Modeling And Control For An Elastic-driven Gantry Robot

This dissertation mainly studies the modeling and control of two-axis belt-driven gantry robots. Such robots provide two orthogonal motions, a head sliding along a beam (x-axis motion) and the beam sliding along a frame (y-axis motion). The two axes are coupled in the sense that the x-axis position influences the y-axis dynamics. This coupling arises because the location of the head on the beam determines the mass distribution and hence the vibration characteristics for y-axis motion. Belt-pulley transmissions convert rotary motor torque into linear forces that drive the two-axis mechanism. The control objective is to move the gantry head to the target position as fast as possible, yet also settle quickly withμm accuracy. But friction force disturbances, structural vibrations in the gantry beam, transmission resonance and the coupling effect of the two-axis mechanism add difficulties to achieve this objective. At present, the study about the gantry robots which inclue both drive elasticity and structure flexibility is very few.Firstly, the modeling for the x-axis dynamic of the gantry robot is deduced. To suppress the vibration of the linear belt-driven system and improve the transient response performance, a double closed-loop control system is constructed and the mechanical resonance of the belt-driven system is analyzed and classified into two categories: low frequency resonance and high frequency resonance, which is crucial for guiding the design of controller. A notch filter is adopted to attenuate the high-frequency vibration. A new kind of input pre-shaping method producing an appropriate reference profile accompanied with a PID controller is proposed for suppressing the low frequency vibration to ensure fast point-to-point motions with minimum residual vibration. As an off-line method, the proposed method can be easily and effectively adopted to the existing elastic-driven system without any modification of the hardware setup. Next, the y-axis dynamic of the gantry robot is modeled. The model considers the structure flexibility and drive elasticity in addition to their coupling effect. The structure flexibility is embodied through three types of vibration, namely, the torsional vibration of a flexible beam in rigid motion mode, the transverse vibration of the flexibility beam with supports on torsional spring at one end and the vibration of the head which is simplified as a moving oscillator. Based on analysis of the vibration characteristic in the system, the improvement measures of the mechanical design are proposed.In addition, the design method of the H_∞output feedback controller for the flexible beam in y-direction with stationary and moving head is studied respectively. When the head is stationary in x-direction, the optimum output feedback controller of the system is devised based on the linear matrix inequality (LMI) approach. When the bonding head moves along the flexible beam, the dynamic model of the gantry robot in y-direction can be considered as a linear parameter-varying (LPV) system. The general LPV system is transformed into a simplified model using strict equivalent transformation. Using parameter-varying H_∞performance, the controller design is translated into the solution of parameter matrices which satisfy the constraints of LMI. And the design method of the gain scheduling full order output feedback controller without parameter-rate feedback is also proposed. In succession, based on the concept of"H_∞performance covering", the interpolation method which meets the demands of H_∞performance preserved is introduced. Simulation results indicate that the H_∞controller provides small settling times with reduced structural vibration and disturbance attenuation. In addition, the design method of the gain-scheduling H_∞controller proposed in this dissertation can reduce the conservation of the system effectively. Then, in order to overcome the deficiency of the ordinary H_∞controller design method, such as the complication of the design procedure and difficulities of the weight selection, a loop shaping design procedure using H_∞synthesis is introduced and applied to the gantry robot. To get the continuous gain-scheduling controller of LPV system, these designed linear controllers for the selections of scheduling variable shoule be interpolated in the scheduling variable set. This dissertation provides a sufficient condition on the selections of scheduling variable for which output feedback controllers are designed such that a stability preserving interpolation of the linear controllers can be calculated. Once the interpolation is computed, an upper bound on the rate of variation of the scheduling variable to assure exponentially stability can be calculated. Because the controller achieved from this design method generally has high orders, it is necessary to reduce the controller order for the convenience of engineering applications. A gain-scheduling PID controller is presented to approximate the high-order robust controller so that the last H_∞control structure is transformed into the form of"PID+filters". Simulation results verify the effectiveness of the proposed control method.Lastly, the integration design methods of gantry robot which is used in RFID package equipment pre-bonding module are introduced. And the realization methods of the academic research achievements, which are proposed in this paper and will be used on the gantry robot, are also developed.