Robust optimal control of profiles using multiple CD actuator systems

• Published in: Pulp & paper Canada Vol. 104; no. 11; pp. 24 - 27
• Main Authors: SHAKESPEARE, J, PAJUNEN, J, NIEMINEN, V, METSÄLÄ, T
• Format: Conference Proceeding Magazine Article
• Language: English
• Published: Don Mills, ON Southam 01.11.2003; Annex Publishing & Printing, Inc
• Subjects: Algorithms; Applied sciences; Exact sciences and technology; Machinery; Paper making; Paper, paperboard, non wovens; Polymer industry, paints, wood; Process controls; Properties and testing; Quality control; Wood. Paper. Non wovens; Water content; Theoretical study; Paper; Numerical simulation; Controller; Variance analysis; Optimization; Actuator
• ISSN: 0316-4004; 1923-3515

q = P[Symbol Not Transcribed] P + [Symbol Not Transcribed] [lambda][Symbol Not Transcribed][Symbol Not Transcribed] [delta]U[Symbol Not Transcribed] [Symbol Not Transcribed] [delta]U + [Symbol Not Transcribed] [lambda][Symbol Not Transcribed] (D[Symbol Not Transcribed][Symbol Not Transcribed] [delta]U)[Symbol Not Transcribed] (D[Symbol Not Transcribed][Symbol Not Transcribed] [delta]U) + [Symbol Not Transcribed] [lambda][Symbol Not Transcribed](D[Symbol Not Transcribed][Symbol Not Transcribed] [delta]U)[Symbol Not Transcribed] (D[Symbol Not Transcribed][Symbol Not Transcribed] [delta]U) q = P[Symbol Not Transcribed] QP + [Symbol Not Transcribed] [lambda][Symbol Not Transcribed]U[Symbol Not Transcribed]U + [Symbol Not Transcribed] [lambda][Symbol Not Transcribed](D[Symbol Not Transcribed]U) [Symbol Not Transcribed](D[Symbol Not Transcribed]U) + [Symbol Not Transcribed] [lambda][Symbol Not Transcribed](D[Symbol Not Transcribed]U)[Symbol Not Transcribed] (D[Symbol Not Transcribed]U)+... where U is either the actuator position or its deviation from a reference or minimum cost state for the actuator, and Q is a symmetric weighting matrix. With this algorithm, the actuator profile will remain reasonably smooth if [Symbol Not Transcribed] [lambda][Symbol Not Transcribed] or [Symbol Not Transcribed] [lambda][Symbol Not Transcribed] is nonzero, and will remain in the neighbourhood of its reference state if [Symbol Not Transcribed] [lambda][Symbol Not Transcribed] is nonzero. Smoothness is a requirement for actuators such as slice lip and coater blade, for which algorithms (5) and (7) are unsuitable. Algorithm (8), with [Symbol Not Transcribed] [lambda][Symbol Not Transcribed] and [Symbol Not Transcribed] [lambda][Symbol Not Transcribed] set to zero, and [Symbol Not Transcribed]2 = 0.5 gives CD performance indices of 95.2, 94.4, and 91.2, respectively, for mapping errors of 0, 2, and 4 cm. Note that the performance index of 95.2 is effectively the minimum variance for this situation, since a slice lip is not arbitrarily deformable.