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Vibration Analysis and Control New Trends and Developments Part 7

Tham khảo tài liệu 'vibration analysis and control new trends and developments part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 140 Vibration Analysis and Control - New Trends and Developments derivatives of the flat output required for implementation of the controller 20 71 72 72 73 Ì3 m iji 1 bu cb1 2 cb2 3 cbr-1 ữr eb r 0 y 71 L where 1 2 CỚ 3 cP CẠ- r 1 . A Luenberger observer for the system 22 is then given by 71 72 Ar 3 y - y 72 73 Ar 2 y - y 73 74 Ar 1 y - y y4 1 bu Ar y - y CP1 2 Ar-1 y - y 2 3 Ar-2 y - y cPr-1 r A1 y - y â r A0 y - y y 71 The estimation error dynamics e1 y - y satisfies the following dynamics c r 4 A. Ẩr 3h- A. np r 2 A. . c. r 1 4 A.e r e1 Ar 3e1 Ar 2e1 Àr 1e1 Are1 Ảr-1e1r 1 À2 e Ả1é1 À0e1 0 22 23 24 Therefore the design parameters Ải i 0 r 3 can be chosen so that the output estimation error e1 exponentially asymptotically converges to zero. On the other hand it is assumed that the perturbation input signal f can be locally approximated by a family of Taylor polynomials of fourth degree. Therefore the characteristic polynomial for the dynamics of output observation error 24 is given by Po2 s Ảgs Ả7S Ảị6s A5 s Ả4 s4 A3 s3 Ả2 Ả1 s Ả0 25 It is then proposed the following Hurwitz polynomial to compute the proper gains for the observer Po2 s s P2 s2 2Z2W2S W2 26 Control of Nonlinear Active Vehicle Suspension Systems Using Disturbance Observers 141 One then obtains that Aq P2 8 A1 2 8p2 Z2 7 A 2 8 7 Z2 24 P2 ịíị 4 P2 2 A3 24 2Z2 4 6 32 P2 5z2 24P2 2 Z2 A4 32 2z2 24 2 Z2 16 P2 4z2 48p2 2Z2 6p2 2 A5 16 2 z2 48 4 Z2 6 2 32 P2 3z2 24p2 2Z2 A6 32 2Z2 24 3 Z2 24 P2 2z2 4 P2 2 A7 24 2 Z2 4 2 8P2 2Z2 A8 P2 8 2 Z2 with P2 2 Z2 0. From the practical viewpoint main advantage of this high-gain observer is that it could be employed for hydraulic or electromagnetic active vehicle suspension systems requiring only information of the stiffness constant of tire kt and the unsprung mass mu. In addition it can be shown that the proposed observer design methodology is quite robust with respect to parameter uncertainty and unmodeled dynamics by considering the parameter variations into the