In this Chapter, an indirect-type ILCIndirect-type ILC design based on the classical PID control loop is presented for application to industrial batch processesBatch process subject to time-varyingTime-varying uncertainties. By taking a state-space model description of such a batch process together with norm-bounded uncertainties, a robust PID tuning algorithm is firstly offered in terms of the \({\mathcal{H}}_{\infty}\) control objectiveControl objective, which is primarily responsible for maintaining the closed-loop systemClosed-loop systemrobust stabilityRobust stability and no steady output deviation. Then, an ILC scheme consisting of the learning controllers to adjust the set-point commandSet-point command and the feedforward controllersFeedforward control to adjust the process input is proposed to realize robust trackingRobust tracking against time-varying uncertainties and load disturbanceLoad disturbance. Accordingly, the PID tuning and the ILCIterative Learning Control (ILC) design can be conducted relatively independent of each other. By analyzing the sufficient conditions in terms of LMILinear Matrix Inequality (LMI) constraints for maintaining robust stabilityRobust stability of the PID control loop and theRobust convergencerobust convergenceConvergence of the ILC scheme, respectively, the PID and ILC controllers are derived along with an adjustable robust \({\mathcal{H}}_{\infty}\) performance level. The effectiveness of the proposed method is demonstrated through an illustrative example of an injection model machine.

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Proportional-Integral-Derivative (PID) Based Iterative Learning Control

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

摘要

In this Chapter, an indirect-type ILCIndirect-type ILC design based on the classical PID control loop is presented for application to industrial batch processesBatch process subject to time-varyingTime-varying uncertainties. By taking a state-space model description of such a batch process together with norm-bounded uncertainties, a robust PID tuning algorithm is firstly offered in terms of the \({\mathcal{H}}_{\infty}\) control objectiveControl objective, which is primarily responsible for maintaining the closed-loop systemClosed-loop systemrobust stabilityRobust stability and no steady output deviation. Then, an ILC scheme consisting of the learning controllers to adjust the set-point commandSet-point command and the feedforward controllersFeedforward control to adjust the process input is proposed to realize robust trackingRobust tracking against time-varying uncertainties and load disturbanceLoad disturbance. Accordingly, the PID tuning and the ILCIterative Learning Control (ILC) design can be conducted relatively independent of each other. By analyzing the sufficient conditions in terms of LMILinear Matrix Inequality (LMI) constraints for maintaining robust stabilityRobust stability of the PID control loop and theRobust convergencerobust convergenceConvergence of the ILC scheme, respectively, the PID and ILC controllers are derived along with an adjustable robust \({\mathcal{H}}_{\infty}\) performance level. The effectiveness of the proposed method is demonstrated through an illustrative example of an injection model machine.