This paper presents a frequency domain learning control scheme for a class of nonlinear systems and its application to the process feedback control of the noncircular turning process for camshaft machining. In frequency domain, periodic signals are represented by the Fourier expansions that are nonzero only at discrete frequency points. An input dependent system matrix can be used to describe the input-output relationship of a class of nonlinear systems with periodic input and output signals. A learning controller is designed based on the system matrix and the bound of unmodeled dynamics. Conditions to achieve asymptotic stability and tracking performance are derived. To further improve system robustness, a low pass filter is used to turn off the learning scheme at high frequencies. The learning control scheme is then applied to the process feedback control of camshaft machining using the noncircular turning process. A two level control structure is adopted. The first level is servo control that ensures precise tool slide motion. The second level is frequency domain learning control that compensates machined profile errors due to the effects of tool/workpiece geometry, tool wears, machine deformations, and spindle runout errors. Relationship between the servo control and learning control is discussed. Implementation of the process feedback control on a steel camshaft turning demonstrates improvement of the maximum cam profile errors from 80 μm to within 20 μm in five iterations.
|Original language||English (US)|
|Journal||Journal of Dynamic Systems, Measurement and Control, Transactions of the ASME|
|State||Published - May 2008|