Vibration Suppression of a High-Speed Macro–Micro Integrated System Using Computational Optimal Control

Deep learning‐based optimal tracking control of flow front position in an injection molding machine

The product quality of injection‐molded plastic is closely related to the injection flow velocity of molten plastics. In this article, an optimal tracking control problem for the injection flow front position arising in the filling process in the injection molding machine (IMM) is considered, and an intelligent real‐time optimal control method based on deep neural networks (DNNs) is developed for the online tracking of the flow front position to improve the efficient production process of the plastics. To this end, a highly nonlinear dynamic model describing the filling process is first proposed and then an optimal control problem is formulated. A high‐fidelity numerical optimization approach known as the Gauss pseudospectral method is used to numerically obtain the optimal state‐control solutions, which can then be saved as a huge training data set for the DNNs. The DNNs architecture is then developed and offline trained using the obtained data set to determine the best state–control relationship. As a consequence, the well‐trained DNN may be utilized to produce the matching optimum feedback action on‐board. Numerical studies are also carried out to verify the performance of our proposed approach.

Optimal setting strategy of electrocoagulation process in heavy metal wastewater treatment plant

With the increasingly stringent environmental protection policies of various countries, the contradiction between the treatment cost and the purification degree of environmental pollutants has become increasingly significant, which has become a major factor restricting the efficient operation of wastewater treatment plants. Hence, keeping the ion concentration at the outlet as low as possible while reducing the cost are the main objectives of treating heavy metal wastewater by electrocoagulation (EC) process. However, due to the complicated mechanism and uncertain production conditions, it is difficult to achieve those goals by manually setting the current through operators' experience. In this paper, we develop a dynamic multi-objective optimization strategy for EC process to balance these two conflicting production targets. First, we define the removal efficiency (RE) to measure the effectiveness of the EC process. Due to the anodic passivation and cathodic polarization in the EC process, the current reversing period (CRP) is proposed and optimized to ensure the stable performance of the electrodes. Then the current setting problem is formulated as a constrained multi-objective optimization problem with competing objectives of RE and cost. An interval-adjustable control parameterization (CP) approach is developed to reduce the complexity of this optimization problem. To compute this optimization problem, a heuristic method named multi-objective state transition algorithm (MOSTA) with evaluation value is investigated. The effectiveness of our model and optimization strategy is demonstrated by a successful implementation in an EC process of a wastewater treatment plant in Chenzhou, China.

Fast control parameterization optimal control with improved Polak-Ribière-Polyak conjugate gradient implementation for industrial dynamic processes

This paper proposes a fast control parameterization optimal control algorithm for industrial dynamic process with constraints. Derived from the frame of control variable parameterization (CVP) technique, the proposed method combines an efficient gradient computation strategy with an improved nonlinear optimization computation approach to overcome the challenge of computation efficiency caused by gradients and bounds in optimal control problems. Firstly, a fast gradient computation method based on the costate system of Hamiltonian function is developed to decrease the computational expense of gradients by employing approximate treatments and numerical integration strategy. Then, a trigonometric function transformation scheme is presented to tackle the boundary constraints so that the original optimal control problem is further converted into an unconstrained one. On this basis, an improved restricted Polak-Ribière-Polyak (PRP) conjugate gradient approach is introduced to solve the nonlinear optimization problem by using conjugate gradient iterations and strong Wolfe line search. Meanwhile, to enhance the convergence, a restricting condition is imposed in strong Wolfe line search to create iteration step-length. Finally, the proposed algorithm is implemented on three dynamic processes. The detailed comparison among the classical CVP method, literature results and the proposed method are carried out. Simulation studies show that the proposed fast approach averagely saves more than 90% computation time in contrast to the classical CVP method, demonstrating the effectiveness of the proposed fast optimal control approach.