An algorithm for minimum variance control of a dynamic time-delay system to reduce product variability
A minimum variance feedback control algorithm (MVFCA) for a second-order dynamic time-delay system described in this paper calculates a series of adjustments required at the input that minimise the variance (mean square error, MSE) of the output variable. The formulation of the algorithm (MVFCA) takes into consideration feedback (closed-loop) control stability of the time-delay system and the steady-state gain in the feedback loop. This paper aims to reduce variance at the output by using the feedback control algorithm (MVFCA). A steady-state stability limit exists in the allowable feedback gain that amounts to a trade-off between performance and stable operation of the time-delay system. For stability reasons, as a special case, attention is restricted to the `critically damped' behaviour of the time-delay system. The MVFCA has an integral control term and a dead-time compensation term that facilitates its practical application in the manufacturing industry. The integral term provides the discrete analogue of integral control and the time-delay (dead-time) compensation term has a stabilising effect on the time-delay system. A discrete (sampled-data) feedback controller is designed on the basis of the control algorithm (MVFCA) and the simulation shows that to maintain the mean of the product quality variable at or near controller set point reduces product variability.
minimum variance critically damped integral control dead-time compensation