Deep Learning-based Optimal Tracking Control Of Flow Front Position In An Injection Molding Machine

The research of injection molding machine involves many technical fields.It is a typical mechatronics multi-technology and multi-discipline integrated system,which is widely used in all kinds of plastic industry.Injection molding plastic products depends largely on the quality of the filling process of injection screw melt to the injection speed of mold,the injection speed can be controlled by controlling the input current,the control current of the servo valve control to adjust the size of the torque motor,and it is based on the quadratic performance index to optimize the minimum value.Currently most of the injection molding machine is calculated by microcomputer monitor optimal input,and the injection molding process was open loop/closed loop control,by comparing the surface quality of the products of different control input and residual stress distribution for evaluating the effectiveness of the optimal control system,but there is a high time cost and stable real-time character flaws.In order to overcome the shortcomings of the above traditional control methods and improve the anti-interference and intelligence of injection molding machine control,this paper proposes a real-time optimal control algorithm based on the combination of computational optimal control and Deep Neural Network（DNN）.The advantages of this method are that it is easy to control and cost is low.Through solving the optimal control problem and deep network training and learning,the real-time optimal control of disturbance in any reasonable range of injection molding machine can be realized.The injection process control problem of injection molding machine needs to be transformed into an optimal control problem,and numerical solution is often the most common in the optimal control solution,which mainly includes direct method and indirect method.But they have some defects,such as: in view of the boundary value problem on both sides,the indirect method because of its limitations solving difficulty exponentially,there is long complicated derivation,convergence region is small,the initial value is difficult to estimate such as faults,and every time as long as the changes occurred in the initial state,all need to re-run iteration,a dynamic model for complex,real time not guaranteed.And the numerical solution method in the direct method,in solving most of the problems are commonly used method,although the real time is insufficient,but its solving speed and convergence is much better than the indirect method.The dynamic model is established through practical problems,and then solved by the optimal control.The state-control pair obtained by the solution is used as the data set of neural network training,and then DNN is trained off-line,and applied to the real-time online control of injection molding machine.The whole training process,first of all,it avoids the traditional optimal control method to repeatedly solve the injection molding machine dynamics model in the injection molding machine speed control problem.The traditional optimal control method is to establish a dynamic model,optimize the performance index under the constraints of the corresponding conditions,and then solve the optimal control problem,but the time calculation cost of this method is large,especially for highly complex nonlinear systems.In other words,most of them can only get numerical solutions,so a cyclic iterative solution process is required,the time cost is unpredictable and the convergence of the algorithm cannot be guaranteed,coupled with the disturbance of the initial point,the iteration time is doubled.The method designed in this paper can avoid repeated iterations to solve the optimal control problem of the model and reduce the time cost.Next,the DNN method is used for online optimal control of injection molding machines.In this paper,the traditional optimal control method is combined with DNN,and the Gauss pseudospectral method of adaptive grid is used to solve the optimal control problem,obtain a large number of optimal control numerical solutions,and store the obtained solutions as a training data set to form the optimal control problem.The optimal state-control pair samples,train the DNN-based speed controller offline,and then predict the output of the optimal control in real time.Because the calculation is performed offline,and there is no need to solve the optimal control problem online,the prediction of the trained DNN model only requires simple vector/matrix multiplication operations of the input and hidden nodes,so it is possible to achieve the approximate best performance under the premise of ensuring real-time performance.Excellent control.Finally,in order to verify the performance of the DNN,random initial conditions are selected,which can realize the real-time optimal control of the injection molding machine.The traditional optimal control problem of the injection molding machine is a boundary value problem at both ends.It is usually assumed that the initial state of the injection molding machine is known and fixed in advance,but in practical applications,due to the uncertainty of the initial state of the injection molding machine itself or the processing material.Due to the strong fitting performance and generalization ability of DNN,it can guide from any set initial state to the optimal target state,and achieve the optimal target state.Excellent control effect,high accuracy and generalization ability,and stronger autonomy and robustness in real-time applications.