Priced timed automata (PTA) are discrete-event system models with temporal constraints and a cost function and are used to pose optimal scheduling and routing problems. To date, solutions to these problems have been found offline and executed open loop. This open-loop control strategy makes it impossible to account for disturbances, i.e., changes in costs or scheduling constraints over time. To address this shortcoming, this work's first contribution is a closed-loop model predictive control (MPC) framework for PTA, enabling decision-making based on real-time model updates. To ensure the feasibility of an MPC problem, it is often desirable to soften constraints. However, the contemporary PTA theory does not consider soft constraints. Thus, this work's second contribution is to integrate constraint softening with PTA control by harnessing the capabilities of new solvers enabled by the recasting of the models and control problem into first-order logic by employing modified encoding schemes based on existing works. Finally, the proposed control framework and implementation are demonstrated in a simulation case study on the guidance of a product through a manufacturing system.
Electrohydrodynamic jet (e-jet) printing is a microscale additive manufacturing technique used to print microscale constructs, including next-generation biological and optical sensors. Despite the many advantages to e-jet over competing microscale additive manufacturing techniques, there do not exist validated models of build material drop formation in e-jet, relegating process design and control to be heuristic and ad hoc. This work provides a model to map deposited drop volume to final spread topography and validates this model over the drop volume range of 0.68–13.4 pL. The model couples a spherical cap volume conservation law to a molecular kinetic relationship for contact line velocity and assumes an initial contact angle of 180 deg to predict the drop shape dynamics of dynamic contact angle and dynamic base radius. For validation, the spreading of e-jet-printed drops of a viscous adhesive is captured by high-speed microscopy. Our model is validated to have a relative error less than 3% in dynamic contact angle and 1% in dynamic base radius.
Output reference tracking can be improved by iteratively learning from past data to inform the design of feedforward control inputs for subsequent tracking attempts. This process is called iterative learning control (ILC). This article develops a method to apply ILC to systems with nonlinear discrete-time dynamical models with unstable inverses (i.e. discrete-time nonlinear non-minimum phase models). This class of systems includes piezoactuators, electric power converters, and manipulators with flexible links, which may be found in nanopositioning stages, rolling mills, and robotic arms, respectively. As these devices may be required to execute fine transient reference tracking tasks repetitively in contexts such as manufacturing, they may benefit from ILC. Specifically, this article facilitates ILC of such systems by presenting a new ILC synthesis framework that allows combination of the principles of Newton's root finding algorithm with stable inversion, a technique for generating stable trajectories from unstable models. The new framework, called Invert-Linearize ILC (ILILC), is validated in simulation on a cart-and-pendulum system with model error, process noise, and measurement noise. Where preexisting Newton-based ILC diverges, ILILC with stable inversion converges, and does so in less than one third the number of trials necessary for the convergence of a gradient-descent-based ILC technique used as a benchmark.
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