Jay H. Lee

A model-based predictive control approach to repetitive control of continuous processes with periodic operations

Abstract A novel model-based predictive control (MPC) method is developed with the aim of applying it to periodic process control problems. By borrowing concepts from repetitive control (RC), we endow the MPC method with the ability to make continuous period-to-period improvements. The method uses a linear time-varying system description of a periodic process and can handle constraints on inputs and outputs. Some numerical examples are shown to illustrate performance improvements that can be achieved by the new method over the conventional MPC and RC methods.

Repetitive model predictive control applied to a simulated moving bed chromatography system

Abstract In this paper, we investigate the application of the repetitive model predictive control (RMPC) technique on a simulated moving bed (SMB) process that performs continuous chromatographic separation of a phenylalanine—tryptophan mixture. RMPC is a model-based control technique developed by incorporating the basic concept from repetitive control into the model predictive control technique; it is specifically suited for continuous processes with periodic operation patterns or behavior. Balanced model reduction is used to reduce a finite difference approximation of a PDE model drawn from a material balance of the SMB system. The reduced order state space model is used for the control calculation. Start-up control of the SMB process is simulated and the results are presented.

A set based approach to detection and isolation of faults in multivariable systems

Abstract In this paper, we propose a set based approach for detecting faults in input/output channels of a closed-loop multivariable system. This approach works with deterministic bounds on measurement noises, disturbances, and fault signals, which may be attractive in some applications. The fault detection problem is formulated as an optimization problem in the state space framework. The dimensionality of the optimization problem increases with time. In order to allow the problem dimension to be fixed at a pre-specified value, a moving horizon based approach is proposed. When the horizon is moved, a parallelotope covering the feasible region of the initial state is propagated by using the ‘Recursive Optimal Bounding Parallelotope’ methodology. Diagnosis of the location of a fault is carried out by using a series of detection tests. The usefulness of the algorithm for detection and diagnosis is demonstrated by using a heat exchanger example.

Data-based construction of feedback-corrected nonlinear prediction model using feedback neural networks

Abstract We propose to fit a recurrent feedback neural network structure to input–output data through prediction error minimization. The recurrent feedback neural network structure takes the form of a nonlinear state estimator, which can compactly represent a multivariable dynamic system with stochastic inputs. The inclusion of the feedback error term as an input to the model allows the user to update the model based on feedback measurements in real-time uses. The model can be useful in a variety of applications including software sensing, process monitoring, and predictive control. A dynamic learning algorithm for training the recurrent neural network has been developed. Through some examples, we evaluate the efficacy of the proposed method and the prediction improvement achieved by the inclusion of the feedback error term.

Use of two-stage optimization in model predictive control of stable and integrating systems

Abstract A two-stage model predictive control formulation for stable and integrating systems is proposed. The formulation allows the user to solve an economic optimization at steady state to find the most desirable setpoint values for the subsequent dynamic control calculation. The settling values of the integrating outputs are related to a particular input value combination for efficient optimization. A simple numerical example is provided.

Integrated quality and tracking control of a batch PMMA reactor using a QBMPC technique

Abstract QBMPC is a recently developed technique for combined quality and tracking control of batch processes where prediction-based real-time control and batch-wise integral control are conducted simultaneously. The most important advantage of QBMPC is that both quality and tracking variables converge to the optima dictated by the objective function despite model uncertainty and run-wise repeating disturbances. In this paper, with the purpose to enhance the quality control aspect, the QBMPC algorithm has been newly formulated based on a time-varying state space model. The new algorithm has been applied to a batch reactor model for methylmethacrylate (MMA) polymerization where the weight-average molecular weight and polydispersity index of the end product, and monomer conversion are considered important quality variables to control. Key steps for the controller design are described and the resulting control performance is demonstrated.

An on-line batch span minimization and quality control strategy for batch and semi-batch processes

Abstract A novel strategy is proposed to minimize the operation time of batch and semi-batch processes. The proposed on-line strategy is based on linear regression models and employs a cascade control structure in which the primary controller calculates an optimal operation profile for the secondary controller to follow. A special feature of the proposed on-line strategy is that it conducts run-wise information feedback and achieves the attainable minimum operation time as the batch run is repeated despite model uncertainty. The performance of the proposed strategy is illustrated through simulation studies involving an exothermic batch reactor and a semi-batch reactor producing 2-acetoacetyl pyrrole.

An On-line Batch Span Minimization and Quality Control Strategy for Batch and Semi-Batch Processes

Abstract A novel strategy is proposed to minimize the operation time of batch and semi-batch processes. The proposed on-line strategy is based on linear regression models and employs a cascade control structure in which the primary controller calculates an optimal operation profile for the secondary controller to follow. A special feature of the proposed on-line strategy is that it conducts run-wise information feedback and achieves the attainable minimum operation time as the batch run is repeated despite model uncertainty. The performance of the proposed strategy is illustrated through simulation studies involving an exothermic batch reactor and a semi-batch reactor producing 2-acetoacetyl pyrrole.

Nonlinear Dynamic Trend Modeling Using Feedback Neural Networks and Prediction Error Minimization

Abstract We propose a nonlinear system identification method in which a recurrent feedback neural network is fitted to available data through prediction error minimization. The recurrent feedback neural network structure we adopt is in the form of a state estimator for general nonlinear stochastic systems. The adoption of the state-space structure makes the method attractive for treating multivariable dynamic systems and the inclusion of the feedback error term in the model allows for smaller prediction errors, especially in stochastic systems. A dynamic learning algorithm for the recurrent neutral network has been developed. Through some examples, we evaluate the feasibility of the proposed method and the prediction improvement afforded by the inclusion of the feedback error term in the model.

Control of Wafer Temperature Uniformity in Rapid Thermal Processing Using an Optimal Iterative Learning Control Technique

Abstract An iterative learning control technique based on a linear quadratic optimal criterion is proposed for temperature uniformity control of a silicon wafer under rapid thermal processing. The proposed technique enables us to attain the minimum achievable tracking error by run-wise feedback. A simple but effective identification method for a time-varying linear state space model is also proposed as an integral part of the controller design. Performance of the proposed technique is demonstrated numerically in an 8-inch silicon wafer RTP model.