Influence of measurement noises and control saturation on steady state error

The influence of the measurement noise on steady state error, in the relay systems with sliding mode control and in the equivalent continuous systems is analyzed. The original definition of the distribution and distribution density functions is proposed, which makes it possible to calculate the mean value of the control and the static characteristic of the systems under existence of control saturation. It is shown that measurement noise may decrease the replacement gain of the relay and of the amplifier with saturation, which may increase the steady state error of the systems, significantly. Theoretical considerations have been confirmed by the performed simulations. It is shown that the resulting steady state error may be compensated by the saturated integral applied in the regulator.