Continuous Optimal Infeed Control for Cylindrical Plunge Grinding, Part 1: Methodology

2004 ◽  
Vol 126 (2) ◽  
pp. 327-333 ◽  
Author(s):  
Shaoqiang Dong ◽  
Kourosh Danai ◽  
Stephen Malkin ◽  
Abhijit Deshmukh
Keyword(s):  
Optimal Control ◽  
Dynamic Programming ◽  
Cycle Time ◽  
Optimal Policy ◽  
Controller Design ◽  
Control Policy ◽  
Active Constraint ◽  
Plunge Grinding ◽  
On Line ◽  
Sampling Instant

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 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 to then compute the infeed rate according to the optimal policy associated with that state. The optimization policy is described in this paper, and the controller design and its implementation are presented in the following paper [1].

Continuous Optimal Infeed Control for Cylindrical Plunge Grinding, Part 2: Controller Design and Implementation

2004 ◽  
Vol 126 (2) ◽  
pp. 334-340 ◽  
Author(s):  
Shaoqiang Dong ◽  
Kourosh Danai ◽  
Stephen Malkin
Keyword(s):  
Control System ◽  
Controller Design ◽  
Control Policy ◽  
Noise Robustness ◽  
Practical Implementation ◽  
Wheel Wear ◽  
Plunge Grinding ◽  
Cylindrical Grinding ◽  
Safety Margins ◽  
On Line

This is the second of two papers concerned with on-line optimization of cylindrical plunge grinding cycles with continuously varying infeed control. In the first paper [1], dynamic programming was applied to a simulation of the cylindrical grinding process in order to explore the characteristics of optimal grinding cycles. Optimal cycles were found to consist of distinct segments each with predominant constraints. An optimal control policy was formulated with the infeed rate within each segment determined according to the prevailing constraint. The present paper is concerned with the design of the controller and its implementation. The control system to implement the optimization policy is described 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.

Methodology for Continuous Infeed Cylindrical Plunge Grinding

2001 ◽  
Author(s):  
Heng Xu ◽  
Kourosh Danai ◽  
Stephen Malkin
Keyword(s):  
Optimal Control ◽  
Model Predictive Control ◽  
Predictive Control ◽  
New Method ◽  
Process Variables ◽  
Plunge Grinding ◽  
Preliminary Results ◽  
Part Quality ◽  
On Line ◽  
Sampling Instant

Abstract A method for optimal control of cylindrical plunge grinding cycles is introduced. Unlike conventional cycles which have a few pre-determined sequential steps with discrete infeed rates, the new method will continually vary the infeed velocity. The proposed method utilizes the Model Predictive Control (MPC) approach whereby the control action at each sampling instant is selected in accordance with its effect on the future values of process variables and part quality attributes. This paper describes the problem and presents some preliminary results. It also discusses the difficulties that will need to be overcome before the controller can be implemented on-line.

Optimal Infeed Control for Accelerated Spark-Out in Plunge Grinding

1984 ◽  
Vol 106 (1) ◽  
pp. 70-74 ◽  
Author(s):  
S. Malkin ◽  
Y. Koren
Keyword(s):  
Direct Measurement ◽  
Time Constant ◽  
Cycle Time ◽  
Characteristic Time ◽  
Control Policy ◽  
Plunge Grinding ◽  
Elastic Deflection ◽  
Time Required

An optimal infeed control policy is proposed to minimize the cycle time in cylindrical plunge grinding. As compared with conventional infeed control consisting of roughing followed by spark-out, the proposed infeed control policy accelerates the spark-out by reducing the time required to recover the accumulated elastic deflection in the system and to reduce the infeed velocity to its final required value. This optimal infeed control policy is particularly advantageous for grinding systems having a long characteristic time constant. A practial method is described for implementing the optimal infeed control policy based upon direct measurement of the radial allowance remaining on the workpiece.

OPTIMAL POLICY FOR A PRODUCTION–INVENTORY SYSTEM WITH SETUP COST AND AVERAGE COST CRITERION

2012 ◽  
Vol 26 (4) ◽  
pp. 457-481 ◽  
Author(s):  
Xiuli Chao ◽  
Yifan Xu ◽  
Baimei Yang
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Production Capacity ◽  
Control Policy ◽  
Inventory System ◽  
Setup Cost ◽  
Inventory Theory ◽  
Cost Rate ◽  
Production Inventory ◽  
Production Inventory System

One of the most fundamental results in inventory theory is the optimality of (s, S) policy for inventory systems with setup cost. This result is established under a key assumption of infinite ordering/production capacity. Several studies have shown that, when the ordering/production capacity is finite, the optimal policy for the inventory system with setup cost is very complicated and indeed, only partial characterization for the optimal policy is possible. In this paper, we consider a continuous review production/inventory system with finite capacity and setup cost. The demand follows a Poisson process and a demand that cannot be satisfied upon arrival is backlogged. We show that the optimal control policy has a very simple structure when the holding/shortage cost rate is quasi-convex. We also develop efficient algorithms to compute the optimal control parameters.

scholarly journals Nonlinear State–Space Predictive Control with On–Line Linearisation and State Estimation

2015 ◽  
Vol 25 (4) ◽  
pp. 833-847 ◽  
Author(s):  
Maciej Ławryńczuk
Keyword(s):  
State Estimation ◽  
State Space ◽  
Predictive Control ◽  
Control Policy ◽  
Computationally Efficient ◽  
State Observers ◽  
Constant Type ◽  
The Future ◽  
On Line ◽  
Sampling Instant

Abstract This paper describes computationally efficient model predictive control (MPC) algorithms for nonlinear dynamic systems represented by discrete-time state-space models. Two approaches are detailed: in the first one the model is successively linearised on-line and used for prediction, while in the second one a linear approximation of the future process trajectory is directly found on-line. In both the cases, as a result of linearisation, the future control policy is calculated by means of quadratic optimisation. For state estimation, the extended Kalman filter is used. The discussed MPC algorithms, although disturbance state observers are not used, are able to compensate for deterministic constant-type external and internal disturbances. In order to illustrate implementation steps and compare the efficiency of the algorithms, a polymerisation reactor benchmark system is considered. In particular, the described MPC algorithms with on-line linearisation are compared with a truly nonlinear MPC approach with nonlinear optimisation repeated at each sampling instant.

scholarly journals Optimal Control of fed batch bioreactor

2021 ◽  
Vol 9 (5) ◽  
pp. 1-5
Author(s):  
Durgesh Bonde ◽  
Dr. Satish Inamdar
Keyword(s):  
Optimal Control ◽  
Optimal Policy ◽  
Initial Conditions ◽  
Batch Reactor ◽  
Optimal Solution ◽  
Control Policy ◽  
Reactor Operation ◽  
Fed Batch ◽  
Batch Bioreactor ◽  
Parameter Values

In this paper, we will consider the problem of optimal control of a fed batch reactor. Our objective is to simulate the fed batch reactor under specified conditions in order to find an optimal control policy. Thus, for any specified initial conditions and parameter values the optimal policy for reactor operation can be obtained from simulation. We have an example system of nosiheptide [1] and used gradient method to find optimal policy. Although the convergence is slow, an optimal solution is obtained and various plots are prepared that illustrate the applicability of the method well.

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