Tham khảo tài liệu 'advances in pid 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 | 110 Advances in PID Control Figure 8 shows how with increasing time the value of the adaptive gain draws even closer to zero. The same can be said of the error in Figure 9 and of z in Figure 10. 1 to c O 0 0 cc -C I E s -1 x 10 396 397 398 399 400 Time seconds Fig. 8. Controller Performance Adaptive Gain detail . Time seconds Fig. 9. Controller Performance Position Error detail . Adaptive Gain PID Control for Mechanical Systems 111 Fig. 10. Controller Performance Error Integral detail . 8. Conclusions An extension to the traditional PID controller has been presented that incorporates an adaptive gain. The adaptive gain PID controller presented is demonstrated to asymptotically stabilize the system this is shown in the simulations where the position error converges to zero. In the presented analysis considerations using known bounds of the system such as friction coefficients are used to show the stability of the system as well as to tune the controller gains Kp and Kd. 9. References Alvarez J. Santibanez V. Campa R. 2008 . Stability of Robot Manipulators Under Saturated PID Compensation. IEEE Transactions on Control Systems Technology Vol. 16 No. 6 Nov 2008 1333 - 1341 ISSN 1063-6536 Ang K. H. Chong G. Li Y. 2005 . PID Control System Analysis Design and Technology. IEEE Transactions on Control Systems Technology Vol. 13 No. 4 Jul 2005 559 - 576 ISSN 1063-6536 Canudas de Wit C. Olsson H. Astrom . Lischinsky P. 1995 . A new model for control of systems with friction. IEEE Transactions on Automatic Control Vol. 40 No. 3 Mar 1995 419 - 425 ISSN 0018-9286 Chang P H. Jung . 2009 . A Systematic Method for Gain Selection of Robust PID Control for Nonlinear Plants of Second-Order Controller Canonical Form. IEEE Transactions on Automatic Control Vol. 17 No. 2 Mar 2009 473 - 483 ISSN .
