State-space digital PID controller design for linear stochastic multivariable systems with input delay

In this paper, a centralized digital PID control scheme is proposed for linear stochastic multivariable systems with input delay. The discrete linear quadratic regulator (LQR) approach with pole placement is used to achieve satisfactory setpoint tracking with guaranteed closed-loop stability. In addition, the innovation form of Kalman gain is employed for stochastic disturbance regulation with no prior knowledge of noise properties. Compared with existing designs, the proposed scheme provides an optimal closed-loop design via the digitally implementable PID controller for linear stochastic multivariable systems with input delay. Its effectiveness would be demonstrated by simulation study on a dry rotary cement kiln.