Modelling and control of a two-link flexible manipulator using finite element modal analysis

This thesis focuses on Finite Element (FE) modeling and robust control of a two-link flexible manipulator based on a high resolution FE model and the system vibration modes. A new FE model is derived using Euler-Bernoulli beam elements, and the model is validated using commercial software Abaqus CAE. The frequency and time domain analysis reveal that the response of the FE model substantially varies with changing the number of elements, unless a high number of elements (100 elements in this work) is used. The gap between the complexity of the high order FE model capable of predicting dynamics of the multibody system, and suitability of the model for controller design is bridged by designing control schemes based on the reduced order models obtained using modal truncation/H8 techniques. Two reduced order multi-input multi-output modal control algorithms composed of a robust feedback controller along with a feed-forward compensator are designed. The first controller, Inversion-based Two Mode Controller (ITMC), is designed using a mixed-sensitivity H8 synthesis and a modal inversion-based compensator. The second controller, Shaping Two-Mode Controller (STMC), is designed with H8 loopshaping using the modal characteristics of the system. Stability robustness against unmodelled dynamics due to the model reduction is shown using the small gain theorem. Performance of the feedback controllers are compared with Linear Quadratic Gaussian designs and are shown to have better tracking characteristics. Effectiveness of the control schemes is shown by simulation of rest-to-rest maneuver of the manipulator to a set of desired points in the joint space. The ITMC is shown to have more precise tracking performance, while STMC has higher control over vibration of the tip, at the expense of more tracking errors

Identification of natural frequency components of articulated flexible structures

M.S.Wayne J. Boo

Development of New Adaptive Control Strategies for a Two-Link Flexible Manipulator

Manipulators with thin and light weight arms or links are called as Flexible-Link Manipulators (FLMs). FLMs offer several advantages over rigid-link manipulators such as achieving highspeed operation, lower energy consumption, and increase in payload carrying capacity and find applications where manipulators are to be operated in large workspace like assembly of freeflying space structures, hazardous material management from safer distance, detection of flaws in large structure like airplane and submarines. However, designing a feedback control system for a flexible-link manipulator is challenging due the system being non-minimum phase, underactuated and non-collocated. Further difficulties are encountered when such manipulators handle unknown payloads. Overall deflection of the flexible manipulator are governed by the different vibrating modes (excited at different frequencies) present along the length of the link. Due to change in payload, the flexible modes (at higher frequencies) are excited giving rise to uncertainties in the dynamics of the FLM. To achieve effective tip trajectory tracking whilst quickly suppressing tip deflections when the FLM carries varying payloads adaptive control is necessary instead of fixed gain controller to cope up with the changing dynamics of the manipulator. Considerable research has been directed in the past to design adaptive controllers based on either linear identified model of a FLM or error signal driven intelligent supervised learning e.g. neural network, fuzzy logic and hybrid neuro-fuzzy. However, the dynamics of the FLM being nonlinear there is a scope of exploiting nonlinear modeling approach to design adaptive controllers. The objective of the thesis is to design advanced adaptive control strategies for a two-link flexible manipulator (TLFM) to control the tip trajectory tracking and its deflections while handling unknown payloads. To achieve tip trajectory control and simultaneously suppressing the tip deflection quickly when subjected to unknown payloads, first a direct adaptive control (DAC) is proposed. The proposed DAC uses a Lyapunov based nonlinear adaptive control scheme ensuring overall system stability for the control of TLFM. For the developed control laws, the stability proof of the closed-loop system is also presented. The design of this DAC involves choosing a control law with tunable TLFM parameters, and then an adaptation law is developed using the closed loop error dynamics. The performance of the developed controller is then compared with that of a fuzzy learning based adaptive controller (FLAC). The FLAC consists of three major components namely a fuzzy logic controller, a reference model and a learning mechanism. It utilizes a learning mechanism, which automatically adjusts the rule base of the fuzzy controller so that the closed loop performs according to the user defined reference model containing information of the desired behavior of the controlled system. Although the proposed DAC shows better performance compared to FLAC but it suffers from the complexity of formulating a multivariable regressor vector for the TLFM. Also, the adaptive mechanism for parameter updates of both the DAC and FLAC depend upon feedback error based supervised learning. Hence, a reinforcement learning (RL) technique is employed to derive an adaptive controller for the TLFM. The new reinforcement learning based adaptive control (RLAC) has an advantage that it attains optimal control adaptively in on-line. Also, the performance of the RLAC is compared with that of the DAC and FLAC. In the past, most of the indirect adaptive controls for a FLM are based on linear identified model. However, the considered TLFM dynamics is highly nonlinear. Hence, a nonlinear autoregressive moving average with exogenous input (NARMAX) model based new Self-Tuning Control (NMSTC) is proposed. The proposed adaptive controller uses a multivariable Proportional Integral Derivative (PID) self-tuning control strategy. The parameters of the PID are adapted online using a nonlinear autoregressive moving average with exogenous-input (NARMAX) model of the TLFM. Performance of the proposed NMSTC is compared with that of RLAC. The proposed NMSTC law suffers from over-parameterization of the controller. To overcome this a new nonlinear adaptive model predictive control using the NARMAX model of the TLFM (NMPC) developed next. For the proposed NMPC, the current control action is obtained by solving a finite horizon open loop optimal control problem on-line, at each sampling instant, using the future predicted model of the TLFM. NMPC is based on minimization of a set of predicted system errors based on available input-output data, with some constraints placed on the projected control signals resulting in an optimal control sequence. The performance of the proposed NMPC is also compared with that of the NMSTC. Performances of all the developed algorithms are assessed by numerical simulation in MATLAB/SIMULINK environment and also validated through experimental studies using a physical TLFM set-up available in Advanced Control and Robotics Research Laboratory, National Institute of Technology Rourkela. It is observed from the comparative assessment of the performances of the developed adaptive controllers that proposed NMPC exhibits superior 7performance in terms of accurate tip position tracking (steady state error ≈ 0.01°) while suppressing the tip deflections (maximum amplitude of the tip deflection ≈ 0.1 mm) when the manipulator handles variation in payload (increased payload of 0.3 kg). The adaptive control strategies proposed in this thesis can be applied to control of complex flexible space shuttle systems, long reach manipulators for hazardous waste management from safer distance and for damping of oscillations for similar vibration systems

Modeling and sliding-mode control of flexible-link robotic structures for vibration suppression

In many applications, the use of slender and light flexible structures has increased due to the requirement of more energetically efficient structures. This kind of structures is easily prone to vibrate due to external forces or due to forces generated in the inner structure during the movement. One objective of this work is to generate models of flexible-link structures: cantilever beam, one flexible-link robot and two flexible-link robot; which include rotational actuators, piezoelectric actuators, and different kinds of sensors (acceleration and deformation). The models are obtained under a classical mechanics approach of Lagrange Euler energy balance; the assumed mode method is used to approximate the flexibility of the elastic components. In the model formulation, new rotation angles are introduced in the distal joints and the joint inertia is separated according to this new kinematic consideration. Some parts of the resulting model involving integral terms are calculated using symbolic programming software; whereas other parts are implemented and calculated dynamically during simulation. The resulting models are programmed in Matlab/Simulink subjected to a novel verification methodology and then validated experimentally in a platform constructed for the implementation. The second objective is to develop, from simplified models of the flexible-link structures, robust controllers for joint tracking and active vibration suppression. Therefore, robust control is used with two basic purposes: to face the model uncertainties due to the discrepancies between the models and real systems and to suppress the vibration of the flexible-link structures. Three control strategies are proposed: Dual loop control approach, decentralized and centralized Lyapunov model-based sliding mode control approach. The values required for the implementation of the controller are obtained from the formulated models. The controllers were implemented in a dSPACE rapid prototyping control card and the experimental results show the effectiveness of the proposed control strategies in terms of joint tracking and vibration suppression.In viele Anwendungen, die Nutzung von schlanken und leichten Strukturen ist wegen Energieanforderungen gestiegen. Solche Strukturen sind anfällig für Schwingung wegen äußere Kräfte oder innere erzeugen Kräfte während der Bewegung. Ein Ziel dieser Arbeit handelt sich um die Erzeugung von verschiedener flexiblen-Glied Strukturen z.B. Kragarm, ein und zwei flexibel-Glied Roboter. Die Strukturen enthalten: rotatotische Aktoren, piezoelektrische Aktoren und verschiedene Sensoren (Beschleunigung und Dehnung). Die Modelle werden im Rahmen klassisches Ansatz von Lagrange Euler Energiebilanz entwickelt; die Angenommene Mode Methode (Assumed Mode Method) wird verwendet, um die Flexibilität der elastischen Komponenten zu approximieren. In der Modellformulierung werden neue Rotationswinkel in die distalen Gelenke eingeführt und die gemeinsame Trägheit gemäß dieser neuen kinematischen Betrachtung getrennt. Einige Elemente des resultierenden Modells integrale Begriffe beinhalten, werden mit symbolischen Programmiersoftware berechnet; während andere Teile umgesetzt und dynamisch aus der Simulation berechnet. Die resultierenden Modelle werden in Matlab/Simulink programmiert, sie werden unter eine neuartige Methodologie verifiziert unterworfen und dann validiert in experimentell in einem Prüfstand. Das zweite Ziel ist von vereinfachten Modellen robuste Controller für die Gelenkablaufverfolgung und aktive Schwingungsunterdrückung zu entwickeln. Daher ist eine robuste Regelung mit zwei grundlegende Zwecke verwendet: die Modellunsicherheiten zu berücksichtigen aufgrund der Unterschiede zwischen den Modellen und realen Systemen und die Schwingung der flexiblen Strukturen zu unterdrücken. Drei Kontrollstrategien werden vorgeschlagen: Dual Regel Ansatz, dezentrale und zentrale Lyapunov modellbasierten Sliding Mode Control Ansätze. Die erforderlichen Werte für die Ausführung der Steuerung sind aus den formulierten Modellen erhalten. Die Regler wurden in einer dSPACE Rapid-Prototyping-Steuerkarte implementiert. Die experimentellen Ergebnisse zeigen die Wirksamkeit der vorgeschlagenen Kontrollstrategien in Bezug auf die Gelenkablaufverfolgung und Schwingungsunterdrückung