1. Hierarchical Control of Manufacturing Equipment and Processes Hesam Zomorodi Moghadam Advisor: Dr. Robert G. Landers, Dr. S. N. Balakrishnan Mechanical and Aerospace Engineering

2. Hierarchical Optimal Contour Control of Motion Systems OBJECTIVES Create a general methodology for systematically balancing the demand between contour and axial tracking. Analyze the performance of the proposed methodology for general trajectories via experimental implementation on a mini CNC machine. Hesam Zomorodi Moghadam Mechanical and Aerospace Engineering Hesam Zomorodi Moghadam Mechanical and Aerospace Engineering BACKGROUND Contour error (i.e., minimum distance from the reference path) shows the part quality better than axial error, especially where allowable tolerances are very small like in micro machining. Some times by increasing axial errors contour error can be decreased An intelligent method is needed to manipulate axial errors in a proper way to reduce contour error. APPROACH A hierarchical optimal control technique with top level goal defined as zero contour error and bottom level goal defined as zero axial error is proposed. Relative importance of each level’s goal can be changed by adjusting the weighting matrices, Q and Q bo t. Dr. Robert G. Landers and Dr. S.N. Balakrishnan Mechanical and Aerospace Engineering Dr. Robert G. Landers and Dr. S.N. Balakrishnan Mechanical and Aerospace Engineering FREEFORM CONTOUR EXPERIMENTAL SETUP CONCLUDING REMARKS The methodology is capable of weighting the relative importance between axial and contour errors. The transient errors generally decreased when the contour error was weighted more heavily than the axial errors for both contours. The steady–state errors were independent of the relative weighting (within approximately two encoder resolutions). The hierarchical optimal contour control methodology can be applied to any motion system with multiple axes whose motion must be coordinated. DIAMOND CONTOUR Here Q = q and Q bot = q bot I 4x4. Three cases were conducted, where q/q bot increased from 0.01 (i.e., high weight on axial error) to 100 (i.e., high weight on contour error). FUTURE WORK Extend the methodology to simultaneously regulate CNC equipment position errors and cutting force in a micro end milling process. Study the application of the method to control other processes (e.g., fuel cells) to accomplish complex tasks. Acknowledgements: This research was supported by the Missouri S&T Intelligent Systems Center i-th measured point with contour controller i-th reference point i-th measured point without contour control x y i-th reference point ε i-th measured point eyey x y Encoders (resolution: 0.1075 μm) Control signals to motors NI 6040E DAQ card XPC Target real time computer Table Top CNC Host PC Measurement data Controller structure CaseIIIIII Q10 –3 I 6 0.1I 6 q bot 0.1 0.001 q/q bot 0.011100 Diamond contour schematic. Right corner transient responses for Cases I–III. Bottom corner transient responses for Cases I–III. Experimental results for Case I. Freeform contour schematic. Transient errors for Cases I–III. Experimental results for Case III. Experimental results for Case I. Aggregation relationship optimal control: where General tracking with Internal Model Principle exex axis control contour Transient errors for Cases I–V.