| A new methodology is developed for optimal infeed control of cylindrical plunge grinding cycles. Unlike conventional cycles having a few sequential stages with discrete infeed rates, the new methodology allows for continuous variation of the infeed rate to further reduce the cycle time. Distinctive characteristics of optimal grinding cycles with variable infeed rates were first investigated by applying dynamic programming to a simulation of the grinding cycle. The simulated optimal cycles were found to consist of distinct segments with predominant constraints. This provided the basis for an optimal control policy whereby the infeed rate is determined according to the active constraint at each segment of the cycle. Accordingly, the controller is designed to identify the state of the cycle at each sampling instant from on-line measurements of power and size, and compute the infeed rate according to the optimal policy associated with that state. The control system to implement the optimization policy is proposed together with provisions to enhance robustness to modeling uncertainty and measurement noise. Robustness provisions include model adaptation by parameter estimation from on-line measurements of size and power, and incorporation of safety margins in the optimization process. Problems associated with practical implementation of the control system, stemming from power limitations and wheel wear, are also discussed. The controller performance is demonstrated on an instrumented internal cylindrical grinding machine. |
