Parameter identification and filter design for a repetitive controller of hot rolling mills

U výrobků válcoven za tepla se vyskytují periodické povrchové defekty v důsledku inherentní excentricity přítomné ve válcích. Tyto vady lze považovat za periodické rušení systému. Pro odstranění těchto závad je zkoumán návrh regulátoru založený na metodě opakované kontroly. První aproximací válcovacích tratí za tepla z experimentálních dat jako systémů s časovým zpožděním prvního řádu se získají potřebné podmínky regulátoru a vlastnosti, které musí být splněny pro periodické vyřazování poruch, pro konkrétní typ systémů s interním ovladačem modelu. S ohledem na tyto podmínky je pak navržena a testována metodika získávání filtrů, které mají klíčovou roli v opakované kontrole, pro její účinnost a robustnost při dosahování úspěšné kontroly při poruše a nesouladu mezi zařízeními a modely.In hot rolling mill products, periodic surface defects are encountered due to the inherent eccentricity present in the rolls. These defects can be considered as a periodic disturbance to the system. To remove these defects, a controller design based on Repetitive Control method is investigated. By first approximating hot rolling mills from experimental data as first-order time delayed systems, the necessary controller conditions and properties that need to be satisfied for periodic disturbance rejection are obtained for the particular type of systems with Internal Model Controller. Then with respect to these conditions, a methodology to obtain filters which hold a key part in Repetitive Control is proposed and tested for its effectiveness and robustness in achieving successful control under disturbance and plant/model mismatch

A CAD Method of Multivariable Control Systems Using Generalized Gershgorin Bands

The design method proposed here is a frequency-domain method and uses a certain class of generalized Gershgorin bands mapped onto the gain-phase plane, which are referred to as the generalized Gershgorin pseudo-bands. The main advantages are that the generalized Gershgorin pseudo-bands have the same width for all loops, that the width of the pseudo-bands is invariant under the changes of the diagonal compensator and under the changes of the unit system at outputs and inputs, that no diagonal dominance is required at high frequencies, and that a quantitative guide line for pseudo-diagonalization is given based on the interaction index which is a satisfactory scalor measure of the cross interaction

A detection theory account of change detection

Previous studies have suggested that visual short-term memory (VSTM) has a storage limit of approximately four items. However, the type of high-threshold (HT) model used to derive this estimate is based on a number of assumptions that have been criticized in other experimental paradigms (e.g., visual search). Here we report findings from nine experiments in which VSTM for color, spatial frequency, and orientation was modeled using a signal detection theory (SDT) approach. In Experiments 1-6, two arrays composed of multiple stimulus elements were presented for 100 ms with a 1500 ms ISI. Observers were asked to report in a yes/no fashion whether there was any difference between the first and second arrays, and to rate their confidence in their response on a 1-4 scale. In Experiments 1-3, only one stimulus element difference could occur (T = 1) while set size was varied. In Experiments 4-6, set size was fixed while the number of stimuli that might change was varied (T = 1, 2, 3, and 4). Three general models were tested against the receiver operating characteristics generated by the six experiments. In addition to the HT model, two SDT models were tried: one assuming summation of signals prior to a decision, the other using a max rule. In Experiments 7-9, observers were asked to directly report the relevant feature attribute of a stimulus presented 1500 ms previously, from an array of varying set size. Overall, the results suggest that observers encode stimuli independently and in parallel, and that performance is limited by internal noise, which is a function of set size

Convex searches for discrete-time Zames-Falb multipliers

In this paper we develop and analyse convex searches for Zames--Falb multipliers. We present two different approaches: Infinite Impulse Response (IIR) and Finite Impulse Response (FIR) multipliers. The set of FIR multipliers is complete in that any IIR multipliers can be phase-substituted by an arbitrarily large order FIR multiplier. We show that searches in discrete-time for FIR multipliers are effective even for large orders. As expected, the numerical results provide the best $\ell_{2}$-stability results in the literature for slope-restricted nonlinearities. Finally, we demonstrate that the discrete-time search can provide an effective method to find suitable continuous-time multipliers.Comment: 12 page

Optimal Output Modification and Robust Control Using Minimum Gain and the Large Gain Theorem

When confronted with a control problem, the input-output properties of the system to be controlled play an important role in determining strategies that can or should be applied, as well as the achievable closed-loop performance. Optimal output modification is a process in which the system output is modified in such a manner that the modified system has a desired input-output property and the modified output is as similar as possible to a specified desired output. The first part of this dissertation develops linear matrix inequality (LMI)-based optimal output modification techniques to render a linear time-invariant (LTI) system minimum phase using parallel feedforward control or strictly positive real by linearly interpolating sensor measurements. H-ininifty-optimal parallel feedforward controller synthesis methods that rely on the input-output system property of minimum gain are derived and tested on a numerical example. The H2- and H-infinity-optimal sensor interpolation techniques are implemented in numerical simulations of noncolocated elastic mechanical systems. All mathematical models of physical systems are, to some degree, uncertain. Robust control can provide a guarantee of closed-loop stability and/or performance of a system subject to uncertainty, and is often performed using the well-known Small Gain Theorem. The second part of this dissertation introduces the lessor-known Large Gain Theorem and establishes its use for robust control. A proof of the Large Gain Theorem for LTI systems using the familiar Nyquist stability criterion is derived, with the goal of drawing parallels to the Small Gain Theorem and increasing the understanding and appreciation of this theorem within the control systems community. LMI-based robust controller synthesis methods using the Large Gain Theorem are presented and tested numerically on a robust control benchmark problem with a comparison to H-infinity robust control. The numerical results demonstrate the practicality of performing robust control with the Large Gain Theorem, including its ability to guarantee an uncertain closed-loop system is minimum phase, which is a robust performance problem that previous robust control techniques could not solve.PHDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/143934/1/caverly_1.pd

Practical robustness measures in multivariable control system analysis

The robustness of the stability of multivariable linear time invariant feedback control systems with respect to model uncertainty is considered using frequency domain criteria. Available robustness tests are unified under a common framework based on the nature and structure of model errors. These results are derived using a multivariable version of Nyquist's stability theorem in which the minimum singular value of the return difference transfer matrix is shown to be the multivariable generalization of the distance to the critical point on a single input, single output Nyquist diagram. Using the return difference transfer matrix, a very general robustness theorem is presented from which all of the robustness tests dealing with specific model errors may be derived. The robustness tests that explicitly utilized model error structure are able to guarantee feedback system stability in the face of model errors of larger magnitude than those robustness tests that do not. The robustness of linear quadratic Gaussian control systems are analyzed