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Em um sistema came-seguidor a dinâmica do sistema seguidor faz com que o movimento final se desvie daquele especificado. Este efeito pode ser compensado considerando-se o modelo dinâmico inverso do sistema seguidor no projeto da lei de movimento do came. Considerando-se constante a velocidade do came, o sistema seguidor tem dinâmica linear. Entretanto, devido à razão de transmissão variável, e devido a outros efeitos não lineares, o sistema de acionamento como um todo é não linear, e procedimentos não lineares devem ser utilizados para se ajustar a lei de movimento do came. Uma análise teórica, suportada por simulações, mostra o potencial deste procedimento, ao menos no caso de uma dinâmica simples do sistema seguidor: uma considerável redução do erro de movimento, e uma boa robustez relativa a erros na freqüência de ressonância e razão de amortecimento estimadas. Experimentos com o acionamento por um servomotor sub-dimensionado, como é de se esperar, mostram resultados diferentes, devido à velocidade angular não constante. A flutuação observada na velocidade angular em torno do valor constante é então levada em consideração para o projeto da lei de movimento com nonlinear feedforward. / In a cam-follower system the dynamics of the follower-train mechanism cause an actual motion which deviates from the desired one. This effect can be compensated by taking into account the inverse dynamic model of the follower-train in the design of the cam motion law. By considering a constant cam velocity, the follower-train has linear dynamics. However, due to the varying transmission ratio, and due to other nonlinear effects, the whole drive train is a nonlinear system, and nonlinear procedures should be used to fit a motion law. A theoretical analysis with only the linear feed-forward compensation, supported by simulation results, has shown the potential of this approach, at least in the case of simple follower-train dynamics: a considerable reduction of the motion error, and a good robustness with respect to errors in the estimated resonance frequency and damping ratio of the follower-train. Experiments with a small driving servomotor, as expected, show differerit results, due to the non-constant angular velocity. The observed cam angular velocity ripple is then taken into account to design a complete nonlinear feedforward motion law.

Em um sistema came-seguidor a dinâmica do sistema seguidor faz com que o movimento final se desvie daquele especificado. Este efeito pode ser compensado considerando-se o modelo dinâmico inverso do sistema seguidor no projeto da lei de movimento do came. Considerando-se constante a velocidade do came, o sistema seguidor tem dinâmica linear. Entretanto, devido à razão de transmissão variável, e devido a outros efeitos não lineares, o sistema de acionamento como um todo é não linear, e procedimentos não lineares devem ser utilizados para se ajustar a lei de movimento do came. Uma análise teórica, suportada por simulações, mostra o potencial deste procedimento, ao menos no caso de uma dinâmica simples do sistema seguidor: uma considerável redução do erro de movimento, e uma boa robustez relativa a erros na freqüência de ressonância e razão de amortecimento estimadas. Experimentos com o acionamento por um servomotor sub-dimensionado, como é de se esperar, mostram resultados diferentes, devido à velocidade angular não constante. A flutuação observada na velocidade angular em torno do valor constante é então levada em consideração para o projeto da lei de movimento com nonlinear feedforward. / In a cam-follower system the dynamics of the follower-train mechanism cause an actual motion which deviates from the desired one. This effect can be compensated by taking into account the inverse dynamic model of the follower-train in the design of the cam motion law. By considering a constant cam velocity, the follower-train has linear dynamics. However, due to the varying transmission ratio, and due to other nonlinear effects, the whole drive train is a nonlinear system, and nonlinear procedures should be used to fit a motion law. A theoretical analysis with only the linear feed-forward compensation, supported by simulation results, has shown the potential of this approach, at least in the case of simple follower-train dynamics: a considerable reduction of the motion error, and a good robustness with respect to errors in the estimated resonance frequency and damping ratio of the follower-train. Experiments with a small driving servomotor, as expected, show differerit results, due to the non-constant angular velocity. The observed cam angular velocity ripple is then taken into account to design a complete nonlinear feedforward motion law.

La prochaine génération de télescopes spatiaux devra repousser les limites des technologies actuelles afin d’accroitre les performances techniques et opérationnelles. Dans le cas d’observations difficiles, l'utilisation de plus grandes ouvertures des miroirs primaires est essentielle pour obtenir la résolution optique et la sensibilité requises. Toutefois, les grandes ouvertures primaires induisent un certain nombre de défis techniques tels que la masse, le volume et la raideur du miroir. La masse et le volume doivent rester acceptables par rapport au lanceur et la raideur du miroir, qui diminue avec l’augmentation du diamètre du miroir, doit être suffisante afin que les performances ne soient pas altérées par les déformations statiques et dynamiques. Pour surmonter ces limitations, des configurations de miroirs déformables comportant des éléments de contrôle actifs sont étudiées pour les futurs télescopes spatiaux. Les actionneurs piézoélectriques, qui répondent aux exigences de puissance massique et de bande passante, peuvent être utilisés comme éléments de contrôle actifs intégrés dans la structure de miroir. Toutefois, ces actionneurs montrent en fonctionnement en boucle ouverte des comportements non linéaires indésirables, comme le fluage et l'hystérésis, qui peuvent conduire à des inexactitudes indésirables et limiter les performances des systèmes. Par conséquent, pour les miroirs déformables activés par des actionneurs piézoélectriques, la compensation des non linéarités dans les actionneurs piézoélectriques est indispensable.La conception d’un miroir léger, compact et déformable à raideur adéquate est un défi très important pour les télescopes spatiaux mais n'est pas abordée dans cette thèse. Cette thèse porte sur le contrôle de surfaces de miroirs déformables actionnés par des actionneurs piézoélectriques et en particulier sur la compensation du fluage et de l'hystérésis dans les actionneurs piézoélectriques. La technologie de miroir actif étudié (avec des pieds activés, type miroir fakir) requiert un grand nombre d’actionneurs afin de tenir les exigences en termes de planéité de surface et ne permet pas un contrôle en boucle fermée de chaque actionneur (ce type de contrôle est trop exigeant en nombre de capteurs). La compensation du fluage et de l’hystérésis est donc réalisée en boucle ouverte et s’appuie sur des modèles précis des non linéarités à compenser et sur l’implémentation de modèles inverses. Un support d’étude expérimental a été élaboré au cours de la thèse afin de valider les études théoriques par des résultats expérimentaux. Il représente une partie d’un miroir de grande taille et consiste en une plaque de verre circulaire de diamètre 300mm dont la surface peut être actionnée par 7 actionneurs piézoélectriques annulaires.Les premières chapitres de la thèse concernent l’étude de la compensation en boucle ouverte du fluage et de l’hystérésis dans un seul actionneur qui est alors considéré comme un système SISO (single input – single output). Dans le dernier chapitre de la thèse, le fluage et de l’hystérésis sont compensés dans 3 actionneurs simultanément, ceux-ci formant un système MIMO (multi input – multi output). Les apports de la thèse concernent le développement de nouveaux modèles directs et inverses de fluage et d’hystérésis qui ont été validés par des expérimentations réalisées dans un contexte difficile de par la faible étendue des amplitudes de déplacement ( de l’ordre du micromètre). / The next generation of space-based observation systems will make use of larger primary mirrors to achieve higher image resolution. Large primary mirrors lead to the increase of structural flexibility and are more susceptible to distortions. Thus maintaining optical tolerances across the mirror surface becomes increasingly difficult. The techniques of active shape control may be required for spatial mirror surfaces in future space observation systems. Piezoelectric actuators are often studied as embedded elements for the active control of mirror structures due to their excellent properties. However, unwanted nonlinear effects in piezoelectric actuators, i.e., hysteresis and creep, severely limit the service performance. This thesis aims at developing openloopcontrol laws to compensate hysteresis and creep effects in piezoelectric actuators. The studies led during this thesis are applied to the shape control of spatial mirror surfaces. An experimental setup with a small-scale mirror test structure involving multiple piezoelectric actuators is first developed and is used as support for all the measurements conducted during this thesis. Then the open-loop control methodologies of creep compensation, hysteresis compensation, and simultaneous compensation of both the nonlinear effects in a single piezoelectric actuator are respectively developed. To compensate creep, a nonlinear viscoelastic model is used to portray creep, and a new inverse model of creep based on the concept of “voltage relaxation” is proposedRegarding the hysteresis compensation, the classical Preisach model is modified by adding a derivative term in parallel to describe hysteresis more accurately with relatively few measurements, and the new inverse model is constructed in the similar way. For the simultaneous compensation of the two nonlinear effects, the hysteresis is first compensated and then, the creepof the hysteresis-compensated piezoelectric actuator is attenuated by open-loop control. The methodology is first developed for a single actuator. Finally, the shape control of a mirror surface with several piezoelectric actuators is achieved by actuating the points on the mirror surface in such a way as to reach the required displacements. The mirror test structure involving multiplepiezoelectric actuators compensated in hysteresis and creep is considered as a linear system on which the superposition principle can be applied. The influence coefficients characterizing the coupling effect between the piezoelectric actuators are determined by measurements. The influence coefficient matrix is first constructed using the superposition principle, and is then inverted. By insertion of the inverse matrix in cascade with multiple piezoelectric actuators with hysteresis and creep compensation, a feed-forward control approach to actuate the multiple interesting points of the mirror surface is developed. A number of experimental results demonstrate that the developed control methodologies are effective and feasible in practice.

Main aim of this master’s thesis is to identify, model and control robotic manipulator with three degrees of freedom. The thesis is a part of major project [17], the aim of which is to create an educational platform. In the thesis the simple PID control and the PID with feedforward compensation control is tested on the model of simple pendulum. In the next part models of DC motors, which are used for construction of the manipulator, are developed and the inverse dynamics model of manipulator is developed. This model is used for feedforward control of the manipulator. In the final part the application was developed, which allows the manipulator to be taught some movements, which can be later on, executed. For the simple control of the application the graphical user interface was programmed.

Tato práce se zabývá návrhem adaptivního řídícího algortitmu pro konkrétní třídu elektromechanických aktuátorů, založeného na principu dopředného řízení pomocí inverzního dynamického modelu. Adaptibilita řízení spočívá v mechanismu získání inverzního dynamického modelu. Tato práce se zaměřuje na jeho online aproximaci pomocí lokálních aproximačních metod. Výstupem práce je shrnutí analýzy, simulačního testování a reálných experimentů, které testovaly možnosti praktického využití lokálných aproximačních metod pro účely adaptivního řízení v reálném prostředí.

The Permanent Magnet Synchronous Motor (PMSM, also known as the servo motor) is a crucial component within robotic servo systems. To optimally respond to the torque demands sent from the high-level motion controller, the PMSM current controller must track the reference with speed and precision. Nevertheless, the operation of servo motors could be compromised due to the nonlinearity of flux linkage and inaccuracies in parameters induced by unpredictable fluctuations in temperature. This Master’s thesis proposes a novel Robust Nonlinear Deadbeat Predictive Current Control (RN-DPCC) scheme to counter these challenges effectively. The nonlinear mappings between flux linkage and current on the dq-axis are established using polynomial fitting based on experimental data. Furthermore, the Nonlinear Deadbeat Predictive Current Control (N-DPCC) is derived using nonlinear feedforward. Meanwhile, Delayed Integral Action (DIA) is introduced as a robustness-enhancing measure for N-DPCC, thus evolving it into the Robust N-DPCC (RN-DPCC). Compared to conventional Integral Action (IA), DIA effectively curtails overshoot triggered by integral error and accelerates the current transient without incorporating additional tunable parameters. Numerical simulations that leverage the mathematical modeling of the converter and nonlinear PMSM are implemented using fundamental blocks in Simulink, which replicates the actual experimental setup employed within the Motor Control Lab at ABB Corporate Research. The effectiveness of employing nonlinear feedforward compensation is confirmed through a comparative analysis of the simulation results from N-DPCC and conventional Deadbeat Predictive Current Control (DPCC). The enhancements in transient response brought about by DIA are demonstrated through a comparison of RNDPCC and N-DPCC with IA. The robustness of RN-DPCC is demonstrated by comparing it with N-DPCC under conditions where parameter inaccuracies are present. / Den permanenta magnet-synkronmotorn (PMSM, även känd som servomotorn) är en avgörande komponent inom robotiserade servosystem. För att optimalt kunna reagera på momentkraven som skickas från högnivårörelsekontrollern måste PMSM-strömregulatorn följa referensen med hastighet och precision. Trots detta kan driften av servomotorer påverkas av ickelinjäriteter i flödeslänkningen och felaktigheter i parametrar som orsakas av oförutsägbara temperaturfluktuationer. Denna magisteravhandling föreslår en ny robust icke-linjär deadbeat-prediktiv strömreglering (RN-DPCC) för att effektivt hantera dessa utmaningar. De icke-linjära avbildningarna mellan flödeslänkning och ström på dq-axeln etableras med hjälp av polynomisk anpassning baserat på experimentella data. Dessutom härleds den ickelinjära deadbeat-prediktiva strömregleringen (N-DPCC) med hjälp av Ickelinjär feedforward. Samtidigt introduceras fördröjd integralåtgärd (DIA) som en robusthetsförbättrande åtgärd för N-DPCC, vilket förvandlar den till Robust N-DPCC (RN-DPCC). Jämfört med konventionell integralåtgärd (IA) minskar DIA effektivt överhäng som utlöses av integralfel och accelererar strömövergången utan att införa ytterligare justerbara parametrar. Numeriska simuleringar som utnyttjar den matematiska modelleringen av omvandlaren och den icke-linjära PMSM implementeras med hjälp av grundläggande block i Simulink, vilket återskapar den faktiska experimentella uppställningen som används i Motor Control Lab vid ABB Corporate Research. Effektiviteten i att använda icke-linjär framåtmatningskompensation bekräftas genom en jämförande analys av simulationsresultaten från N-DPCC och konventionell deadbeat-prediktiv strömreglering (DPCC). Förbättringarna i transientrespons som DIA medför demonstreras genom en jämförelse av RN-DPCC och NDPCC med IA. Robustheten hos RN-DPCC demonstreras genom att jämföra den med N-DPCC under förhållanden där parameterfel förekommer.