1 / 16

Multiple Model Approach to Multi-Parametric Model Predictive Control of a Nonlinear Process: A Simulation Case Study

This study presents a multiple model approach to multi-parametric model predictive control (MPC) of a nonlinear process. The approach utilizes a hybrid MPC method and a simplified, suboptimal solution. A simulation case study of pressure control in an annealer is presented to demonstrate the effectiveness of the proposed approach.

render
Télécharger la présentation

Multiple Model Approach to Multi-Parametric Model Predictive Control of a Nonlinear Process: A Simulation Case Study

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Multiple Model approach toMulti-Parametric Model PredictiveControl of a Nonlinear Process a simulation case study Boštjan Pregelj, Samo Gerkšič Jožef Stefan Institute, Ljubljana, Slovenia bostjan.pregelj@ijs.si, samo.grerksic@ijs.si 10th PhD Workshop on Systems and Control September 2009, Hluboka nad Vltavou, Czech Republic

  2. Introduction • with explicit solution the MPC is expanding its application area to low-level control • disturbance rejection • offset-free tracking • output feedback (states usually not measurable) • controller – estimatorinterplay • complexity (significant offline computation burden) • hybrid mp-MPC methods • control of hybrid or nonlinear systems • hybrid estimator required • controllerandestimator model stitching/switching • extremlydemandingcomputation & complexpartition • multiple-modelapproach • simplified, suboptimalsolution

  3. Outline • multi-parametric MPC • tracking controller and offset removal • case study plant • pressure control in wire annealer • nonlinear simulation model • controller design • PWA process model • controller & Kalman filter tuning • results • remarks & conclusions

  4. Model predictive controller, an MPC • linear system defined by a SS model • state and input constraints • MPC optimisation problem = CFTOC s.t.:

  5. Explicit solution of MPC • u(k) = function of current state! • PWA on polyhedra control law • where describes i -th region (polyhedron) • properties: • regions have affine boundaries • value function J*k is convex, continuous, piece-wise quadratic function of x(k), • optimizer: x*k is affine function of x(k), possibly discontinuous (at some types of boundaries)

  6. State controller -> Tracking contrl. • offset-free reference tracking • velocity form augmentation • elimination of offset due to disturbance • tracking error integration • disturbance estimation • output feedback • Kalman filter observer • additional integrating disturbance state d(k) • additional KF tuning possibilities • responce tuning with disturb. on states, inputs • input/output step disturbance model

  7. Process:pressure control in annealer • nonlinear high-order process, disturbances • actuators: • pump – slow response, large operating range • valve – fast response, small operating range • two input single output constrained system • additional DOF • constraints 0 < u1 < 50 [s-1], 0 < u2 < 100 [%], -5 < Δu1 < 5 [s-2], -50 < Δu2 < 50 [%/s]. 0 < p < 133 [mbar]

  8. Process: nonlinear simulation model • 2nd order linear dynamics • static input nonlinearities • u1: polynomial function y = f(u1) • u2: affine function • y = kiu2 + ni • i = f (u1) • u2 nonlinearity • narrow the input constraint limit to linear range f(u1) f(u2)

  9. Control design: hybrid PWA model • augment the original linear model with data from other operating points • model switching • f(x2) • f(x2, x4) boundary lines:

  10. gains for each local dynamical model defined in output equation (Wiener model) continuous transitions between models desired controller implementation active controller takes current state and computes control action Control design: PWA process model

  11. Control design: tuning • controller parameter tuning • guide: reasonable computation timeof controller • tuning using LLA (Local Linear Analysis) • root loci of dominant controller poles • parameters: N = 6, Nu = 2, Rdu = diag([0.1 0.05]), Ru = diag([10-6 0.02]) • KF tuning • extended LLA of closed loop system • parameters: QK = diag([10-6 10-6 10-6 10-6 1]) RK = 10-3

  12. MMmp-MPC (N=6,Nu=2) vslinearmp-MPC (N=6, Nu=2) tracking reference signal steps along three local dynamical models) linear model (black) from intermediate OP controllerpartitioncomposedof 3x100 reg. (hybridmp-MPC 200k) Results:simulation studies

  13. MMmp-MPC (N=27,Nu=2) vslinearmp-MPC (N=27, Nu=2) improvedperformancedue to longerhorizons. controllerresuling in ~3x300 regions hybridmp-MPC not reallyfeasible Results:simulation studies

  14. Conclusions • improved performance due do reduced plant-to-model mismatch • low computation demand & complexity • emphasis to nonlinear PWA plane matching • suboptimal solution • controller does not anticipate switch in prediction • controller sellection via scheduling variable • better results achievable • other suboptimal approaches(current&future work) • simplified hybrid mp-MPC • restrict switching among dynamics in prediction • keeps higher level of optimality

  15. Thank you!

  16. Multiple Model approach toMulti-Parametric Model PredictiveControl of a Nonlinear Process a simulation case study Boštjan Pregelj, Samo Gerkšič Jožef Stefan Institute, Ljubljana, Slovenia bostjan.pregelj@ijs.si, samo.grerksic@ijs.si 10th PhD Workshop on Systems and Control September 2009, Hluboka nad Vltavou, Czech Republic

More Related