Chattering Problem in Sliding Mode Control Systems

In practical applications of sliding mode control, engineers may experience undesirable phenomenon of oscillations having finite frequency and amplitude, which is known as `chattering´. At the first stage of sliding mode control theory development the chattering was the main obstacle for its implementation. The major attention was paid to the systems with motion equations in canonical space - space of a system output and its high order derivatives. Small time constants of real differentiators could not be disregarded, if control actions were discontinuous state functions, and they led to oscillations in the vicinity of discontinuity surfaces in the system state space. Chattering is a harmful phenomenon because it leads to low control accuracy, high wear of moving mechanical parts, and high heat losses in power circuits. There are two reasons which can lead to chattering. Similarly to the systems in canonical space, the chattering can be caused by fast dynamics which were neglected in the ideal model. These `unmodeled´ dynamics with small time constants are usually disregarded in models of servomechanisms, sensors and data processors. The second reason of chattering is utilization of digital controllers with finite sampling rate, which causes so called `discretization chatter´. Theoretically the ideal sliding mode implies infinite switching frequency. Since the control is constant within a sampling interval, switching frequency can not exceed that of sampling, which lead to chattering as well