Digital repetitive control under varying frequency conditions

Premi extraordinari doctorat curs 2011-2012, àmbit d’Enginyeria IndustrialThe 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.Award-winningPostprint (published version

Integración de dispositivos y redes industriales seriales con redes TCP/IP usando java

La Celda Manufactura Flexible de Experimental (CMFE) del Laboratorio de Mecatrónica de la Universidad Nacional de Colombia se constituye en un proyecto macro que pretende explorar los sistemas modernos de manufactura del entorno industrial. El proyecto de investigación lleva como título “Investigación Experimental en Automatización para Manufactura Flexible”; como parte de su desarrollo, específicamente en cuanto a los estudios adelantados en las áreas de automatización y comunicaciones industriales y la puesta en funcionamiento de la CMFE, en el presente artículo se desarrolla el proceso de implementación de un sistema de integración y comunicación para la celda flexible, empleando redes de área local basadas en el protocolo TCP/IP. En el documento se describen de manera breve los componentes de la celda experimental, con el propósito de enmarcar el problema de investigación; luego se aborda el diseño y estructura final del sistema de integración

Cinemática inversa de robots industriales

El uso de robots en ambientes industriales, y más precisamente en procesos de manufactura, ha generado toda una línea de investigación y desarrollo en ingeniería. El propósito es el desarrollo de dispositivos encargados del desempeño de operaciones específicas de la función de producción como manejo de materiales, procesamiento de operaciones, ensamble e inspección, realizando labores para las cuales los seres humanos no son aptos, les representa riesgo o dificultad, ejecutando ciclos repetitivos y trabajos de ensamble automatizado en líneas de producción o celdas de manufactura

Adaptive Compensation Strategy For The Tracking/Rejection of Signals with Time-Varying Frequency in Digital Repetitive Control Systems

Digital repetitive control is a technique which al- lows to track periodic references and/or reject peri- odic disturbances. Repetitive controllers are usually de- signed assuming a fixed frequency for the signals to be tracked/rejected, its main drawback being a dramatic per- formance decay when this frequency varies. A usual ap- proach to overcome the problem consists of an adap- tive change of the sampling time according to the refer- ence/disturbance period variation. However, this sam- pling period adaptation implies parametric changes af- fecting the closed-loop system behavior, that may compro- mise the system stability. This article presents a design strategy which allows to compensate for the parametric changes caused by sampling period adjustment. Stabil- ity of the digital repetitive controller working under time- varying sampling period is analyzed. Theoretical devel- opments are illustrated with experimental results.Peer ReviewedPostprint (published version

Non-uniform sampling in digital repetitive control systems: An LMI stability analysis

Digital repetitive control is a technique which allows to track periodic references and/or reject periodic disturbances. Repetitive controllers are usually designed assuming a fixed frequency for the signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A usual approach to overcome the problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. This report presents a stability analysis of a digital repetitive controller working under time-varying sampling period by means of an LMI gridding approach. Theoretical developments are illustrated with experimental results

Design and Analysis Strategies for Digital Repetitive Control Systems with Time-Varying Reference/Disturbance Period

This article introduces and analyzes the performance features of different design schemes for digital repetitive control systems subject to references/disturbances that exhibit non-uniform frequency. Aiming for the maintenance of a constant value for the ratio Tp/Ts, where Tp is the period of the reference/disturbance signal and Ts is the sampling period, two approaches are proposed. The first one deals with the realtime adaptation of Ts to the actual changes of Tp; the stability issue is studied by means of an LMI gridding method and also using robust control techniques. The second one propounds the introduction of an additional compensator that annihilates the effect of the time-varying sampling in the closed-loop system and forces its behavior to coincide with the one corresponding to an a priori selected nominal sampling period; the procedure needs the internal stability of the compensator-plant subsystem, which is checked by means of LMI gridding. The theoretical results are experimentally tested and compared through a mechatronic plant model.Postprint (published version

An educational approach to the internal model principle for periodic signals

This article presents an educational approach to resonant control and repet- itive control, which are Internal Model Principle-based control techniques speci cally de- signed for the tracking/rejection of periodic signals. The analytical formulation is com- pleted by a set of simulations and physical experiments on a mechatronic educational plant integrated in a virtual/remote laboratory. The laboratory features are oriented to realize the limited performance of classic PID control to reject non-constant disturbances and, at the same time, to show the effectiveness of the Internal Model Principle for the rejection of periodic disturbances by means of resonators and repetitive control. Assess- ment based on students' perception reveals it as a useful distance learning tool. The laboratory is integrated in Automatl@bs, a Spanish interuniversity network of web-based laboratories devoted to distance learning of control engineering.Postprint (published version

Odd-harmonic repetitive control of an active filter under varying network frequency: control design and stability analysis

This work deals with the design and analysis of a controller for a shunt active power filter. The design is based on combined feedforward and feedback actions, the last using repetitive control, and aims at the obtention of a good closedloop performance in spite of the possible frequency variations that may occur in the electrical network. As these changes affect the performance of the controller, the proposal includes a compensation technique consisting of an adaptive change of the digital controller’s sampling time according to the network frequency variation. However, this implies structural changes in the closed-loop system that may destabilize the overall system. Hence, this article is also concerned with closed-loop stability of the resulting system, which is analyzed using a robust control approach through the small gain theorem. Experimental results that indicate good performance of the closed-loop system are provided.Postprint (published version

Revisión de control repetitivo digital en condiciones de frecuencia variable

El control repetitivo digital es una técnica que permite el seguimiento y rechazo de señales periódicas. Los controladores repetitivos son diseñados asumiendo que las señales a seguir/rechazar tienen una frecuencia fija y conocida, siendo su principal desventaja la degradación de desempeño cuando esta frecuencia varía. Este artículo presenta una revisión de las diferentes estrategias utilizadas con el fin de solventar dicha problemática.Digital repetitive control is a strategy that allows tracking/rejecting periodic signals. Repetitive controllers are designed assuming that the exogenous signal period is constant and known, its main drawback being the dramatic loss of performance when signal frequency varies. This paper reviews the most relevant proposals advanced for overcoming this problem