Variable Gain Cross-coupled Control Of XY Table Linear Servo System Based On L₁ Monoaxial Speed Controllers

Based on the project supported by Liaoning Provincial Natural Science Foundation (20052045) and Foundation of Liaoning Educational Committee (2004F014) . To weaken the influences of parameter perturbed, load disturbances, and the velocity mismatch between X axis and Y axis to the contour precision of XY table servo system driveled by Permanent Magnet Linear Synchronous Motors, a compound control scheme based on combining robust l\ control and variable gain cross-coupled control is presented in this paper, to enhance the contour error precision of XY table linear servo system.In various NC machine tools, the traditional drive mode, which is generally the rotating servo electrical machine with worm wheel, worm pair and gear pair mechanism, results in motion response slowly, large friction and other nonlinear errors due to mechanical transmission chain, thus it is very difficult to implement high precise processing. The NC machine tools servo system adopting direct drive technique is no medium transmission, and has large thrust, quick response, small friction and high position precision. However, the system is more sensitive to uncertainties such as load disturbances and parameter variations of load, which greatly reduces servo performances. Meanwhile, the research of high speed and high precision processing technology has became the newest research direction, the objects of the research are improving and eliminating contour error, enhancing the performance of control system. Designing a servo controller is required to improve robustness, tracking performance and contour precision.Performance index of H_∞control is to minimize the energy of error, and the method has better robustness and immunity to disturbance. The input signals of H_∞control must are energy bounded signals, however, the disturbance of practical system, such as: step signal generated by disturbance and time-varying bounded signals, all belong to bounded signals of l_∞space, and those meet don't satisfy with the hypothesis, which is disturbance signal is energy bounded. But l\ control is different from H_∞control, its performance index is l₁ norm of relative sensitive function. The l₁ controller can minimize amplitude of maximum output error generated by bounded disturbance. So l₁ control is adapted to design monoaxial speed controller in this paper. based on the discrete time model of PMLSM, the design of l₁ speed controller is changed into the design of optimal controller Q of matching model using youla parameter. From the given controller's order, the problem of infinite dimension l₁ is translated into finite dimension linear programs. Indirectly reduce contour error.A variable gain cross-coupled controller is also designed between X axis and Y axis. Real time correcting the gains of contour error model based on the feedback information and given input of X axis and Y axis, to seek optimal control laws. Redemptive information is send back to X axis and Y axis, to reach the aim of compensating contour error. The distinguish merit of variable gain cross-coupled control is that it improves contour error at any trails.Moreover, currently available permanent magnet linear synchronous motor is considered as the controlled object, its mathematical model is established, and it is necessary to simulate and analyze above control strategies using MATLAB software. Simulation results show that the proposed variable gain cross-coupled control method based on l₁ monoaxial speed controllers can enhance the robustness and contour precision of XY table linear servo system.