Digital design of combined PI and state feedback controller for non-linear stochastic systems

In this paper, a combined Proportional-Integral (PI) and state feedback linear discrete control scheme is proposed for non-linear stochastic systems. The state-dependent optimal linear model of the original non-linear plant is first constructed from system state feedback at each sampling period, then the discrete linear quadratic regulator approach with pole placement is applied to issue and update controller settings. If the system is under stochastic process noise, the innovation form of Kalman gain can be employed for optimal states estimation without requiring prior knowledge of noise properties. Stability conditions for sampled-data non-linear systems are addressed in discrete-time analysis. The effectiveness of the proposed method will be demonstrated by the simulation examples of both single-input single-output and multi-input multi-output non-linear processes.