Sabatier Agrawal Machado Advances in Fractional Calculus Episode 14

Tham khảo tài liệu 'sabatier agrawal machado advances in fractional calculus episode 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | FLATNESS CONTROL OF A FRACTIONAL THERMAL SYSTEM 505 Bode Diagram of Open Loops CRONE PID 200 100 0 -100 -200 . -5 . --4 . --3 . --2 . -1 . .0 .1 .2 .3 10 10 10 10 10 10 10 10 10 -100 -150 -200 -250 -300 -350 -5 -4 -3 -2 -1 0 1 2 3 10-5 10-4 10-3 10-2 10-1 100 101 102 103 Fig. 8. Comparison of both PID and CRONE open-loop Bode diagrams with different gain variations Go 50 grey Go solid Go X 50 dash dotted and Go X 50 dotted . 6 Simulation Results Now the system is studied in closed-loop so as to measure its immunity to different disturbances applied to its input AU and its output AY . The control scheme is presented by Fig. 9 with Uref the control obtained by the flatness principle using the chosen reference trajectory Yref. Fig. 9. Closed-loop control scheme. The PID controller and the CRONE controller are both used in simulation. For this we study the disturbances and gain variation influences on path tracking. For this a 1 control input disturbance is applied at 500 s and a 3 506 Melchior Cugnet Sabatier Poty and Oustaloup output disturbance is applied at 1 500 s. Time responses are given for different gain variations 1 50 and 80 times as much gain . Time s Time s 35 30 25 20 15 10 5 0 -5 Fig. 10. Simulation with no disturbance and no gain variation path dotted CRONE black and PID grey . Time s Time s Fig. 11. Simulation with disturbances and no gain variation path dotted CRONE black and PID grey . Fig. 12. Simulation with disturbances and G0 X 50 gain variation path dotted CRONE black and PID grey . FLATNESS CONTROL OF A FRACTIONAL THERMAL SYSTEM 507 Effective Output C PID CRONE 0 500 1000 1500 2000 2500 Time s 0 -1 -2 0 System Input Control V PID CRONE 500 1000 1500 Time s 2000 2500 Fig. 13. Simulation with disturbances and G0 X 80 gain variation path dotted CRONE black and PID grey . Figure 10 shows the same path tracking for PID and CRONE controllers. In fact the loop has no role in the nominal case. Figure 11 shows a good path tracking in .