(317e) Design of Image Recognition-Based Model Predictive Controller for a Batch Rotational Molding Process

Most industrial processes regardless of the domain, have a common target of achieving high quality products. Sometimes, batch operation is preferred, for example, in pharmaceutical, or biochemical applications when the focus is on the quality requirement rather than the quantity of the products. However, due to this reason, coming up with a suitable control routine for the process becomes an important task to maintain consistency in the product quality. Model predictive controllers (MPC) have been conventionally used for many industrial applications. An MPC has an underlying dynamic process model which allows the controller to predict the future of the process and enables it to take the most optimum control action. Needless to say, arriving at a good model is one of the challenges, especially in processes where there is no first principles model available. An even more pressing challenge and opportunity is the availability of non-traditional sensors such as sounds or images In such cases, the traditional MPC framework needs to be adjusted to pre-process and accommodate high-dimensional output data before being implemented in closed loop.

This work focuses on designing an MPC for a Bi-axial Rotational Molding setup which is a batch process used for manufacturing hollow plastics. The system has only one heater as the input. The mold rotates bi-axially inside the oven and a thermal imaging camera is placed outside the oven to capture the image of the mold, which is the only continuously measured output of the system, through a window slit. Although the rotation speed is given along with the equipment, the rotation is not perfect and hence the camera cannot be hard-coded to take images at particular instances to get the mold in the frame perfectly. Furthermore, there are two quality variables associated with the molded product; the sinkhole area percentage and the impact strength, both which can be measured only through destructive means, only after the experiment is done. It is essential that the MPC is designed taking into consideration, the aforementioned challenges.

The proposed modelling strategy is as follows. First a neural network-based classifier is trained on all the images of a batch, to detect whether or not the box is in the camera frame. Next once the box is detected, we need a way to reduce the high dimensional image data to a representative (lower dimensional) set of variables which reasonably represent the dynamics of the mold temperature. We train an autoencoder on only the images containing the box, to acquire a set of these latent variables. The above two steps can be replaced with a single deep convolutional neural network as well, and both the methods will be explored in this work. There has been work done [1,2,3,4] on this aspect of reducing high dimensional dynamic data but through different routes. These techniques will also be briefly discussed along with an explanation for adopting a different approach. Finally, a Linear Time Invariant State Space (LTI SS) model is built between the input and the previously obtained latent variables and a Partial Least Squares (PLS) model is built between the latent variables and the quality measurements. This entire model is integrated with an MPC designed to achieve products with user specified qualities subject to certain input constraints. The framework is demonstrated by closed-loop experiments on the rotational moulding setup.

References:

1. Lu, Qiugang & Zavala, Victor. (2021). Image-based model predictive control via dynamic mode decomposition. Journal of Process Control. 104. 146-157. 10.1016/j.jprocont.2021.06.009.

2. Gopaluni, R. Bhushan, et al. "Modern machine learning tools for monitoring and control of industrial processes: A survey." IFAC-PapersOnLine 53.2 (2020): 218-229.

3. Masti, Daniele, and Alberto Bemporad. "Learning nonlinear state–space models using autoencoders." Automatica 129 (2021): 109666.

4. Lee, Kookjin, and Kevin T. Carlberg. "Model reduction of dynamical systems on nonlinear manifolds using deep convolutional autoencoders." Journal of Computational Physics 404 (2020): 108973.