Feedback vibration control of a base-isolated building with delayed measurements using h∞ techniques

n this paper we address the problem of vibration reduction of buildings with delayed measurements, where the delays are time-varying and bounded. We focus on a convex optimization approach to the problem of state-feedback H ∞ control design. An appropriate Lyapunov-Krasovskii functional and some free weighting matrices are used to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities (LMIs). The controller, which guarantees asymptotic stability and an H ∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated through the simulation of an n-story base-isolated building

Feedback vibration control of a base-isolated building with delayed measurements using h∞ techniques

Published version of a paper presented at the American Control Conference (ACC), 2010. (c) 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other worksn this paper we address the problem of vibration reduction of buildings with delayed measurements, where the delays are time-varying and bounded. We focus on a convex optimization approach to the problem of state-feedback H ∞ control design. An appropriate Lyapunov-Krasovskii functional and some free weighting matrices are used to establish some delay-range-dependent sufficient conditions for the design of desired controllers in terms of linear matrix inequalities (LMIs). The controller, which guarantees asymptotic stability and an H ∞ performance, simultaneously, for the closed-loop system of the structure, is then developed. The performance of the controller is evaluated through the simulation of an n-story base-isolated building

Precision Control of High Speed Drives using Active Vibration Damping

In order to meet industry demands for improved productivity and part quality, machine tools must be equipped with faster and more accurate feed drives. Over the past two decades, research has focused on the development of new control strategies and smooth trajectory generation techniques. These developments, along with advances in actuator and sensor technology, have greatly improved the accuracy of motion delivery in high speed machine tools. However, further advancement is limited by the vibration of the machine’s structure. The purpose of the research in this thesis is to develop new control techniques that use active vibration damping to achieve bandwidths near the structural frequencies of machine tools, in order to provide better dynamic positioning of the tool and workpiece. Two machine tool drives have been considered in this study. The first is a precision ball screw drive, for which a pole-placement technique is developed to achieve active vibration damping, as well as high bandwidth disturbance rejection and positioning. The pole-placement approach is simple and effective, with an intuitive physical interpretation, which makes the tuning process straightforward in comparison to existing controllers which actively compensate for structural vibrations. The tracking performance of the drive is improved through feedforward control using inverted plant dynamics and a novel trajectory pre-filter. The pre-filter is designed to remove tracking error artifacts correlated to the velocity, acceleration, jerk and snap (4th derivative) of the commanded trajectory. By applying the least-squares method to the results of a single tracking experiment, the pre-filter can be tuned quickly and reliably. The proposed controller has been compared to a controller used commonly in industry (P-PI position-velocity cascade control), and has achieved a 40-55 percent reduction in peak errors during tracking and machining tests. The controller design, stability analysis, and experimental results are discussed. The second drive considered is a linear motor driven X-Y stage arranged as a T-type gantry and worktable. The worktable motion is controlled independently of the gantry using a loop shaping filter. The gantry is actuated by dual direct drive linear motors and is strongly coupled to the worktable position, which determines its inertial characteristics. A 94 Hz yaw mode is handled in the gantry control law using sensor and actuator averaging, and active vibration damping. The stability and robustness of the design are considered using multivariable frequency domain techniques. For the worktable motion along the gantry, a bandwidth of 130 Hz is achieved. The gantry crossover frequency is 52 Hz, which is 3 times higher than the bandwidth that can be achieved using independent PID controllers (16 Hz). The performance of the proposed control scheme has been verified in step disturbance (i.e., rope snap) tests, as well as tracking and contouring experiments

Design and Metrology of a Precision XY Planar Stage

In recent years, the manufacturing industry has seen an increase in demand for micro-components in biomedical, opto-mechatronics, and automotive applications. Traditional machine tools are no longer a viable solution to meet the tolerances required by the customers. Hence, new ultra-precision machine tools have emerged with nanometer level accuracy in response to these demands. This thesis presents a novel ultra-precision machine tool with the intent to bridge the gap between traditional machine tools with larger work volumes and lower accuracy, and ultra-precision machine tools with high accuracy and small work volumes. The machine was designed using a T-type gantry and worktable configuration with a precision ground granite base, to achieve a work area of 300x300 mm2, with a maximum velocity of 1 m/s and a maximum acceleration of 10 m/s2. Actuation is provided by direct drive linear motors with high resolution feedback supplied by 4 µm grating linear encoders with 4096x interpolation. Aerostatic porous bearings are employed to reduce the effect of friction while maintain high stiffness of the guideways and structure. A Vacuum Pre-Loaded (VPL) air bearing supports the worktable on the granite, decoupling vertical load from the gantry. Thermal error reduction is achieved using environmental temperature control (20 ± 0.2°C) to help reduce thermal errors. As well, internally cooled couplings were designed to remove heat generated by the motors, thus further reducing the effects that contribute to thermal error. The target static stiffness of the machine was 50 N/µm and was measured to be 22.2 N/µm and 23.9 N/µm in the x and y axes respectively. Frequency response experiments were used to identify the open-loop transfer functions for each axis. A multivariable framework was implemented for the y-axis due to the cross coupling between the primary and secondary motors of the gantry. Two prominent vibration modes were identified at 68 Hz and 344 Hz. The first mode is attributed to the rigid body yaw mode of the gantry while the higher frequency is related to the bending mode of the beam. The first mode of the x-axis is seen at 220 Hz. A state space, active mode compensation control law was developed for the y-axis, in collaboration with Mr. Daniel Gordon, which eliminates the effects of the 68 Hz mode, allowing for high performance from the motors. The following error during a high speed (200 mm/s) test was measured at 2.74 µm and 2.41 µm in the x and y axes respectively. Metrology tests using laser interferometry were performed in accordance with international and American metrology standards for linear positioning, vertical and horizontal straightness, and yaw and pitch errors. The results will be used for geometric error compensation in future work. Finally, an overall error budget is presented with focus on the geometric, dynamic, servo, and thermal errors, where the maximum static resultant error of the machine was estimated to be 1.44 µm, and the maximum dynamic resultant error of 3.69 µm

Control Methods for Improving Tracking Accuracy and Disturbance Rejection in Ball Screw Feed Drives

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