Zuhua Xu

A method of LPV model identification for control

Nonlinear process identification for control is studied. In identification test, the process is only tested (excited) along its operating-trajectory that includes various working points and transition periods. In model identification, a linear parameter varying (LPV) model is used. First linear models are identified using data sets at various working-points exclusive transition data; then the LPV model is identified by interpolating the linear models using total data. Sufficient conditions for a unique solution in parameter estimation will be given. Simulation study will be used to verify the effectiveness of the method. The identified model is suitable for model predictive control (MPC).

A Two-Time Scale Decentralized Model Predictive Controller Based on Input and Output Model

A decentralized model predictive controller applicable for some systems which exhibit different dynamic characteristics in different channels was presented in this paper. These systems can be regarded as combinations of a fast model and a slow model, the response speeds of which are in two-time scale. Because most practical models used for control are obtained in the form of transfer function matrix by plant tests, a singular perturbation method was firstly used to separate the original transfer function matrix into two models in two-time scale. Then a decentralized model predictive controller was designed based on the two models derived from the original system. And the stability of the control method was proved. Simulations showed that the method was effective.

Development and Application of an Integrated MPC Technology

This work introduces an integrated MPC controller. The integrated MPC consists of three modules: an MPC control module, an online identification module and a control monitor module. The three modules work together coherently in real-time; it can perform automatic controller commissioning and automatic controller maintenance. In MPC commissioning, the online identification module and the MPC control module work together and perform various steps in MPC implementation automatically. When the MPC controller is online, the control monitor module continuously monitors the MPC performance and model quality. When control performance degradation and considerable model error are detected, monitor module will start the maintenance by activating the online identification module. The identification module will re-identify the model and replace the old model. A prototype of the integrated MPC controller has applied successfully to two PTA units and the result will be reported.

Input and state estimation for linear systems with a rank-deficient direct feedthrough matrix

The problem of joint input and state estimation for linear stochastic systems with a rank-deficient direct feedthrough matrix is discussed in this paper. Results from previous studies only solve the state estimation problem; globally optimal estimation of the unknown input is not provided. Based on linear minimum-variance unbiased estimation, a five-step recursive filter with global optimality is proposed to estimate both the unknown input and the state. The relationship between the proposed filter and the existing results is addressed. We show that the unbiased input estimation does not require any new information or additional constraints. Both the state and the unknown input can be estimated under the same unbiasedness condition. Global optimalities of both the state estimator and the unknown input estimator are proven in the minimum-variance unbiased sense.

Model predictive control with an on-line identification model of a supply chain unit

A model predictive controller was designed in this study for a single supply chain unit. A demand model was described using an autoregressive integrated moving average (ARIMA) model, one that is identified on-line to forecast the future demand. Feedback was used to modify the demand prediction, and profit was chosen as the control objective. To imitate reality, the purchase price was assumed to be a piecewise linear form, whereby the control objective became a nonlinear problem. In addition, a genetic algorithm was introduced to solve the problem. Constraints were put on the predictive inventory to control the inventory fluctuation, that is, the bullwhip effect was controllable. The model predictive control (MPC) method was compared with the order-up-to-level (OUL) method in simulations. The results revealed that using the MPC method can result in more profit and make the bullwhip effect controllable.

Fast Model Predictive Control Combining Offline Method and Online Optimization with K-D Tree

Computation time is the main factor that limits the application of model predictive control (MPC). This paper presents a fast model predictive control algorithm that combines offline method and online optimization to solve the MPC problem. The offline method uses a k-d tree instead of a table to implement partial enumeration, which accelerates online searching operation. Only a part of the explicit solution is stored in the k-d tree for online searching, and the k-d tree is updated in runtime to accommodate the change in the operating point. Online optimization is invoked when searching on the k-d tree fails. Numerical experiments show that the proposed algorithm is efficient on both small-scale and large-scale processes. The average speedup factor in the large-scale process is at least 6, the worst-case speedup factor is at least 2, and the performance is less than 0.05% suboptimal.

Dynamic optimization of multivariable endothermic reaction in cascade CSTR

The dynamic optimization problem of a multivariable endothermic reaction in cascade continuous stirred tank reactors is solved with simultaneous method in this paper. Radau collocation is applied in discretization because of its stiff decay and high precision. A two-layer optimization is presented to get a fast convergence rate when dealing with the nonlinear case. In the industry process, the load variation may be very large and may cause output variables big overshoot. In order to reduce the overshoot, a segmentation load variation method is introduced. The good results of this nonlinear ordinary differential equations system show the validity of these methods.

A Scheme of Model Invalidation Assessment for Multivariable Dynamic Matrix Controllers

Model mismatch is an inherent problem in model predictive control (MPC), but the performance of MPC will descend and even be invalid when the model mismatch extent exceeds a certain level. This paper introduces a mechanism for assessing model invalidation for dynamic matrix control (DMC) in a probabilistic framework. The relationship between model predictive error and disturbance series, which can determine model-plant mismatch (MPM), is presented using internal model control (IMC) structure of DMC. Then the difference between these two time series is used to assess model invalidation through statistical inference method. The model is invalid if the calculated statistics is larger than a threshold with a given significant level. Numerical examples demonstrate the effectiveness of proposed method.

Research on tuning parameters for a model predictive controller based on CSA in CSTR process

Continuous Stirred Tank Reactor (CSTR) is a typical and high nonlinear process in process industry .It is difficult to control CSTR process. MPC is an advanced control strategy. But it is hard to tune the MPC parameters. A hybrid algorithm is presented to solve this difficulty and this algorithm is based on the immune clonal selection algorithm and sequential quadratic programming. The framework of tuning parameters based on events trigger is introduced in case of uncertain disturbance. Finally, simulation experiments were done with this algorithm in CSTR .Comparison with the results of set point control proved that the proposed method is more effective than other tuning methods and can be used to control CSTR process.

Internal-growth Strategies for Dynamic Process Optimization with Differential-algebraic Equations

Abstract Simultaneous methods based on numerical differentiation for process dynamic optimization are discussed, and succinct variants of the full discretized models, which are collocated by Lobatto methods, are proposed. With the same original dynamic problem, its discretized models with different number of finite elements have good structural similarity, and their optimal results can also fit well with each other. A novel solving idea is proposed that the low-density discretized solution is interpolated as the starting point for solving high-density discretized model, then the warm-start technology for the interior point method and the initial value setting method of barrier parameter are integrated to develop a fast solving strategy for dynamic optimization, named internal-growth approach. Finally, several test models, including the crystallization process optimization problem, are solved by the proposed approach, and the excellent solving efficiency is illustrated.