Chattering suppression in sliding mode control system

In this dissertation, various known methods to decrease level of chattering caused by unmodeled dynamics are reviewed. And an analysis to understand system behavior in the presence of such unmodeled dynamics and to estimate the amplitude and frequency of chattering using describing function is provided. It is shown that the amplitude is proportional to relay gain of discontinuous control, and the frequency is inversely proportional to the time constant of unmodeled dynamics. Two methods are proposed to change switching magnitude of sliding mode control to reduce chattering. Based on the original idea of Variable Structure System, first method is to use adaptive relay gain which depends on system states. Second method varies switching gain of sliding mode control along the equivalent control. System behaviors with the two controller designs are analyzed, and it is demonstrated by simulations that chattering can be significantly reduced. For systems controlled by on/off switches or fixed switching gain only, chattering also appears if switching frequency is restricted at a finite value. To suppress chattering in such case, a methodology based on the harmonic cancellation is proposed. To fix switching frequency and to obtain desired phase shift between any two consecutive phases, hysteresis loops with adaptive width are implemented in switching elements. The design principle and procedure of the methodology are suggested, and chattering reduction effect of the method is demonstrated by various simulation results. It is also shown that the method using multiple phases may decrease chattering caused by unmodeled dynamics as well with the equivalent width of hysteresis which makes entire phases have the same frequency.