Rejection of periodic disturbances in uncertain nonlinearly perturbed stable infinite dimensional systems

Natarajan, Vivek

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https://hdl.handle.net/2142/42180 Copy

Description

Title

Rejection of periodic disturbances in uncertain nonlinearly perturbed stable infinite dimensional systems

Author(s)

Natarajan, Vivek

Issue Date

2013-02-03T19:18:33Z

Director of Research (if dissertation) or Advisor (if thesis)

Bentsman, Joseph

Doctoral Committee Chair(s)

Bentsman, Joseph

Committee Member(s)

• Basar, Tamer
• Hovakimyan, Naira
• Mehta, Prashant G.

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Periodic disturbance
• Internal model principle
• Nonlinearly perturbed regular linear system
• Mold oscillation
• Continuous casting of steel

Abstract

A motion distortion problem in the mold oscillation system of a continuous caster is addressed. The mold oscillation system consists of a subsystem of beams hinged at the center supporting the mold at one end and excited by an electro-hydraulic actuator at the other end. The actuator piston is attached to the beam subsystem and tracks a reference sinusoid, typically via proportional feedback. When the reference sinusoid frequency is near a submultiple of a beam resonance frequency, the mold velocity profile exhibits distortions. Eliminating these distortions will permit the safe operation of the oscillation system in production using reference sinusoids of larger frequency. This will improve the surface quality of the cast steel slabs which in turn will enable casting of newer grades of steel. An experimental testbed, a simplified construction of the mold oscillation system, consisting of a hollow beam hinged at the center, supporting a mass resembling the mold at one end and excited by an electro-hydraulic actuator at the other end was built by the steel company. This testbed exhibits distortions similar, albeit more pronounced, to the mold oscillation system. Eliminating these distortions from the testbed is a prerequisite for gaining access to the mold oscillation system. Furthermore, access to the mold oscillation system is limited in general. Hence the modeling, problem formulation, controller synthesis, controller validation and rigorous analysis are carried out for the testbed. Then the controller is transitioned, under reasonable assumptions, to eliminate distortions in the mold oscillation system. A fundamentally based analytical model of the testbed was developed as a system of coupled linear partial differential equations and nonlinear ordinary differential equations. Using experimental data it was hypothesized, and then verified using model simulations, that the major source of distortion was the nonlinear actuator dynamics. The nonlinear effects, though insignificant in general, lead to the creation of small amplitude harmonics in the piston position signal that get amplified by the beam to create large distortions in the mold position and velocity profiles. Hence the overall system dynamics, with the piston position as the output, was justified to be that of a nonlinearly perturbed linear infinite dimensional system from whose output the harmonics created by the nonlinearity must be eliminated. First a non-model based control scheme, using the plant gain at the frequency of interest alone, is developed to reject bandlimited periodic disturbances from the output of a nonlinearly perturbed finite dimensional plant. The stability of the closed loop is obtained via block diagram manipulations and small gain theorem. Next this scheme is shown to be applicable for tracking of periodic signals by regular linear systems, a fairly large class of infinite dimensional linear systems, using tools from infinite dimensional control theory. Quantifiable robustness margins, valuable in application, are derived. Finally a class of nonlinearly perturbed regular linear systems, matching the phenomenology of the application, is introduced. Its stability and response to periodic excitation are characterized and the proposed control scheme is rigorously shown to be applicable for rejecting unwanted harmonics from this class. The testbed model is shown, under reasonable assumptions, to belong to the class of systems introduced above. Therefore applying the proposed control scheme in simulations to the testbed model and in experiments to the testbed is justified and is carried out to eliminate the unwanted harmonic. The mold oscillation system and the testbed have a similar structure - flexible components, electro-hydraulic actuator, and end mass. Therefore transitioning the control scheme, developed for the testbed, to the mold oscillation system is reasonable and is performed in the absence of steel to eliminate the unwanted harmonics, thereby removing the distortions from the mold velocity profile. Finally, after refining the code to include calculation of the controller coefficients using explicit functions of the excitation frequency, the control scheme is implemented in production, i.e. in the presence of molten steel, to achieve visibly noticeable improvement in the surface quality of the steel slabs.

Graduation Semester

2012-12

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http://hdl.handle.net/2142/42180

Copyright and License Information

Copyright 2012 Vivek Natarajan

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