Tham khảo tài liệu 'model predictive control part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Model predictive control of nonlinear processes 113 An internal model is used to eliminate the discrepancy between model and process outputs error t at each sampling instant error i y t - ym i 7 where ym t is the one-step ahead model prediction at time t-1 . The estimate of the error is then filtered to produce err t which minimizes the instability introduced by the modeling error feedback. The filter error is given by err t 1-Kf err t-1 Kf error t 8 where Kf is the feedback filter gain which has to be tuned heuristically. Back substitutions transform the prediction model equations into the following form yp t N fN 1y t . fN nyy t - ny 1 fN ny 1u t -1 . fN ny nu-1u t - nu 1 9 gNu . gN mu t m -1 eNerr t The elements f g and e are recursively calculated using the parameters a and p of Eq. 3 . The above equations can be written in a condensed form as Y t F X t G U t E err t 10 where . no WM . . . T 11 X t y t y t-1 . . . y t-ny 1 u t-1 . . . u t-nu 1 T 12 U t u t . . . u t m-1 T 13 f11 f12 .f1 ny nu-1 f11 f12 .f2 ny nu-1 F fN 1 fN12 .fN ny nu-1 g11 0 0 . 0 g21 g21 0 . 0 G gm1 gm2 gm3 gmm gN1 gN2 gN3 . gNm E e1 . . . eN T 114 Model Predictive Control In the above Y t represents the model predictions over the prediction horizon X t is a vector of past plant and controller outputs and U t is a vector of future controller outputs. If the coefficients of F G and E are determined then the transformation can be completed. The number of columns in F is determined by the ARX model structure used to represent the system where as the number of columns in G is determined by the length of the control horizon. The number of rows is fixed by the length of the prediction horizon. Consider a cost function of the form N 2 m J s yp t i -w t i Ej u t i - 1 2 i 1 i 1 N m Y t - W T Y t - W U T U t 14 i 1 i 1 where lA V is a setpoint vector over the prediction horizon W t w t 1 . . . . w t N T 15 The minimization of the cost function J gives optimal controller output sequence U t GTG ỴI pGT
