Kinematic compensation of repetitive errors for non‐circular laser shaping

Multi-rate model predictive control to reject periodic disturbance with reduced ripple

Optical and structural optimization of a large aperture solar parabolic trough collector

The repetitive control technique is widely adopted in ac systems, because of its excellent steady‐state tracking performance and low total harmonic distortion. The repetitive control method with one‐sixth of the system fundamental period T0 as the delay time has been proposed to achieve fast transient response. In this study, an improved control scheme based on the T0/6 repetitive control is proposed for three‐phase grid‐connected inverters. The proposed scheme adopts T0/6 as the delay time in the positive‐rotating and negative‐rotating synchronous reference frames to suppress the 6n ± 1 harmonics. Meanwhile, the proportional‐integral regulator and the plug‐in repetitive controller are combined to reinforce the system performance. A new auxiliary function based on the linear interpolation is proposed to maintain the ideal repetitive control performance when one‐sixth of the ratio of the sampling frequency to the grid fundamental frequency is non‐integer. The effectiveness of the proposed scheme on improving the T0/6 repetitive control is confirmed by simulation and experimental results finally.

One of the most significant sources of tracking error for an X-Y table is static friction, a nonlinear disturbance. Static friction, or stiction, occurs when an axis makes a zero velocity crossing, i.e. when an axis reverses direction. In traversing a circular profile for example. an X-Y table encounters zero velocity crossings at ninety degree intervals around the circle, leaving relatively large tracking errors referred to as "quadrant glitches". To eliminate errors caused by stiction, repetitive control, a subclass of learning control, is employed. Experiments are conducted on the X-Y bed of a CNC milling machine. The repetitive controller is implemented digitally in the position servo loop. The velocity loop is closed internally by an analog PI servo which is part of the original controller of the CNC milling machine. The repetitive controller undergoes successive passes in tracking a profile containing a zero velocity crossing. The repetitive controller contains an internal periodic signal generator which receives the error over repetitive cycles and generates a compensating input for cancellation of the repetitive disturbance. Experimental data indicates that perfect velocity tracking can be achieved in twelve cycles or less. Of particular interest is the velocity command input generated by repetitive control. The input contains feedforward information for developing perfect trajectoris at low velocities. An analysis for using the feedforward information for zero velocity crossings at different local accelerations is developed.

The purpose of this in vitro study was to evaluate the mechanical performance, dimensional accuracy, and bonding behavior of fused filament fabrication (FFF)-printed provisional restorations made from polymethyl methacrylate (PMMA) and polyethylene terephthalate (PET), and compare them with digital light processing (DLP)-printed and computer-aided numerical control (CNC)-milled ones. Occlusal veneers (OV), posterior crowns (PC), and anterior crowns (AC) (n = 30) were fabricated using FFF (PMMA, PET), DLP (acrylate), and CNC (PMMA) to assess initial fracture load (IFL). To determine reproducibility three restorations of each group were scanned and compared with each other; to determine printing accuracy the scanned restorations were compared with the STL generated for manufacturing. For shear bond strength (SBS) testing, 72 PMMA (FFF) specimens were conditioned with either Monobond Plus (MP) or Visiolink (VL) and bonded with acrylic cylinders using a dual-cure luting composite (Variolink Esthetic DC). Half of each group underwent thermocycling (10,000 cycles, 5 °C/55 °C, 30 s dwell time); the remainder was tested initially. Additionally, 48 FFF-printed PC were fabricated from PET and PMMA to investigate the fracture load in relation to the adhesive material (FL). PMMA crowns were conditioned with MP (n = 16) or VL (n = 16) and bonded with Variolink Esthetic DC. PET crowns were cemented with either Meron (ME) or Ketac Cem Plus (KE). Half of the PMMA and all PET crowns were subjected to masticatory simulation (1,200,000 cycles, 5 N, 5 °C/55 °C, 60 s dwell). Data were analyzed using Kolmogorov–Smirnov, Kruskal–Wallis, and Mann–Whitney U tests, including IFL, SBS and FL parametric tests, and comparisons were carried out using an independent t-test ( = 0.05). FFF-fabricated restorations showed the lowest fracture load values and CNC-fabricated the highest (p < 0.001). OV fabricated via DLP and CNC exhibited the highest fracture load (p < 0.001). For FFF, PC demonstrated the highest values (p < 0.028), whereas AC showed the lowest fracture load values (p < 0.001). VL showed higher initial SBS than MP (p < 0.001) and no impact on aging (p < 0.608). All MP samples showed debonding after thermocycling. Within PET and PMMA, no impact of luting/cement material on fracture load was observed (p = 0.116–0.282). The fracture load decreased after masticatory simulation (MP-PMMA: p < 0.001, VL-PMMA: p = 0.27). DLP-fabricated restorations showed the highest reproducibility and printing accuracy. CNC and FFF-PET showed comparable values. FFF-PMMA showed the greatest deviations. CNC-fabricated provisional restorations exhibited the highest fracture load. AC presented the lowest fracture load values. DLP provided the highest reproducibility and accuracy. VL achieved superior bonding to PMMA surfaces. Thermomechanical aging significantly reduced fracture load in both PET and PMMA restorations, regardless of luting material.

SummaryIn this article, the decentralized repetitive tracking controller design for fractional‐order large‐scale Takagi–Sugeno fuzzy system with time delays is developed. We mainly focus on the design of a decentralized repetitive tracking controller based on the Lyapunov stability theory, by which the addressed large‐scale system asymptotically stabilized with performance index. Further, the repetitive control with quantized signal is developed to ensure the good tracking performance with the presence of interconnected model and external disturbances. Specifically, a logarithmic quantizer is used to quantify the control signal which can reduce the data transmission rate in the network. Finally, a numerical example is presented to verify the effectiveness of the proposed controller design technique.

A repetitive controller contains a pure-delay positive-feedback loop that makes it difficult to stabilize a strictly proper system. A low-pass filter is inserted in a repetitive controller to relax the stability condition of the modified repetitive-control system at the cost of degrading the tracking performance. In this study, a modified repetitive-control approach is developed, which reaches a balance between the stability and tracking performance for a class of affine nonlinear systems based on the Takagi–Sugeno fuzzy model. First, a 2D model is established to adjust continuous control and discrete learning actions preferentially induced by exploiting the 2D property in a repetitive-control process. Then, the Lyapunov stability theory and 2D system theory are used to derive a sufficient stability condition in the form of linear matrix inequalities to design parallel-distributed-compensation-based state-feedback controllers. Finally, an application-oriented example is used, and a comparison is performed to show that an extra variable is introduced such that the developed method has a better tracking performance.

The tracking/rejection of periodic signals constitutes a wide field of research in the control theory and applications area and Repetitive Control has proven to be an efficient way to face this topic; however, in some applications the period of the signal to be tracked/rejected changes in time or is uncertain, which causes and important performance degradation in the standard repetitive controller. This thesis presents some contributions to the open topic of repetitive control working under varying frequency conditions. These contributions can be organized as follows: One approach that overcomes the problem of working under time varying frequency conditions is the adaptation of the controller sampling period, nevertheless, the system framework changes from Linear Time Invariant to Linear Time-Varying and the closed-loop stability can be compromised. This work presents two different methodologies aimed at analysing the system stability under these conditions. The first one uses a Linear Matrix Inequality (LMI) gridding approach which provides necessary conditions to accomplish a sufficient condition for the closed-loop Bounded Input Bounded Output stability of the system. The second one applies robust control techniques in order to analyse the stability and yields sufficient stability conditions. Both methodologies yield a frequency variation interval for which the system stability can be assured. Although several approaches exist for the stability analysis of general time-varying sampling period controllers few of them allow an integrated controller design which assures closed-loop stability under such conditions. In this thesis two design methodologies are presented, which assure stability of the repetitive control system working under varying sampling period for a given frequency variation interval: a mu-synthesis technique and a pre-compensation strategy. On a second branch, High Order Repetitive Control (HORC) is mainly used to improve the repetitive control performance robustness under disturbance/reference signals with varying or uncertain frequency. Unlike standard repetitive control, the HORC involves a weighted sum of several signal periods. With a proper selection of the associated weights, this high order function offers a characteristic frequency response in which the high gain peaks located at harmonic frequencies are extended to a wider region around the harmonics. Furthermore, the use of an odd-harmonic internal model will make the system more appropriate for applications where signals have only odd-harmonic components, as in power electronics systems. Thus an Odd-harmonic High Order Repetitive Controller suitable for applications involving odd-harmonic type signals with varying/uncertain frequency is presented. The open loop stability of internal models used in HORC and the one presented here is analysed. Additionally, as a consequence of this analysis, an Anti-Windup (AW) scheme for repetitive control is proposed. This AW proposal is based on the idea of having a small steady state tracking error and fast recovery once the system goes out of saturation. The experimental validation of these proposals has been performed in two different applications: the Roto-magnet plant and the active power filter application. The Roto-magnet plant is an experimental didactic plant used as a tool for analysing and understanding the nature of the periodic disturbances, as well as to study the different control techniques used to tackle this problem. This plant has been adopted as experimental test bench for rotational machines. On the other hand, shunt active power filters have been widely used as a way to overcome power quality problems caused by nonlinear and reactive loads. These power electronics devices are designed with the goal of obtaining a power factor close to 1 and achieving current harmonics and reactive power compensation.

This paper describes the design and implementation of a repetitive controller (RC) for tracking periodic trajectories in aerial robots, such as unmanned aerial vehicles (UAVs). The RC is ideally suited for situations where the robot is required to execute a defined flight pattern, over and over again in a periodic fashion. Applications include precision agriculture, and search and rescue, where the desired trajectory is often periodic in time and known a priori. Compared to iterative learning control (ILC), RC is a feedback-based approach which can be plugged into an existing feedback control loop to improve the tracking of period trajectories. Herein, a plug-in type RC is applied to a micro aerial robot, and a systematic approach is presented for designing the control system. The plug-in nature of the design also allows users to enable/disable the controller on the fly. The proposed RC is also compared to existing approaches, including no-reset ILC, which have recently been applied to control aerial robots. The effectiveness of the RC is demonstrated on a custom-designed experimental micro aerial robot. Tracking of circle, square, and figure-eight trajectories are shown in both simulations and experiments. In these cases, the RC reduces the average tracking error by over 58% compared to a well-tuned PID controller, and simulations that compare to no-reset ILC show that the performance of RC is less sensitive to changes in the reference trajectory.

The most common materials used for fabrication of denture bases are poly methyl methacrylate (PMMA). Preparation of modified heat cured denture base acrylic resin was carried out by preparing of (PMMA)(80%) and poly vinyl pyrrolidon (PVP)(20%) and the liquid part composed of methyl methacrylate (MMA) monomer. A(10) specimens for each experimental group were tested . All specimens were cured by using short curing cycle (90 min.at 74C° followed by 30 min .at 100C°).Evaluation was made by measuring dimensional stability and accuracy of the prepared denture base material in comparison with the control denture base material . The dimensional accuracy of acrylic resin denture base is the main necessity ,where it effects the retention and stability of the denture .A silicon mold was used to prepare a(40) stone mandibular master casts (control and experimental). Acrylic dough was prepared and packed for processing ,the flask were closed with pressure technique and placed in clamps after final closure .Distances were measured between (3) points marked on denture bases before and after thermocycling for both control and experimental groups. For AB and BC distances the PVP had improved the dimensional stability and accuracy before and after thermocycling while for AC distance the control group material before and after thermocycling improved the dimensional stability and accuracy.

During locomotion, Autonomous Ground Vehicles (AGV) need to map the surface of the ground ahead in order to plan a safe route of passage. Algorithms that achieve this are all derived from a basic requirement to track pixels between successive frames. This paper establishes the effect of tracking error on depth estimation with different image-plane geometries and presents an argument for tight control of the camera orientation. It is found that the effect of tracking error is invariant with camera angle for a concave image-plane but varies non-linearly with angle for both flat and inverse-flat image-planes. Pairs of frames are produced by each camera from a simulated scene and a selection of algorithms are used to compute the optical flow. It is shown that current state-of-the-art optical flow algorithms can successfully track pixels across concave and inverse-flat image-planes. This results in comparable depth estimation accuracy to a flat image-plane but allows for improved object tracking.

We propose an adaptive image mapping method that removes image discontinuity, which is the main degradation factor of image quality in an integral floating display. The proposed method is based on a newly modified image mapping algorithm that removes image discontinuity for an observer at a specific location. By taking advantage of an eye tracking scheme, the modified algorithm can produce a floating 3D image in real time for moving observers as well. The observable area of the proposed system is analyzed, and we show that multiple observers in the area can view floating 3D images without interfering with one another's views. The effect of tracking error on the floating 3D image is analyzed, and a strategy to deal with it is also given.

The line current detection type AF is attractive to compensate using only one current sensor and only one AF compensates all harmonics. However, it is difficult to compensate harmonics completely due to stability and a resonance problem. We propose a new method using the repetitive control for the line current detection type active filter. Aiming at a periodicity of the harmonics, the repetitive control is applied to the AF control. The line current harmonics is detected and memorized at every sampling time during the fundamental cycle. The memorized data are given to a reference of the AF after a fundamental period. The AF output current reference is optimized and the deviation in the line current harmonics gradually decreases by repeating the method. Good simulation results of the harmonics compensation by the proposed method are presented

In this paper, a repetitive learning control (RLC) approach is proposed for a class of remote control nonlinear systems satisfying the global Lipschitz condition. Since there exist time delays in the two transmission channels, tracking a desired trajectory through a remote controller is not an easy task. In order to solve this problema predictor is designed on the controller side to predict the future state of the nonlinear system based on the delayed measurements from the sensor. The convergence of the estimation error of the predictor is ensured. The gain design of the predictor applies linear matrix inequality - LMI techniques developed by Lyapunov Kravoskii method for time delay systems. The repetitive learning control law is constructed based on the feedback error from the predicted state. The overall tracking error tends to zero asymptotically over iterations. A numerical simulation example is shown to verify the effectiveness of the proposed approach.

Disturbance observer based reliable H∞ fuzzy attitude tracking control for Mars entry vehicles with actuator failures