Latent variable iterative learning model predictive control for multivariable control of batch processes

A latent variable iterative learning model predictive control (LV-ILMPC) method is presented for trajectory tracking in batch processes. Different from the iterative learning model predictive control (ILMPC) model built from the original variable space, LV-ILMPC develops a latent variable model based on dynamic partial least squares (DyPLS) to capture the dominant features of each batch. In each latent variable space, we use a state–space model to describe the dynamic characteristics of the internal model, and an LV-ILMPC controller is designed. Each LV-ILMPC controller tracks the set points of the current batch projection in the corresponding latent variable space, and the optimal control law is determined and the persistent process disturbances is rejected along both time and batch horizons. The proposed LV-ILMPC formulation is based on general LV-MPC and incorporates an iterative learning function into LV-MPC. In addition, the real physical input that drives the process can be reconstructed from the latent variable space. Therefore, this algorithm is particularly suitable for multiple-input, multiple-output (MIMO) systems with strong coupling and serious collinearity. Three studies are used to illustrate the effectiveness of the proposed LV-ILMPC .     

Optimal control of a nonlinear fed-batch fermentation process using model predictive approach

Bioprocesses are involved in producing different pharmaceutical products. Complicated dynamics, nonlinearity and non-stationarity make controlling them a very delicate task. The main control goal is to get a pure product with a high concentration, which commonly is achieved by regulating temperature or pH at certain levels. This paper discusses model predictive control (MPC) based on a detailed unstructured model for penicillin production in a fed-batch fermentor. The novel approach used here is to use the inverse of penicillin concentration as a cost function instead of a common quadratic regulating one in an optimization block. The result of applying the obtained controller has been displayed and compared with the results of an auto-tuned PID controller used in previous works. Moreover, to avoid high computational cost, the nonlinear model is substituted with neuro-fuzzy piecewise linear models obtained from a method called locally linear model tree (LoLiMoT).     

Multivariate batch to batch optimisation of fermentation processes incorporating validity constraints

This paper presents an innovative optimisation technique, which utilises an adaptive Multiway Partial Least Squares (MPLS) model to track the dynamics of a batch process from one batch to the next. Utilising this model, an optimisation algorithm solves a quadratic cost function that identifies operating conditions for the subsequent batch that should increase yield. Hard constraints are shown to be required when solving the cost function to ensure that batch conditions do not vary too greatly from one batch to the next. Furthermore, validity constraints are imposed to prevent the PLS model from extrapolating significantly when determining new operating conditions. The capabilities of the proposed technique are illustrated through its application to two benchmark fermentation simulations, where its performance is shown to compare favourably with alternative batch-to-batch optimisation techniques.     

A multiple model predictive control strategy in the PLS framework

For chemical processes with a wide range of operating conditions, a switched multiple model predictive control (MMPC) strategy in the partial least squares (PLS) framework is proposed. Interactive MIMO systems can be automatically decoupled with inputs and outputs paired in their dynamic PLS models. Based on the identified PLS models, companion controllers are designed to form the MMPC strategy. A novel switching criterion based on output statistics is proposed to assure each model/control pair works in its operating region spanned by the identification data sets. The control results of disturbance rejection and setpoint tracking in a two-phase chemical reactor process are presented to demonstrate the capability and effectiveness of the proposed MMPC strategy.     

An integrated advanced process control framework using run-to-run control,virtual metrology and fault detection

This paper develops a new advanced process control (APC) system for the multiple-input multiple-output (MIMO) semiconductor processes using the partial least squares (PLS) technique to provide the run-to-run control with the virtual metrology data, via the gradual mode or the rapid mode depending on the current system status, in order to deal with metrology delays and compensate for different types of system disturbances. First, we present a controller called the PLS-MIMO double exponentially weighted moving average (PLS-MIMO DEWMA) controller. It employs the PLS method as the model building/estimation technique to help the DEWMA controller generate more consistent and robust control outputs than purely using the conventional DEWMA controller. To cope with metrology delays, the proposed APC system uses the pre-processing metrology data to build up the virtual metrology (VM) system that can provide the estimated process outputs for the PLS-MIMO DEWMA controller. Lastly, the Fault Detection (FD) system is added based upon the principal components of the PLS modeling outcomes, which supplies the process status for the VM mechanism and the PLS-MIMO DEWMA controller as to how the process faults are responded. Two scenarios of the simulation study are conducted to illustrate the APC system proposed in this paper.     

Fault tolerant control for a dearomatisation process

In this paper, a fault tolerant control (FTC) for a dearomatisation process in the presence of faults in online product quality analysers is presented. The FTC consists of a fault detection system (FDI) and a logic for triggering predefined FTC actions. FDI is achieved by combining several process data driven approaches for detecting faults in online quality analysers. The FTC exploits the diagnostic information in adapting a quality controller (MPC) to the faulty situation by manipulating tuning parameters of the MPC to produce both proactive and reactive strategies. The proposed FTC was implemented, tested offline and validated onsite at the Naantali oil refinery. The successful testing and plant validation results are presented and discussed.     

An integral approach to inferential quality control with self-validating soft-sensors

This paper presents an integral technique for designing an inferential quality control applicable to multivariate processes. The technique includes a self-validating soft-sensor and a multivariate quality control index that depends on the specifications. Based on a partial least squares (PLS) decomposition of the online process measurements, a fault detection and diagnosis technique is used to develop an improved self-validation strategy that is able to confirm, correct or reject the soft-sensor predictions. Model extrapolations, disturbances or sensor faults are first detected through a combined statistic (that considers the calibration region); then, a diagnosis is made by combining statistics pattern recognition, contribution analysis, and disturbance isolation based on historical fault patterns. An off-spec alarm is produced when the proposed index detects that an operating point lies outside the integral design space driven by the specifications. The effectiveness of the proposed technique is evaluated by means of two numerical examples. First, a synthetic example is used to interpret the fundamentals of the method. Then, the technique is applied to the industrial Styrene-Butadiene rubber process, which is emulated through an available numerical simulator.     

Globally stabilizing control of fed-batch processes with Haldane kinetics using growth rate estimation feedback

The regulation of the biomass specific growth rate is an important goal in many biotechnological applications. To achieve this goal in fed-batch processes, several control strategies have been developed employing a closed loop version of the exponential feeding law, an estimation of the controlled variable and some error feedback term. In the case of non-monotonic kinetics, the specified growth rate can be achieved at two different substrate concentration values. Because of the inherent unstable properties of the system in the decreasing portion of the kinetics function, stabilization becomes a crucial problem in this high-substrate operating region. In this context, the dynamic behavior of fed-batch processes with Haldane kinetics is further investigated. In particular, some conditions for global stability and performance improvement are derived. Then, a stabilizing control law based on a partial state feedback with gain dependent on the output error feedback and gain saturation is proposed. Although particular emphasis is put on the critical case of high-substrate operation, low-substrate regulation is also treated.     

PLS based dEWMA run-to-run controller for MIMO non-squared semiconductor processes

This paper focuses on the modification of the PLS (partial least squares) modeling. The new method allows incorporation of a dEWMA (double exponentially weighted moving average) control algorithm into the standard run-to-run controller design for semiconductor processes. The resulting structure of the PLS model can extract the strongest relationship between the input and the output variables. It is particularly useful for inherent noise suppression. In addition, the resulting non-square MIMO control system can be decomposed into a multi-loop control system by employing pre-compensators and post-compensators of the PLS model, which is constructed from the input and output loading matrices. Subsequently, the conventional dEWMA controller can be separately and directly applied to each SISO control loop. The performance of the proposed method is illustrated through a chemical–mechanical polishing process in the manufacturing of the semiconductor.     

Model selection for partial least squares based dimension reduction

Partial least squares (PLS) has been widely applied to process scientific data sets as an effective dimension reduction technique. The main way to determine the number of dimensions extracted by PLS is by using the cross validation method, but its computation load is heavy. Researchers presented fixing the number at three, but intuitively it’s not suitable for all data sets. Based on the intrinsic connection between PLS and the structure of data sets, two novel algorithms are proposed to determine the number of extracted principal components, keeping the valuable information while excluding the trivial. With the merits of variety with different data sets and easy implementation, both algorithms exhibit better performance than the previous works on nine real world data sets.     

Stochastic closed-loop model predictive control of continuous nonlinear chemical processes

A new predictive control framework for chemical processes is presented, that has a number of fundamental differences to classical MPC. Both future disturbances and future process measurements are explicitly introduced in the model prediction, while back-off prevents violation of the inequality constraints. A feedforward trajectory, used for constraint pushing, is optimized simultaneously with a linear time-varying feedback controller, used to minimize the back-off. No feedback is generated by the receding horizon implementation itself. Via several transformations, the resulting optimization problem is rendered convex. For nonlinear processes, this applies to the sub-problem in a sequential conic optimization approach. A two stage LQG approach reduces the complexity even further for large scale systems. The method is illustrated on a HDPE reactor example and compared to a LTV-MPC.     

Model predictive control: Recent developments and future promise

This paper recalls a few past achievements in Model Predictive Control, gives an overview of some current developments and suggests a few avenues for future research.     

Nonlinear one-step-ahead control using neural networks: Control strategy and stability design

A nonlinear one-step-ahead control strategy based on a neural network model is proposed for nonlinear SISO processes. The neural network used for controller design is a feedforward network with external recurrent terms. The training of the neural network model is implemented by using a recursive least-squares (RLS)-based algorithm. Considering the case of the nonlinear processes with time delay, the extension of the mentioned neural control scheme to d-step-ahead predictive neural control is proposed to compensate the influence of the time-delay. Then the stability analysis of the neural-network-based one-step-ahead control system is presented based on Lyapunov theory. From the stability investigation, the stability condition for the neural control system is obtained. The method is illustrated with some simulated examples, including the control of a continuous stirred tank reactor (CSTR).     

一种基于最小二乘支持向量机的预测控制算法

针对工业过程中普遍存在的非线性被控对象，提出一种基于最小二乘支持向量机建模的预测控制算法．首先，用具有RBF核函数的LS-SVM离线建立被控对象的非线性模型；然后，在系统运行过程中，将离线模型在每一个采样周期关于当前采样点进行线性化，并用广义预测算法实现对被控系统的预测控制．仿真结果表明了该算法的有效性和优越性．     

Robust model predictive control of integrating time delay processes

This work focuses on the solution to the problem of model predictive control of time delay processes with both integrating and stable modes and model uncertainty. The controller is developed for the practical case of zone control and input target tracking. The method is based on a state-space model that is equivalent to the analytical form of the step response model corresponding to the system transfer function. Here, this model is extended to the time delay system. The proposed controller is evaluated through simulation of the of two control reactor systems and the results confirms the robustness of the proposed approach.     

Neural network control of multivariable processes with a fast optimisation algorithm

A radial basis function (RBF) neural network model based predictive control scheme is developed for multivariable nonlinear systems in this paper. A fast convergence algorithm is proposed and employed in multidimensional optimisation in the control scheme to reduce the computing time and save required computer memory. The scheme is applied to a simulated two-input two-output nonlinear process for set-point tracking control. Simulation results demonstrate the effectiveness of the control strategy and the fast learning algorithm for multivariable non-linear processes. Comparison of the performance with PID control is included.     

Iterative learning model predictive control for multi-phase batch processes

Multi-phase batch process is common in industry, such as injection molding process, fermentation and sequencing batch reactor; however, it is still an open problem to control and analyze this kind of processes. Motivated by injection molding processes, the multi-phase batch process in each cycle is formulated as a switched system with internally forced switching instant. Controlling multi-phase batch processes can be decomposed into two subtasks: detecting the dynamics-switching-time; designing the control law for each phase with considering switching effect. In this paper, it is assumed that the dynamics-switching-time can be obtained in real-time and only the second subtask is studied. To exploit the repetitive nature of batch processes, iterative learning control scheme is used in batch direction. To deal with constraints, updating law is designed by using model predictive control scheme. An online iterative learning model predictive control (ILMPC) law is first proposed with a quadratic programming problem to be solved online. To reduce computation burden, an offline ILMPC is also proposed and compared. Applications on injection molding processes show that the proposed algorithms can control multi-phase batch processes well.     

Feedforward model predictive control

This paper examines the role played by feedforward in model predictive control (MPC). We contrast feedforward with preview action. The latter is standard in model predictive control, whereas feedforward has been rarely, if ever, used in contemporary formulations of MPC. We argue that feedforward can significantly improve performance in the presence of measurement noise and certain types of model uncertainty.