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A robust ILCIterative Learning Control (ILC) method is proposed for industrial batch processesBatch processwith input delayInput delay subject to time-varyingTime-varying uncertainties, based on a 2D system description of batch processBatch process operation. To compensate for the input delay, a 2D state predictorState predictor is established to predict theAugmented process (system) augmented system states, such that a 2D ILC design is developed for the delay-freeDelay-free 2D system based on using only the measured output errors of current and previous cycles. Delay-dependent stability conditions for the resulting 2D system are established in terms of matrix inequalities by defining a comprehensive 2D Lyapunov–Krasovskii functional candidate along with free-weightingWeighting matrix,matricesFree-weighting matrix. By solving these matrix inequalities using aCone complementarity linearization cone complementarity linearization method, the ILCIterative Learning Control (ILC) controller is explicitly derived together with an adjustable H-infinity performanceH infinity performance index. An important merit is that perfect trackingPerfect tracking can be realized for a batch processBatch process with arbitrarily long input delayInput delay and no time-varyingTime-varying uncertainties, if the delay-freeDelay-free part of the 2D system can be stabilized. Moreover, the time integralTime integralof tracking errorTracking error can be added as an extended 2D system state for ILCIterative Learning Control (ILC) design to eliminate steady-stateSteady-state output error for all batches. An illustrative example of an injection moldingInjection molding machine is given to demonstrate the effectiveness of the proposed method.

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2D State Predictor Based ILC Design Under Input Delay

  • 章节

  • 发表日期：

    2026年

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  • Tao Liu,
  • Shoulin Hao,
  • Youqing Wang,
  • Dewei Li

摘要

A robust ILCIterative Learning Control (ILC) method is proposed for industrial batch processesBatch processwith input delayInput delay subject to time-varyingTime-varying uncertainties, based on a 2D system description of batch processBatch process operation. To compensate for the input delay, a 2D state predictorState predictor is established to predict theAugmented process (system) augmented system states, such that a 2D ILC design is developed for the delay-freeDelay-free 2D system based on using only the measured output errors of current and previous cycles. Delay-dependent stability conditions for the resulting 2D system are established in terms of matrix inequalities by defining a comprehensive 2D Lyapunov–Krasovskii functional candidate along with free-weightingWeighting matrix,matricesFree-weighting matrix. By solving these matrix inequalities using aCone complementarity linearization cone complementarity linearization method, the ILCIterative Learning Control (ILC) controller is explicitly derived together with an adjustable H-infinity performanceH infinity performance index. An important merit is that perfect trackingPerfect tracking can be realized for a batch processBatch process with arbitrarily long input delayInput delay and no time-varyingTime-varying uncertainties, if the delay-freeDelay-free part of the 2D system can be stabilized. Moreover, the time integralTime integralof tracking errorTracking error can be added as an extended 2D system state for ILCIterative Learning Control (ILC) design to eliminate steady-stateSteady-state output error for all batches. An illustrative example of an injection moldingInjection molding machine is given to demonstrate the effectiveness of the proposed method.