Tham khảo tài liệu 'model predictive control part 16', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Nonlinear Predictive Control of Semi-Active Landing Gear 293 problem thus global optimum can not be obtained. Furthermore due to its high computational requirement SQP method is not suitable for online optimization. To the semi-active landing gear control problem a nonlinear output-tracking predictive control approach Lu 1998 is adopted here considering its effectiveness to constrained control problems and real-time performance. The basic principle of this control approach is to get a nonlinear feedback control law by solving an approximate receding-horizon control problem via a multi-step predictive control formulation. The nonlinear state equation and output equation are defined by eq. 28-29 . And the following receding-horizon problem can be set up for providing the output-tracking control min J x t t u min - i eT r Qe r uT t Ru r d 31 u u 2 Jt subject to the state equations 28 and e t T 0 32 where e t y t - yd t . Then we shall approximate the above receding-horizon control problem by the following multi-step-ahead predictive control formulation. Define h T N with N is control number during the prediction horizon. The output y t kh is approximated by the first-order Taylor series expansion y t kh y t C x t x t kh - x t 1 k N 33 where C Õc x õx . The desired output yd t kh is predicted similarly by recursive first-order Taylor series expansions yd t h - yd t hy d t yd t 2h - yd t h hy d t h - yd t hy d t h y d t hyd t where another first-order expansion y d t h y d t hyd t then we have yd t kh - yd t hE 1 hPý pyd t 34 i 0 where p d dt is the differentiation operator. Combining the predictions of y t kh and yd t kh we obtain the prediction of the tracking error 294 Model Predictive Control e t kh y t kh - yd t kh h S C I hF 1 f k 1 i 0 35 s C I hF y gu t k -1 - 1 h - 1 hp 1 pyd t 1 0 where F x cf x dx. Approximating the cost function by the trapezoidal rule it can be written as a quadratic function J 2 vT H x v r T x v q e x yd 36 where v col u t u t h . u t N 1
