Application strategy of variable structure PID controller for stochastic systems

In this paper, proportional-integral-derivative (PID) control is extended into nonlinear system control field. First, variable structure control (VSC) of linear stochastic system with constraints of pole and covariance is discussed. The sliding surface is calculated to ensure that the covariance is small and the poles of closed-loop sub-system are allocated in the specified sector region, i.e., there is lower steady variance in linear control part and the state of closed-loop system could arrive at the sliding surface in the limited time from initial position in nonlinear control part, then the integrator is added to obtain one variable structural PID control with state feedback. The LMI method is used to ensure the system having a smaller variance and the pole being in the given place. This design method combines variable structure control with PID, which provides a new way to solve PID control problem in practical engineering