Tham khảo tài liệu 'sliding mode control part 3', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Sliding Mode Control for Industrial Controllers 59 For the desire an output voltage vsp the needed set point value for the inductor current is found as . vC i sp ER 47 The motion after sliding mode is enforced is governed by the following equation dvC 1 E . VC C É - dt C ị_vC sp R 48 It is evident that the unique equilibrium point of the zero dynamics is indeed an asymptotically stable one. To proof this let s consider the following Laypunov candidate function V 1 VC -Vsp 2 The time derivative of this Lyapunov candidate function is 49 V vC -Vsp C E ---i_ C _VC sp - r. .2 _VC R v -V -1 - - C sp C VCR -E1 vC CvC C - V vC -vsp 2 vC -vsp VC VC R sp 50 The time derivative of the Lyapunov candidate function is negative around the equilibrium point vsp given that vC 0 around the equilibrium. To demonstrate the efficiency of the indirect control method figure 11 shows simulation result when using the following parameters L 40mH C 4 pF R 40 Q E 20 V v 40 V. 6. Chattering reduction in multiphase DC-DC power converters One of the most irritating problems encountered when implementing sliding mode control is chattering. Chattering refers to the presence of undesirable finite-amplitude and frequency oscillation when implementing sliding mode controller. These harmful oscillations usually lead to dangerous and disappointing results . wear of moving mechanical devices low accuracy instability and disappearance of sliding mode. Chattering may be due to the discrete-time implementation of sliding mode control . with digital controller. Another cause of chattering is the presence of unmodeled dynamics that might be excited by the high frequency switching in sliding mode. Researchers have suggested different methods to overcome the problem of chattering. For example chattering can be reduced by replacing the discontinuous control action with a continuous function that approximates the sign s t function in a boundary later layer of 60 Sliding Mode Control the manifold 5 t 0 .
