Hesam Zomorodi Moghadam Advisor: Dr. Robert G. Landers, Dr. S. N. Balakrishnan

1. Application of Hierarchical Optimal Control in Force-Position control of Complex Manufacturing Processes Hesam Zomorodi Moghadam Advisor: Dr. Robert G. Landers, Dr. S. N. Balakrishnan Mechanical and Aerospace Engineering

2. Application of Hierarchical Optimal Control in Force–Position Control of Complex Manufacturing Processes Dr. Robert G. Landers Dr. S.N. Balakrishnan Mechanical and Aerospace Engineering Hesam Zomorodi Moghadam Mechanical and Aerospace Engineering • OBJECTIVES • Developing a hierarchical optimal controller to regulate the cutting force and tool position, simultaneously, in a micro end milling process. • Analyze the performance of the proposed methodology for a sharp corner and compare to normal methods. Results Aggregating top level error • Tracking diamond profile while keeping the maximum cutting force at a desired value • Two control structures were compared; • Hierarchical controller • Decentralized controller (q = 0, i.e., no coupling between axes) • Higher Level Goal: Keep maximum value • of normal cutting force per each spindle revolution at a specified value • Modeling forces in end milling processes • BACKGROUND • Micro machining: • Position tracking versus forces • Axes can be treated as subsystems • Decentralized control • Simple structure • Not proper for coupled systems • Unsynchronized motion • Distributed control • Interaction among local controllers • Communication delays • Approximations apply • Hierarchical control • Higher level coordinators • Lower communication delays • Simpler structure • An intelligent method is needed to • simultaneously regulate axial and • machining force errors. fi,j is the instantaneous feed (mm) d is the depth of cut (mm) V is the cutting velocity (mm/min) ai,j is the chip area (mm2) http://cuttingtoolschicago.com http://www.alibaba.com Tool wear monitor M.W. Cho,2007, Journal of ECERS http://karnataka.inetgiant.in • Finding Unknown Model Parameters • Emphasis on ex decreases • New • 10 slots • 5 slots • 15 slots Data acquisition (Labview) Amplifier - part clamped on dynamometer- different depths of cut and feeds NI SCXI-1143 DAQ card Results for hierarchical controller • Results for decentralized controller • Fitting simulated forces to measured forces using particle swarm optimization • Discussion and CONCLUDING REMARKS • A Hierarchical Optimal controller combined with Internal Model Principle was proposed. • A decentralized controller was tested with the same conditions. • Decrease in emphasis on axial error resulted in an increase in transient axial error as well as the settling time; however, it caused a decrease in transient cutting force error. • When decentralized controller was implemented, cutting force error generally had larger overshoot values and, even when the error was comparable to the error from the hierarchical controller, axial errors were larger (i.e., almost two times). • APPROACH • Hierarchical optimal control method with modified cost function. • Higher level goal (zero cutting force tracking error) is expressed by bottom level states. • Relationship between cutting force and axial errors. • Machining force in an end milling process is a function of depth of cut, spindle speed and the feed. Optimization index history for the second goal function • A curve was fit to maximum value of normal cutting force per spindle revolution aggregation relationship general tracking with Internal Model Principle • FUTURE WORK • Apply this methodology on a parallel CNC machine with six axes to perform a complex end milling tasks. • Improve robustness properties of the controller for process uncertainties. Top level error Simulation results vs. experimental data Ns = 7000 rpm, feed rate = 0.5 in/min and d = 0.02, 0.03. 0.04 and 0.05 in top level goal modified cost function Acknowledgements This research was supported by the Missouri S&T Intelligent Systems Center Linearizing around the operating point control axes