Modeling and Feedforward Vibration Compensation of Advanced Manipulators for Extrusion-Based Additive Manufacturing

Abstract

There are several challenges impeding widespread adoption of AM. In extrusion-based AM, which is the focus of this dissertation, slow production speed and position accuracy in the end-use parts are significant problems. Comparatively, mass-manufacturing processes can make accurate parts with fast production rates. Fortunately, innovative architectures capable of reaching higher speeds, such as the H-frame and delta robot manipulators, are being introduced for use in extrusion-based AM. For these manipulators, maintaining position accuracy at high speeds is challenging because they have complex (i.e., coupled and nonlinear) dynamics: they have nonlinear motion errors that are difficult to model and compensate. The major contributions of this dissertation are to present novel methods to characterize their dynamics with linear parameter-varying (i.e., position-dependent) models and apply feedforward vibration compensation to mitigate their motion-induced errors. In the vibration compensation literature, researchers have used a model-based vibration control technique known as the FBS approach to increase production rates on traditional printer architectures by 2x without sacrificing accuracy. The FBS approach executes tracking control of a given trajectory by first expressing the control input to the machine as a linear combination of B-spline basis functions. The basis functions are then forward filtered through the machine’s dynamics and the coefficients are obtained such that the tracking error is minimized. In this manner, a desired manufacturing trajectory can be accurately tracked at high speeds. However, the FBS approach has only been applied to systems with linear time-invariant dynamics and has not been applied to systems with coupled and position-dependent dynamics. Additionally, coupled dynamics result in larger inversion problems when calculating the FBS controller and position-dependent dynamics require recomputing the models to account for changing dynamics. Both phenomena lead to increased computational effort required to implement FBS. To decrease the computational effort of deploying FBS on advanced manipulators, this dissertation proposes methods to: (1) decouple the coupled dynamics while maintaining high control accuracy and (2) efficiently compute and invert position-dependent models during real-time manufacturing by separating time-invariant and time-varying parts of the model, parameterizing time-varying models, and using efficient matrix methods for computation. We present numerical simulations that demonstrate the effectiveness of these methods to bolster computational efficiency. For example, we implement FBS on the delta robot with a nearly 40% improvement in computational efficiency when compared to a standard FBS approach that does not use the new methods. Successful vibration compensation also depends on having accurate mathematical models of the controlled system. To obtain the models, we approximate the nonlinear models of the manipulators as linear models using linearization methods and validate that the approximations do not result in loss of accuracy using data from the machines. Additionally, to facilitate adoption of the proposed control approach, this dissertation presents techniques for efficient identification of the model parameters with a few measurements from the H-frame and delta manipulators. We outline the experimental procedures necessary to perform the system identification and present data from commercial 3D printers demonstrating that the prediction model matches the real system at different operating positions---up to 50% better than predicting with a model measured at one central location. More importantly, we show that using these models results in up to 39% reduction of vibration-induced accelerations when compared to a model that does not change based on the printer's position.