Low Velocity Friction Compensation and Feedforward Solution based on Repetitive Control

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.

Ball-screw-driven stages are often used as feed systems of machine tools. Precise control of the stage is desired; however, rolling friction degrades tracking accuracy and causes a large tracking error called a quadrant glitch. Although model-based feedforward friction compensation effectively suppresses the tracking error, the compensation often results in a negative quadrant glitch, which is the tracking error in the direction opposite to the quadrant glitch. This study aims to present a suppression method of the negative quadrant glitch. In this study, initial value compensation with additional input is exploited. The approach is evaluated through simulations and experiments.

This paper presents an approach for kinematic compensation of the laser shaping process which is capable of achieving improved dimensional accuracy for non‐circular profiles. In this approach, a plug‐in repetitive controller is added into the existing position servo loop to improve tracking of the desired sinusoidal trajectory and subsequently reduce tracking errors. The effect of tracking errors on different dimensional error modes in the non‐circular shaping process is identified. Simulation models are developed for testing the performance of the repetitive controller in shaping various non‐circular profiles with different operating parameters such as oscillating amplitudes and sampling time. Simulation results show that better tracking performance can be obtained with the addition of the repetitive controller. Experimental results include fabrication of single‐harmonic‐term profiles such as triangular, square, hexagonal and octagonal profiles and multiple‐harmonic‐term profiles such as diamond‐shaped profiles in polymethyl methacrylate with both control algorithms. The non‐circular profiles are measured through optical CMM to determine the dimensional accuracy in edge straightness, angularity, parallelism and feature size.

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.

Ball-screw-driven stages are often used as feed systems of machine tools. A problem of tracking control of the stages is rolling friction, which degrades tracking accuracy around the velocity reversal point and causes a large tracking error called a quadrant glitch. Although the model-based feedforward friction compensation effectively reduces the tracking error, the compensation often results in an inverse response, which is the tracking error in the direction opposite to the quadrant glitch. This study aims to provide an analysis and a suppression approach to the inverse response. First, the inverse response is analyzed through the simulations. Next, a suppression approach of the inverse response is proposed. In the proposed approach, a step input is injected and cancel the inverse response. The proposed approach is evaluated through the simulations and experiments.

Implementation of Plug-in Type Repetitive Controller for Position-based Periodic Control Systems

Harmonic current sources (HCS) that can provide variable-frequency and amplitude output current are widely used in automatic testing of the electrical equipments. Digital repetitive control (RC) can achieve zero steady-state error tracking of any periodic signal with known integer period, hence, it's suitable for harmonic control, but it usually fails to provide precise tracking of variable frequency periodical waveform with fractional time delay. In this paper, a fraction order delay FIR filter based on Lagrange interpolation is used to approximate the factional delay items in RC. The design criteria is summarized in a simple form, and the stability of Fractional order RC is also analyzed in this paper, experiments is conducted to verify the effectiveness of the proposed FORC strategy.

This research utilizes the repetitive control approach in morphing a high-speed cam mechanism so that its output displacement tracks the desired output trajectory. The main objective is to reduce the output tracking error, which is the difference between the actual and desired output displacements of the output mass. A 3-degree of freedom mathematical model is used to analyze and represent the cam follower system. The output tracking error in cam follower systems is generally caused by errors in cam profile manufacturing, variation in the speed of the driving motor and the dynamics of the cam follower system. Theoretical and experimental results show that the output tracking error is greatly reduced after repetitive control has been applied to the system. As a result, the actual output displacement tracks the desired output displacement very closely.

In the paper, a digital repetitive control scheme is proposed for the single-phase inverters to achieve the high-quality sinusoidal output voltages and the minimum total harmonics distortion. In the proposed control scheme, the repetitive controller is plugged into the stable state feedback controlled single-phase inverter system. The repetitive controller is designed to eliminate the periodic disturbance and track the periodic or dc reference signal with zero tracking error. The design method of the controller is described systematically, besides the stability of system is analysed. Simulation results illustrate the availability of the proposed scheme.

Directional Repetitive Control of a Metrological AFM

In this paper, a cascaded voltage-current control strategy for a four-leg DC-AC converter is proposed. The main objective of the proposed controller is to control the DC voltage while tracking the reference output current. The control scheme includes an outer voltage loop and an inner current loop. The voltage loop can provide the maximum power point tracking function used in green power, such as wind and photovoltaic power generation. The inner loop current controller consists of an internal model and a stabilising compensator, which is designed using the H∞ control theory. The internal model contains a delay line and a low-pass filter. To formulate the H∞ problem, two additional parameters are introduced. The stabilising compensator of the internal model is obtained by solving the H∞ problem. The tracking error of the proposed current controller is very small, and the robustness of the controller is very excellent. Experiments are carried out to compare the proposed controller with traditional proportional-resonant and proportional-integral controllers. The results show that the proposed controller has a smaller tracking error with better robustness.

In this paper, a cascaded voltage-current control strategy for a four-leg DC-AC converter is proposed. The main objective of the proposed controller is to control the DC voltage while tracking the reference output current. The control scheme includes an outer voltage loop and an inner current loop. The voltage loop can provide the maximum power point tracking function used in green power, such as wind and photovoltaic power generation. The inner loop current controller consists of an internal model and a stabilising compensator, which is designed using the H infinity control theory. The internal model contains a delay line and a low-pass filter. To formulate the H infinity problem, two additional parameters are introduced. The stabilising compensator of the internal model is obtained by solving the H infinity problem. The tracking error of the proposed current controller is very small, and the robustness of the controller is very excellent. Experiments are carried out to compare the proposed controller with traditional proportional-resonant and proportional-integral controllers. The results show that the proposed controller has a smaller tracking error with better robustness.

Dynamic voltage restorer (DVR) has been demonstrated to be a very effective mechanism to deal with key voltage-quality disturbances. Although the dynamic response requirement for voltage sag could be satisfied with a feedforward control strategy, the steady-state requirement and zero-error tracking need an advanced feedback control strategy. This paper proposes a fast repetitive controller based feedback control strategy for DVR system. In the control system, the feedforward control loop could meet the dynamic requirement; the repetitive controller based feedback control loop could realize zero steady-state error tracking for fundamental voltage and harmonic components. The fast repetitive controller: 1) could eliminate all odd signals (including fundamental component); 2) could be simply implemented in digital signal processors just with a time delay loop; 3) has fast dynamic response when compared with traditional repetitive controller as its delay time is reduced to half of traditional's. This paper also chooses the small gain theorem for control system analysis and parameters design. The simulation on MATLAB/simulink also demonstrates the validity and superiority of proposed control strategy.

In order to effectively solve a series of problems caused by harmonics in power system, an active power filter based on ANFIS-PI and repetitive control is designed. The traditional single control method cannot balance control accuracy and response speed, so a compound control strategy is adopted. Repetitive control can produce the same output as the harmonic current, so it can achieve zero steady-state error tracking compensation for each harmonic, but its dynamic performance is not good. As a traditional control method, the PI control method has a fast response speed, but in the actual application process, when the load changes suddenly, that is, when the system parameters change, its tracking effect is not ideal. Therefore, a composite control strategy of ANFIS-PI and repeated control is proposed. It has been proved that its compensation accuracy and dynamic response speed have been significantly improved.