14 research outputs found
Iterative learning control for LTV systems with applications to an industrial robot
Get PDFIndustrial robots are widely used in industry because of their dexterity, the high manipulation speed and the relatively low price. However, the applicability of these robots is limited by the mediocre accuracy resulting from the low bandwidth of standard industrial controllers. Fortunately, the repeatability of industrial robots is often much better than their tracking accuracy, which can be exploited to improve the accuracy by the application of Iterative Learning Control (ILC). ILC is a control technique that reduces the tracking error along a trajectory that is traced repeatedly by the iterative refinement of a feedforward signal. The tracking accuracy of industrial robots can be improved substantially with ILC by reducing the frequency components of the tracking error beyond the low bandwidth of the standard industrial controller. Below this bandwidth the non-linear dynamics of the robot mechanism are linearised by the controller, but at higher frequencies the closed-loop dynamics depend on the configuration of the robot mechanism. These configuration dependent dynamics can be approximated as linear time-varying (LTV) for small deviations from the repetitive large-scale motion. Therefore, two ILC algorithms for systems with LTV dynamics are developed in this thesis. The norm-optimal ILC algorithm iteratively computes the feedforward that minimises a weighted sum of the norm of the error and the growth of the feedforward. The error is predicted from an LTV dynamic model. The computation of the optimal feedforward is formulated as a finite-time optimal control problem and it is shown that this optimisation problem can be solved using an existing, computationally efficient algorithm. The robust ILC algorithm iteratively computes the feedforward that optimises the reduction of the error for an LTV dynamic model with a given uncertainty. A sufficient condition is derived under which the feedforward reduces the error with a specified fraction for the worst case effect of the uncertainty. This condition takes the finite length of the iteration and the LTV dynamics into account. The computation of the optimal feedforward is formulated as a finitetime dynamic game and the check of the convergence condition is formulated as an anti-causal optimal control problem. It is shown that the dynamic game and the optimal control problem can be solved using existing, computationally efficient algorithms. Convergence analysis shows that the proposed ILC algorithms make the error converge to zero with an adjustable convergence rate if the dynamic model is sufficiently accurate. Increasing the convergence rate reduces the allowable model error. A model error that is too large results in divergence of the tracking error. The allowable model error can be increased by using a robustness filter that removes the components of the feedforward to which the dynamic response is not modelled sufficiently accurate. However, the removed components of the feedforward cannot be used to compensate for the error, which typically results in a non-zero error after convergence. The proposed algorithms are suited for systems with LTV dynamics, they are computationally efficient and they are able to reduce the error monotonically with an adjustable convergence rate. This unique combination of properties makes the algorithms suited for improving the tracking accuracy of industrial robots and other systems with LTV dynamics in practice. The performance of the ILC algorithms is tested experimentally by the application to the industrial St¨aubli RX90 robot. The setpoints for the position of the robot are adjusted with ILC to reduce the tracking error at its end-effector, which is measured with an optical sensor. The experimental results show that the proposed ILC algorithms are able to reduce the measured tracking error substantially, especially if an LTV model of the configuration dependent highfrequency dynamics of the robot is used. The reduction of the tracking error is sufficient for the application of the robot to laser welding of complex trajectories at high speed
Comparison of Feedback Control Techniques for a Flexure-based 6-RSS Parallel Precision Manipulator
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A beam element with arbitrary active cross sections for multibody simulation of large-deflection flexure mechanisms
Get PDFDamping parasitic vibrations in flexure mechanisms can be achieved by integrating piezoelectric material in the flexures. Efficient models of such active flexures can aid in the design and optimization of such mechanisms to meet ever-increasing performance targets. In this paper, we present a novel beam element that is able to accurately and efficiently capture the large-deflection behavior of active flexures. The element combines a cross-sectional analysis based on the variational asymptotic method with the generalized strain beam formulation used in the multibody software SPACAR. The cross-sectional analysis converts an arbitrary active-section geometry to an asymptotically accurate equivalent beam model. This model is then used in the formulation of the geometrically nonlinear beam element. The element is validated against existing approaches and a challenging case study is presented, which shows that the element can be used to simulate complex active flexure mechanisms undergoing large deflection. The element is able to achieve results with a fraction of the computational effort required by a 3D finite-element package, with only a minor decrease in accuracy.</p
Dynamic error budgeting based robust system and control co-design for active vibration isolation systems
No full textThis paper proposes a novel method to optimize active vibration isolation systems based on H2-criteria using the dynamic error budgeting framework and H∞ constraints to guarantee robust stability. This method explicitly takes into account all noise sources and disturbances present in active vibration isolation systems. The dynamic error budget is interpreted as an H2 optimal control problem with a specific set of input weighting functions, that are models of the input signal spectra. This is extended with H∞ constraints to guarantee stability robustness of the controller. The constrained optimization problem is solved in a structured control setting, with a non-smooth sub-gradient descent method. This is used to optimize the controller and system parameters simultaneously. First an explorative study is done for a single axis active vibration isolation system, and it is shown that the performance improves significantly relative to a passive vibration isolation system and a benchmark active vibration isolation system. The optimal control formulation is thereafter applied to an experimental system, and performance improvements are obtained by a factor 2.3–4.1 in internal deformation power, and 2.9–13.7 in sensitive payload acceleration power with respect to the previous controller based on engineering intuition.</p
Frequency domain stability and relaxed convergence conditions for filtered error adaptive feedforward
Get PDFThe convergence of filtered error and filtered reference adaptive feedforward is limited by three effects: model mismatch, unintended input-disturbance interaction and too fast parameter adaptation. In this article, the first two effects are considered for MIMO systems under the slow parameter adaptation assumption. The convergence with model mismatch is conventionally guaranteed using a strictly positive-real condition. This condition can be easily verified in the frequency domain, but due the high-frequency parasitic dynamics of real systems, it is hardly ever satisfied. Nevertheless, filtered error and filtered reference adaptive feedforward have successfully been implemented in numerous applications without satisfying the strictly positive-real condition. It is shown in this article that the strictly positive-real condition can be relaxed to a power-weighted integral condition, that is less conservative and provides a practical check for the convergence of filtered error adaptive feedforward for real systems in the frequency domain. The effects of input-disturbance interaction are analysed and conditions for the stability are given in the frequency domain. Both conditions give clear indicators for frequency domain filter tuning, and are verified on an experimental active vibration isolation system.</p
Using Time Delayed Disturbance Compensation for Sliding Mode Control
Get PDFUnder the framework of using Time Delay Control (TDC) for disturbance compensation in Sliding Mode Control (SMC), we address two practical problems. The first problem involves mitigating chattering in SMC caused by input delay, while the second problem focuses on designing TDC under conditions of limited measurements. Our research demonstrates that incorporating TDC as a phase lead compensator in the first problem can effectively accommodate larger input delays. To reduce the chattering, we propose a switching gain design, consisting of reference signals rather than measured states, resulting in an ultimately bounded solution. In the second problem, when acceleration measurements are unavailable, we provide stability conditions under which TDC can be designed with acceleration construction using delayed velocity signals. By constructing a modified sliding surface that incorporates the integral error remainder associated with the acceleration construction, our approach ensures switching gain are kept at minimal, with robust disturbance compensation at higher frequencies. We perform a simulation investigation of an autonomous underwater vehicle under input delay and disturbance to demonstrate the efficiency of the approach
Vibration Isolation by an Actively Compliantly Mounted Sensor Applied to a Coriolis Mass-Flow Meter
Get PDFIn this paper, a vibration isolated design of a Coriolis mass-flow meter (CMFM) is proposed by introducing a compliant connection between the casing and the tube displacement sensors, with the objective to obtain a relative displacement measurement of the fluid conveying tube, dependent on the tube actuation and mass-flow, but independent of external vibrations. The transfer from external vibrations to the relative displacement measurement is analyzed and the design is optimized to minimize this transfer. The influence of external vibrations on a compliant sensor element and the tube are made equal by tuning the resonance frequency and damping of the compliant sensor element and therefore the influence on the relative displacement measurement is minimized. The optimal tuning of the parameters is done actively by acceleration feedback. Based on simulation results, a prototype is built and validated. The validated design shows more than 24 dB reduction of the influence of external vibrations on the mass-flow measurement value of a CMFM, without affecting the sensitivity for mass-flow
