SUBOPTIMAL NONLINEAR CONTROL OF PACKAGING MACHINERY DRIVE
Keywords:«feeder» drive, suboptimal nonlinear control, position control loop, invariant «immersion» method, dynamic programming method, packaging machinery
AbstractThis paper deals with the procedure of synthesis of a nonlinear position controller for the «feeder» of packaging mechanism. The mathematical model of «feeder» drive with regard to the restriction on the control output of external PLC. Linearization of nonlinear characteristic by the «secants» method is implemented and selected functional quality that defines the minimal time of transients is selected. Quality functional in the form of a quadratic functional with a variable weighting factor is presented. To find the suboptimal control law, the method of dynamic programming method using the concept of an invariant «immersion» is used. In this case, the original nonlinear problem is decomposed into several linear optimal control problems. The problem of synthesis of the position controller «in the small» and «in the large» is solved; the analytical expressions for the control actions are obtained. As a result of the synthesis of the nonlinear control law, containing linear and cubic components of the state variables is obtained. The dynamic characteristics of the «feeder» drive with the standard linear position control, as well as synthetic nonlinear control method of digital simulation are presented.
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Copyright (c) 2014 V. F. Kudin, A. V. Toropov
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