From Data to Nonlinear Predictive Control. 2. Improving Regulatory Performance Using Identified Observers

Abstract

The development of schemes for effectively examining unmeasured disturbances and plant−model mismatch in nonlinear model predictive control (NMPC) is an important area, which has attracted considerable attention over the past decade. In this work, we propose NMPC formulations for improving regulatory performance using nonlinear state space models identified from input−output data. The NARX-type MISO and MIMO nonlinear models identified in Srinivasarao et al.17 are used to develop the state estimators and the predictors in the proposed NMPC formulations. We show that these models provide information about the covariances of the fast changing disturbances that are necessary for developing an extended Kalman filter (EKF) used in an NMPC scheme (EKF−NMPC). Rather than formulating an EKF to reject these disturbances, which we show has certain drawbacks, we proceed to propose an alternate prediction scheme based on the direct use of the identified noise model for future trajectory predictions. We show that the resulting NMPC formulation (DC−NMPC) is relatively easy to tune to achieve disturbance rejection as well as offset removal. The efficacy of the proposed control schemes is demonstrated using simulation studies on two benchmark control problems: (a) regulatory control of a continuously stirred tank reactor (CSTR) exhibiting input multiplicity at a singular point, and (b) servo control of a CSTR exhibiting output multiplicities. The analysis of simulation results reveals that the proposed EKF−NMPC and DC−NMPC schemes consistently generate significantly better regulatory performances, when compared to the performance of a conventional NDMC-type formulation, even in the presence of significant plant-model mismatch. In particular, the DC−NMPC performs significantly better than the EKF−NMPC formulation and can be tuned to achieve excellent regulatory performance without causing excessive input variability using parameters of a single disturbance filter. The conclusions reached through simulation studies are validated by conducting servo and regulatory control experiments on a laboratory-scale heater−mixer setup.