Adamu Yebi

A hybrid modeling and optimal control framework for layer-by-layer radiative processing of thick sections

This paper introduces a hybrid modeling and optimal control framework for a class of layer-by-layer manufacturing processes. Specifically, a stepped-concurrent layer-by-layer process is offered as a solution for overcoming the challenge of maintaining through-cure during thick-part fabrication using Ultraviolet (UV) radiation inputs that are subject to in-domain attenuation. The layering and curing sequence is modeled as a hybrid system, where the layering steps constitute discrete events on otherwise continuous curing kinetics and thermal processes. It is shown that the UV intensity as well as the inter-layer hold times can be selected optimally by posing an optimal control problem with the objective of minimizing the overall cure deviation in the thick multi-layer part. The necessary conditions for optimality are explicitly derived by adjoining the coupled PDE and ODE constraints of the process model. The potential benefit of the proposed optimization scheme is demonstrated considering simulations of a composite laminate curing process. It is found that, compared to traditional equal-interval layering, optimal layering time control gives significantly improved performance in terms of minimizing cure-level deviation, for comparable total energy usage. There is also some added benefit to optimizing the inter-layer UV input as well.

Optimal Layering Time Control for Stepped-Concurrent Radiative Curing Process

This paper makes the following main proposals: (1) a stepped-concurrent curing (SCC) approach for making thick parts using ultraviolet (UV) radiative curing and (2) an optimal interlayer hold time control scheme to maximize the benefit of the SCC approach. The SCC approach seeks to reduce cure level deviations across a thick part by introducing new layers before earlier ones cure completely. A model of the UV curing process that includes the coupled cure kinetics and heat transfer is used to motivate the SCC scheme as well as the inherent optimization problem in this process. Then, the SCC process is cast as a hybrid system in which the addition of each layer switches the underlying state space to one with a higher dimension. Minimization of the overall cure deviation is set as the objective of the process and the necessary conditions for the optimal interlayer hold time control sequence are explicitly derived and solved via a steepest descent algorithm. Applications of the proposed scheme to a composite laminate curing process show that the so computed optimal layering time control sequence indeed gives the best performance in terms of closely tracking a target cure level distribution, compared to equal-time SCC or one-shot curing of the whole thick part. [DOI: 10.1115/1.4029023]

Feedback compensation of the in-domain attenuation of inputs in diffusion processes

This paper addresses the problem of compensating for the in-domain attenuation of inputs for a class of process control applications. Specific examples include the challenge of maintaining uniform temperatures or through-cure during thick-film radiative drying and curing processes in the face of the effective inputs variation with film depth due to the so-called Beer-Lambert effect. These distributed parameter control problems are modeled with parabolic PDEs for the diffusion processes along with an in-domain input with a spatial attenuation function. The approach presented in this paper involves transforming the original model to an equivalent boundary input problem to which existing output feedback backstepping boundary control design methods can be applied. The resulting compensation scheme includes a mechanism for tuning the closed-loop performance. The performance of this scheme is compared with a controller designed via modal approximation of the PDE.

Estimation and Predictive Control of a Parallel Evaporator Diesel Engine Waste Heat Recovery System

This paper proposes a real-time capable augmented control scheme for a parallel evaporator organic Rankine cycle (ORC) waste heat recovery system for a heavy-duty diesel engine, which ensures efficient and safe ORC system operation. Assuming a time constant separation between the thermal and pressure dynamics, a nonlinear model predictive control (NMPC) is designed to regulate the mixed working fluid (WF) outlet temperature and the differential temperature between the two parallel evaporator outlets. Meanwhile, the evaporator pressure is regulated by an external PID control. The NMPC is designed using a reduced order, moving boundary control model of the heat exchanger system. In the NMPC formulation, state feedback is constructed from the estimated state via an unscented Kalman filter based on temperature measurements of the exhaust gas and WF at the evaporator outlet. The performance of the proposed control scheme is demonstrated in simulation over an experimentally validated, high fidelity, and physics-based ORC plant model during a transient constant speed and variable load engine drive cycle. The performance of the proposed control scheme (NMPC plus PID) is further validated via comparison with a conventional, multiple-loop PID controlling both the mixed evaporator outlet WF temperature, and the evaporator pressure. The simulation results demonstrate that the proposed control scheme outperforms a multiple-loop PID control in terms of both safety and total recovered thermal energy by up to 12% and 9%, respectively.

Hybrid Modeling and Robust Control for Layer-by-Layer Manufacturing Processes

This paper presents a hybrid system modeling and robust process optimization and control scheme for a layer-by-layer manufacturing process. In particular, the optimization of the layering times is offered as a solution for overcoming the challenge of maintaining through-cure during thick-part fabrication using ultraviolet radiation inputs that are subjected to in-domain attenuation. The layer deposition and curing sequence is modeled as a hybrid system by treating the underlying cure kinetics and the associated thermal process as a continuous dynamics switched by the discrete layering events. The interlayer hold times are taken as the control variables that can be optimally selected to minimize the final cure deviation across all layers. A robust optimization problem is posed that includes the sensitivity of the objective function to process the model parameter uncertainty. By adjoining the hybrid system model and the associated sensitivity constraints to the objective, the necessary conditions of optimality are derived. The advantages of the proposed robust optimization scheme are then demonstrated by simulating a layer-by-layer thick composite laminate fabrication process. It is shown that, compared with the use of nominal optimal layering time control, robust optimal layering time control significantly improves the performance in terms of closely tracking a desired final cure level distribution in the presence of parametric uncertainty.

OBSERVER DESIGN FOR STATE ESTIMATION OF UV CURING PROCESSES

This article discusses the challenges of non-intrusive state measurement for the purposes of online monitoring and control of Ultraviolet (UV) curing processes. It then proposes a two-step observer design scheme involving the estimation of distributed temperature from boundary sensing cascaded with nonlinear cure state observers. For the temperature observer, backstepping techniques are applied to derive the observer partial differential equations along with the gain kernels. For subsequent cure state estimation, a nonlinear observer is derived along with analysis of its convergence characteristics. While illustrative simulation results are included for a composite laminate curing application, it is apparent that the approach can also be adopted for other UV processing applications in advanced manufacturing.© 2014 ASME

Model-based optimal control of layering time for layer-by-layer UV processing of resin infused laminates

This paper first discusses experimental verifications of a 1D process model for layer-by-layer UV curing of thick composite laminates. The layer-by-layer UV curing process is modelled as a hybrid dynamic system by treating the underlying cure kinetics and associated thermal process as continuous dynamics switched by the discrete layering events. An additional heat transfer model is introduced to take into account the cooling effect of practical process delays of physically introducing each new layer. The successive layering times are treated as the control inputs that can be selected optimally via an optimization scheme that searches for the optimal layer addition times which result in minimal cure deviations across all layers of the laminate at final time. The potential benefit of the proposed optimal control scheme is demonstrated by considering both simulations and an experimental study on layer-by-layer fabrication of a thick composite laminate.

Partial Differential Equation-Based Process Control for Ultraviolet Curing of Thick Film Resins

This paper proposes a feedback control system for curing thick film resins using ultraviolet (UV) radiation. A model-based distributed parameter control scheme is constructed for addressing the challenge of achieving through cure while reducing temperature gradients in thick films in composite laminates. The UV curing process is modeled with a parabolic partial differential equation (PDE) that includes an in-domain radiative input along with a nonlinear spatial attenuation function. The control problem is first cast as a distributed temperature trajectory-tracking problem where only surface temperature measurements are available. By transforming the original process model to an equivalent boundary input problem, backstepping boundary PDE control designs are applied to explicitly obtain both the controller and the observer gain kernels. Offline optimization may be used to generate the desired temperature trajectory, considering quality constraints such as prespecified spatial gradients and UV source limitations. The workings and the performance of the proposed control scheme are illustrated through simulations of the process model. It is shown that feedforward compensation can be added to achieve improved tracking with the PDE controller in the presence of measurement noise and other process disturbances. [DOI: 10.1115/1.4030818]