Control Methods for Improving Tracking Accuracy and Disturbance Rejection in Ball Screw Feed Drives
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This thesis studies in detail the dynamics of ball screw feed drives and expands understanding of the factors that impose limitations on their performance. This knowledge is then used for developing control strategies that provide adequate command following and disturbance rejection. High performance control strategies proposed in this thesis are designed for, and implemented on, a custom-made ball screw drive. A hybrid Finite Element (FE) model for the ball screw drive is developed and coded in Matlab programming language. This FE model is employed for prediction of natural frequencies, mode shapes, and Frequency Response Functions (FRFs) of the ball screw setup. The accuracy of FRFs predicted for the ball screw mechanism alone is validated against the experimental measurements obtained through impact hammer testing. Next, the FE model for the entire test setup is validated. The dynamic characteristics of the actuator current controller are also modeled. In addition, the modal parameters of the mechanical structure are extracted from measured FRFs, which include the effects of current loop dynamics. To ensure adequate command following and disturbance rejection, three motion controllers with active vibration damping capability are developed. The first is based on the sensor averaging concept which facilitates position control of the rigid body dynamics. Active damping is added to suppress vibrations. To achieve satisfactory steady state response, integral action over the tracking error is included. The stability analysis and tuning procedure for this controller is presented together with experimental results that prove the effectiveness of this method in high-speed tracking and cutting applications. The second design uses the pole placement technique to move the real component of two of the oscillatory poles further to the left along the real axis. This yields a faster rigid body response with less vibration. However, the time delay from the current loop dynamics imposes a limitation on how much the poles can be shifted to the left without jeopardizing the system’s stability. To overcome this issue, a lead filter is designed to recover the system phase at the crossover frequency. When designing the Pole Placement Controller (PPC) and the lead filter concurrently, the objective is to minimize the load side disturbance response against the disturbances. This controller is also tested in high-speed tracking and cutting experiments. The third control method is developed around the idea of using the pole placement technique for active damping of not only the first mode of vibration, but also the second and third modes as well. A Kalman filter is designed to estimate a state vector for the system, from the control input and the position measurements obtained from the rotary and linear encoders. The state estimates are then fed back to the PPC controller. Although for this control design, promising results in terms of disturbance rejection are obtained in simulations, the Nyquist stability analysis shows that the closed loop system has poor stability margins. To improve the stability margins, the McFarlane-Glover robustness optimization method is attempted, and as a result, the stability margins are improved, but at the cost of degraded performance. The practical implementation of the third controller, was, unfortunately, not successful. This thesis concludes by addressing the problem of harmonic disturbance rejection in ball screw drives. It is shown that for cases where a ball screw drive is subject to high-frequency disturbances, the dynamic positioning accuracy of the ball screw drive can be improved significantly by adopting an additional control scheme known as Adaptive Feedforward Cancellation (AFC). Details of parameter tuning and stability analysis for AFC are presented. At the end, successful implementation and effectiveness of AFC is demonstrated in applications involving time periodic or space periodic disturbances. The conclusions drawn about the effectiveness of the AFC are based on results obtained from the high-speed tracking and end-milling experiments.