Control‐oriented modeling of sheet and film processes

Abstract

Sheet and film processes pose a challenging identification and control problem due to

Structured spatial control of the reaction-diffusion equation with parametric uncertainties

“…Unlike most processes [8], this large condition number does not induce any uncertainties in the decoupling matrix R or the subprocess 1 [·] is the nearest integer function [10] transfer functions in (23)- (24), as these operators were derived analytically as a result of process symmetry rather than identified from experimental data. We will see later that, for the feedback controller design in this paper, these properties of P (s) do not result in sensitivity to manipulation inaccuracies, which is very different for other symmetric circulant processes such as blown film extrusion [7] or for most other processes such as distillation columns [26]. …”

“…This control problem is motivated by processes with circular symmetry, such as in silicon wafer processing [31] and blown film extrusion [7], and by spatial field control problems for reaction-diffusion processes that arise in drug delivery [25], tissue engineering [18], epidemiology [11], and cancer treatment [27]. chemical process, u(θ, t) would be the injection of molecules along the circumference, whereas u(θ, t) for a biological process would be the injection of nutrients (e.g., glucose).…”

Convex relaxation of sequential optimal input design for a class of structured large-scale systems: process gain estimation

“…The transfer function matrix of a linearized process dynamics is assumed to be represented as a singular value decomposition (SVD) in which the associated unitary matrices are independent of frequency and the diagonal terms are frequencydependent transfer functions corresponding to linear timeinvariant systems. In [10], [12]- [15], it was shown that the accuracy of the diagonal elements of the transfer function For the input design of process gain estimation for largescale processes, this paper presents convex relaxation methods for the original nonconvex NP-hard problems and sequential modifications of the objective function for iterative design. The convex relaxation methods used in this paper have been also popular in other applications such as signal processing [16], information theory [17], and combinatorial optimization [18]- [20] and provide quantifiable performance bounds on the achievable optimal value for some special cases.…”

When is constrained control necessary for large scale processes?

“…For example, a control algorithm implemented on an industrial-scale adhesive coater at the Avery-Dennison company handled constraints with nearly optimal performance by just scaling back the unconstrained manipulated variable vector whenever the constraints were violated [l]. For a blown f i l m extruder, a controller designed to not manipulate uncontrollable plant directions did not need constraint-handling to achieve the desired closed loop performance [5]. It was Explicit conditions are derived which identify whether constraint-handling is needed for a particular process.…”