Robust Tuning of Machine Directional Predictive Control of Paper Machines

Abstract

In this work, a parameter tuning problem of two-degrees-of-freedom model predictive control of industrial paper-making processes is explored to achieve satisfactory time-domain robust closed-loop performance in terms of worst-case overshoots and worst-case settling times, under user-specified parametric uncertainties. An efficient visualization method is first developed to characterize the set of time-domain closed-loop responses in the presence of parametric model–plant mismatch. On the basis of the visualization technique and the unmodality/monotonicity properties of the performance indices with respect to the tuning parameters, the feasibility of the tuning problem can be analyzed, and a three-step iterative line-search based automatic tuning algorithm is proposed to determine the controller parameters that meet the time-domain performance requirements robustly for the given parametric uncertainty specifications. The effectiveness of the algorithm is illustrated by applying the results to a process from stock to conditioned weight in an industrial paper machine and by comparing the performance of the algorithm with that of brutal search.

An Improved Approach for Robust MPC Tuning Based on Machine Learning

“…Considering the requirement of the BPNN in this work, the 2mΔ groups of datasets are obtained when training RBF network is directly utilized, and therefore, it is necessary to have at least 2mΔ × 2 d curves to generate a reasonable result. e reason to consider 2 d curves is that in order to characterize the worst-case performance, the polyhedron system representation [3] in robust control theory is employed, which indicates that the worst performance of the uncertain system mostly appears at the vertex system of the polyhedron system, and therefore, the largest and smallest possible values of each model parameter of the uncertain system need to be considered, resulting in 2 d curves for each group of robust indices. Note that, compared with the existing method to evaluate the worst-case time-domain performance (e.g., brutal search method), the aforementioned method is much simpler, since the required number of curves is significantly reduced, which helps to achieve the network in a more efficient way.…”

“…Model predictive control (MPC) has been widely used in industrial communities due to its robustness, ability to tackle safety constraints, and inaccurate model [1,2]. As we all know, PID control is normally applied at the system's base layer, while the MPC controllers are usually employed at the supervisory layer [3]. In MPC applications, the prediction horizon, control horizon, and weighting matrices in the cost function will significantly affect the closed-loop performance of the controlled system, and thus, the selection of the aforementioned parameters becomes one of the most important tasks for MPC design [4].…”

Impact of model plant mismatch on performance of control systems: An application to paper machine control

“…The following equation shows the relation between the mentioned variables. This model is widely used in pulp and paper industry (Astrom, 1967;Backström & Baker, 2008;Chu, Gheorghe, Backstrom, Forbes, & Chu, 2011;Shi, Wang, Forbes, Backstrom, & Chen, 2015): ( ) For such a system, each transfer function P ij is specified as a first order transfer function with a dead time (Table 2). These transfer functions are used as the plant model to design a controller.…”

Study of control parameters tuning method for hydro-viscous driver system

“…In a sense, the system can be approximated as a first-order plus time delay system (FOPTD), which can be made full use of to design the controller and finish the subsequent simulation and experiment. The stable FOPTD model can be described by [12]:…”