI and objective at each operation layer step. Then, a networked case is studied considering unreliable data transmission described by a stochastic packet dropout model. Finally, a rougher flotation process model is employed to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

Optimizing the final grinding production indices (GPIs), which include the product particle size and the grinding production rate, to meet the overall manufacturing performance requirements is the main function of automatic control of a grinding circuit (GC). However, the complex and time-varying nature of the GC process dictates that these GPIs cannot be optimized solely by the lower-level distributed control systems (DCS), therefore an operator is often incorporated to manually determine the set-points for the DCS using his/her operational experience. With a human being involved, the performance and even the safety and stability of the GC operation is subject to human errors. Focusing on this practical challenge, this paper proposes an intelligence-based supervisory control strategy that consists of a control loop set-point optimization module, an artificial neural network-based soft-sensor module, a fuzzy logic-based dynamic adjustor, and an expert-based overload diagnosis and adjustment module to perform the control tasks for the GC system. This hybrid system can automatically adjust the set-points for the DCS-controlled grinding system in response to the changes in boundary conditions or the imminent overload conditions, thereby eliminating the need for an operator. Practical applications have shown the validity and effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, a novel knowledge-based global operation approach is proposed to minimize the effect on the production performance caused by unexpected variations in the operation of a mineral processing plant subjected to uncertainties. For this purpose, a feedback compensation and adaptation signal discovered from process operational data is employed to construct a closed-loop dynamic operation strategy. It uses the signal to regulate the outputs of the existing open-loop and steady-state based system so as to compensate the uncertainty in the steady-state operation at the plant-wide level. The utilization mechanism of operational data through constructing increment association rules is firstly described. Then, a rough set based rule extraction approach is developed to generate the compensation rules. This includes two steps, namely the determination of the variables to be compensated based on the significance of attributes in the rough set theory and the extraction of the compensation rules from process data. Based upon the operational data of the mineral processing plant, relevant rules are obtained. Both simulation and industrial experiments are carried out for the proposed global operation, where the effectiveness of the proposed approach has been clearly justified. [ABSTRACT FROM PUBLISHER]

This paper proposes an intelligent switching control strategy for the pulverizing system for an alumina sintering process. The control strategy consists of a coordinating controller, a proportional-integral (PI) controller, a rule-based reasoning controller and a switching mechanism. The practical application to a pulverizing system in an alumina sintering process has shown that when the hot air temperature is low and varies frequently, this control strategy ensures that the mill load and the temperature of the mill outlet are both within their required ranges, and also controls the mill load at the level corresponding to the maximum mill output. Moreover, it has been observed that the proposed control strategy can avoid the fault operating condition and effectively reduce the unit energy consumption. [ABSTRACT FROM PUBLISHER]

This paper presents a novel offline modeling for product quality prediction of mineral processing which consists of a number of unit processes in series. The prediction of the product quality of the whole mineral process (i.e., the mixed concentrate grade) plays an important role and the establishment of its predictive model is a key issue for the plantwide optimization. For this purpose, a hybrid modeling approach of the mixed concentrate grade prediction is proposed, which consists of a linear model and a nonlinear model. The least-squares support vector machine is adopted to establish the nonlinear model. The inputs of the predictive model are the performance indices of each unit process, while the output is the mixed concentrate grade. In this paper, the model parameter selection is transformed into the shape control of the probability density function (PDF) of the modeling error. In this context, both the PDF-control-based and minimum-entropy-based model parameter selection approaches are proposed. Indeed, this is the first time that the PDF shape control idea is used to deal with system modeling, where the key idea is to turn model parameters so that either the modeling error PDF is controlled to follow a target PDF or the modeling error entropy is minimized. The experimental results using the real plant data and the comparison of the two approaches are discussed. The results show the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

The 17 papers in this special section focus on integrated optimization of industrial automation. [ABSTRACT FROM AUTHOR]