(713g) A New Extended Prediction Self-Adaptive Control (EPSAC) Strategy for Batch Control

It is well documented that linear model predictive control (MPC) techniques are predominantly used in industrial applications¹. Driven by the stringent specifications on product quality, tighter environmental regulation of effluent streams, and higher competition in the process industries, the development of nonlinear model predictive control (NMPC) techniques is of interest to both the academic and industrial sectors. The main benefit of NMPC lies in its capability to handle nonlinearities and time-varying characteristics inherent in process dynamics while performing real-time dynamic optimization with constraints and bounds on both system states and manipulated variables^2,3. Toward this end, various methods have been employed to approximate the process nonlinearity in the various NMPC design methods reported in the literature, including successive linearization⁴, neural networks⁵, multiple local models^6,7, piecewise linearization⁸, andhybrid models⁹.

     Among the aforementioned NMPC design methods, the extended prediction self-adaptive control (EPSAC) algorithm¹⁰adopted a distinct approach by approximating process variables through iterative optimization around the pre-specified base input trajectory and corresponding base output trajectory. In this manner, the outputs in the prediction horizon are obtained as the sum of a base term and a deviation term. The former is computed from the nonlinear process model based on current value of input variable given by the predefined base input trajectory, while the latter obtained from finite step response or impulse response models, from which a quadratic programming (QP) problem is formulated and can be solved iteratively¹¹. Though successful applications of EPSAC have been reported^10-13, one potential drawback of the previous EPSAC algorithms is the incorporation of finite step response or impulse models in the formulation of the control algorithm. Since model parameters are obtained by introducing a step change to the current input value specified by the base input trajectory, those model parameters obtained further away from the current time become less accurate due to process nonlinearity, leading to inevitable modeling error that degrades the achievable control performance. This shortcoming may become even worse when the EPSAC is applied in batch process control, where the objective is often to control the product quality at batch end. As a large number of step response parameters are needed at the beginning of the batch run to predict the future process outputs for the remaining batch, this eventually leads to inaccurate predicted outputs and poor control performance. Furthermore, another aim of this paper is to formulate the EPSAC algorithm to use state-space models due to its inherent flexibility to represent stable, integrating, and unstable processes^{1-3, 14}.    

     Motivated by the aforementioned discussion, a new EPSAC algorithm based on the Just-in-Time Learning (JITL) method¹⁵ is developed in this work. The JITL method is a data-based modeling methodology that approximates a nonlinear system with a set of local models valid in the relevant operating regimes. In the proposed JITL-based EPSAC design, the deviation term is obtained by a set of local state-space models identified by the JITL method along the base trajectories. In simulation results of case studies for batch control of end-product quality, including an evaporative crystallizer¹⁶and a bioreactor¹⁷, the proposed EPSAC algorithm provides better closed-loop performance than its previous counterpart¹¹.

 

References

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