ROBUST REGULATION FOR SYSTEMS WITH POLYNOMIAL NONLINEARITY APPLIED TO RAPID THERMAL PROCESSES
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Abstract. A problem of output robust control for a system with power nonlinearity is considered. The considered problem can be rewritten as a stabilization problem for a system with polynomial nonlinearity by introducing the error term. The problem of temperature regulation is considered as application; the rapid thermal processes in vapor deposition processing are studied. Modern industrial equipment uses complex sensors and control systems; these devices are not available for laboratory setups. The limited amount of available sensors and other technical restrictions for laboratory setups make it an actual problem to design simple low-order output control laws. The problem is solved by the consecutive compensator approach. The paper deals with a new type of restriction which is a combination of linear and power restrictions. It is shown that the polynomial nonlinearity satisfies this restriction. Asymptotical stability of the closed-loop system is proved by the Lyapunov functions approach for the considered nonlinear function; this contribution extends previously known results. Numerical simulation of the vapor deposition processing illustrates that the proposed approach results in zero-mean tracking error with standard deviation less than 1K.
Acknowledgements. This work was partially financially supported by the Government of the Russian Federation grant 074-U01), the Russian Ministry of Education and Science (project 14.Z50.31.0031)