Model Predictive Control Part 11

Tham khảo tài liệu 'model predictive control part 11', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Model Predictive Trajectory Control for High-Speed Rack Feeders 193 2 -2y 0 5 10 t in s 15 Fig. 4. Desired trajectories for the cage motion desired and actual position in horizontal direction upper left corner desired and actual position in vertical direction upper right corner actual velocity in horizontal direction lower left corner and actual velocity in vertical direction lower right corner . and its first three time derivatives are considered. Including the equations of motion 12 yields the following set of equations yKd Ơ ys t 2 K2 3 - K Vi t 49 yKd t ys t 2 K2 3 - K vi t 50 yKd t ys t 1K2 3 - K vi t yK vi t ys t V1 t ud t K 51 y Kd t yK v1 t ys t V1 t ud t ud t K . 52 Solving equation 49 to 52 for the system states results in the desired state vector xd t ysd yKd t yKd t yKd t yKd t ud t ud t K vid yKd t yKd t t ud t ud t k ysd yKd t yKd fi t ud t ud t K vid yKd t yKd t y Kd t ud t ud t K 53 This equation still contains the inverse dynamics Ud t and its time derivative Ud. Substituting Ud for equation 48 and Ud t for the time derivative of 48 which can be calculated analyti- 194 Model Predictive Control cally finally leads to 54 ysd yKd yKd yKd t y Kd yKd t y Kd t K vid yKd t i Kd t yKd t y Kd t yKd t y Kd t K ySd yKd t yKd t yKd t yKd t yKd t y Kd t K vid yKd t yKd t yKd t yKd t y Kd t y Kd t K Fig. 5. Tracking error ey t for the cage motion in horizontal direction. Fig. 6. Tracking error ex t for the cage motion in vertical direction. Model Predictive Trajectory Control for High-Speed Rack Feeders 195 5. Experimental validation on the test rig The benefits and the efficiency of the proposed control measures shall be pointed out by experimental results obtained from the test set-up available at the Chair of Mechatronics University of Rostock. For this purpose a synchronous four times continuously differentiable desired trajectory is considered for the position of the cage in both x- and y-direction. The desired trajectory is given by polynomial .