On Averaging and Vibrational Control of Mechanical Systems With Multifrequency Inputs

Many interesting control are mechanical control systems. In spite of this, there has not been much effort to develop methods which use the special structure of mechanical to obtain analysis tools which are suitable for these systems. In this dissertation we take the first steps towards a methodical treatment of mechanical control systems. First we develop a framework for analysis of certain classes of mechanical control systems. In the Lagrangian formulation we study mechanical control systems whose Lagrangian is kinetic energy minus potential energy. We propose a new and useful definition of controllability for these and obtain a computable set of conditions for this new version of controllability. We also obtain decompositions of simple mechanical in the case when they are not controllable. In the Hamiltonian formulation we study whose control vector fields are Hamiltonian. We obtain decompositions which describe the controllable and uncontrollable dynamics. In each case, the dynamics are shown to be Hamiltonian in a suitably general sense. Next we develop intrinsic descriptions of Lagrangian and Hamiltonian mechanics in the presence of external inputs. This development is a first step towards a control theory for general Lagrangian and Hamiltonian control systems. Systems with constraints are also studied. We first give a thorough overview of variational methods including a comparison of the nonholonomic and vakonomic methods. We also give a generalised definition for a constraint and, with this more general definition, we are able to give some preliminary controllability results for constrained systems.

This paper describes nonlinear control of a two degree of freedom mechanical system which models a bird perched on a branch or cable. The primary contribution is the implementation, in a controlled laboratory experiment, of the recently developed C\ adaptive control approach. This technique, which allows fast adaptation with guaranteed stability margins, has been proposed for use in a variety of more sophisticated applications. Experimental results for this simple mechanical control system provide further motivation to pursue those applications. The system being considered is a variation of Spong's "Acrobot", a classic example of an underactuated mechanical control system. In addition to the C\ controller, a swing-up controller based on Spong's original work on collocated partial feedback linearization is implemented with switching logic.

This paper presents a study on the performance of adaptive control algorithms designed to reduce the vibration of mechanical systems excited by a harmonic disturbance. The mechanical system consists of a mass suspended on a spring and a damper. The system is equipped with a force actuator in parallel with the suspension. The control signal driving the actuator is generated by adjusting the amplitude and phase of a sinusoidal reference signal at the same frequency as the excitation. An adaptive feedforward control algorithm is used to adapt the amplitude and phase of the control signal, to minimise the mean square velocity of the mass. Two adaptation strategies are considered in which the control signal is either updated after each period of the oscillation or at every time sample. The first strategy is traditionally used in vibration control in helicopters for example; the second strategy is normally referred to as the filtered-x least mean square algorithm and is often used to control engine noise in cars. The two adaptation strategies are compared through a parametric study, which investigates the influence of the properties of both the mechanical system and the control system on the convergence speed of the two algorithms.

The superior performance of active vibration control systems largely depends on the four‐quadrant controllable execution capability in the available force‐velocity diagram of active actuators. Although semi‐active vibration control systems have the advantages of low energy consumption, simple structure, and high reliability, the system performance is not comparable to active control systems, due to the partial capability in only the first and third quadrants. On the basis of the comprehensive advantages of active and semi‐active actuators, to reform the design philosophy of semi‐active actuators to realize pseudo‐active actuators that have both mechanical properties of active actuators and energy consumption advantages of semi‐active actuators, that is, new semi‐active actuators with four‐quadrant controllable execution capability, will very likely cause a revolution in the related fields of mechanical design and system control. The basic design principle of pseudo‐active actuators that use semi‐active controllable actuators to achieve active actuator performance in the way of conceptual analysis is proposed. The proposed pseudo‐active actuators should consist of two half‐four‐quadrant actuators, that is, one is for the first and third quadrants and the other one for the second and fourth quadrants. This study employs two semi‐active controllable damping actuators and one mechanical compensation mechanism. One of the actuators provides the damping force in the first and third quadrants, and the other one combining with the mechanical compensation mechanism is for the second and fourth quadrants. A global mathematical model of the proposed actuator is established to describe the four different operational modes of the proposed actuator. It is proved that the two operational modes of the proposed actuator can realize active vibration control, and a case study of realizing active control is presented. The other two operational modes are compared with the conventional two‐degree‐of‐freedom model. More specifically, the application cases of the pseudo‐active operational mode of the proposed actuator in the quarter‐car/body‐powertrain suspension system are given, a pseudo‐active suspension named dual‐hook automobile suspension is presented. Furthermore, an equivalent expression of the electrical network is given for the mechanical network under different operational modes of the proposed actuator.

This paper presents how the temperature dependence of the friction phenomena can be handled in mechanical control systems using state estimation techniques. The method is based on the dynamic friction model, originally introduced by Batista and Carlson (Physical Rev. E; 1996, 1998), where the temperature dependence of friction is described by an un-measurable internal state. According to the author's knowledge this model was not applied before in mechanical control system analysis and design. For the model a state estimator was developed based on the theory of hybrid systems. A robust tracking control algorithm was also developed for mechanical systems with temperature dependent friction. Simulation measurements are provided in the second part of the paper to show the applicability of the theoretical results.

Dynamic vibration absorbers are efficient devices used in vibration and noise control of several mechanical systems. In recent years, some studies about these control devices comprising systems with nonlinear characteristics have emerged. In those cases, either the primary system or the dynamic absorber, or even both, can be nonlinear in terms of their stiffness. On the other hand, the absorber damping is generally modeled as viscous. The viscous damping model is widely used in numerical simulations but is very difficult to achieve in real situations. An alternative is the use of viscoelastic damping models, which brings flexibility for vibration control actions. In this work, a methodology to optimally design a viscoelastic dynamic vibration absorber when attached to a nonlinear single-degree-of-freedom system will be presented. The mathematical formulation of the problem is based on the generalized equivalent parameters concept along with the harmonic balance method. The cubic nonlinearity is considered in the primary system and the viscoelastic material is represented by the four-parameter fractional derivative model. Numerical simulations to find the optimal parameters of the absorber are performed for three different types of viscoelastic materials using nonlinear optimization techniques. For some conditions, the results show that the viscoelastic absorber "linearizes" the compound system when this device is properly designed and attached to it. This is mainly due to the reaction forces introduced by the absorber and the large dissipation of vibratory energy introduced by the viscoelastic material. A study of the stability of the compound system reveals that, for most of the time, the periodic solution remains stable for the whole frequency range of concern.

Tracking the path of development in different Engineering disciplines, it can be easily observed that, right from the primitive stage, several tools, devices, and techniques may be identified, which happened by virtue of the evolution of human intelligence, getting transformed into various engineering applications. Although, later different engineering disciplines evolved, where most of the exhaustive development could be undertaken in that discipline. Likewise, in the field of mechanical engineering to various types of mechanical systems, according to the requirement in that field, were developed, in order to provide support of mechanization. Prime movers used to be an important part of these mechanical systems, which provided energy input as well as actuation required for providing the machines the desired kinematics. Most of the mechanical systems developed has been operated by conventional engine system using one or other fuel. Apart from the actuation by mechanical means, there are other means also through which mechanical actuation with better control, flexibility, and manipulation may be utilized in mechanical systems. A different category of systems, called Mechatronic systems has been developed in the recent past, which involves the vivid scope of use of techniques, devices, and components generally used in various other engineering fields of electrical, electronics, hydraulics, and pneumatics, etc. Subsequently, there have been several inventions, design & development which have added new levels in every field. Mechanical systems have been generally composed of various mechanical elements, which are designed to follow certain kinematics. The performance of the Actuation system plays an important role in the overall performance of the mechanical systems. There are several alternative actuation systems, which are not mechanical. These actuation systems may be categorized into electrical, electronics, hydraulic and pneumatic types. The features of these actuation systems, are so peculiar, that typical kinematic movement may be manipulated that too with more precision. Better control of mechanical systems may be realized, which is otherwise difficult with mechanical systems. In this paper, an effort has been made to review the possibilities, prospects as well as scope with various actuation systems.

Recently, the necessity of lighting and high-speed for the machines is increasing. This paper concerns the vibration and motion control by the the control system which combined a servo controller with a hybrid dynamic absorber. In our method, the vibration control and the servo control are designed independently. Firstly, the dynamics of the tower structure and the servo motor are modeled. It is shown experimentally that although vibration control by the servo controller alone causes the instability due to nonlinear elements such as the friction or the rattle, the hybrid dynamic absorber is hard to cause this sort of the instability. On the comparison of the vibration control effect and the control force, the hybrid dynamic absorber needs the less force. Finally, to know its effect we evaluated the motion (triangle wave, sine wave) of the flexible structure. Effectiveness of this vibration and motion control method to the flexible structure is demonstrated by simulation and experiment.

Leighton Chajnantor Telescope (LCT) will be moved from the summit of Maunakea, Hawaii to Chajnantor Plateau, Chile and be refurbished there. Strong wind disturbance at the new site will bring great challenges to the servo control of LCT. It is necessary and important to develop a simulation platform that behaves as close as possible to the real telescope for testing the performance of the designed servo controller. In this paper, a collaborative simulation platform of LCT based on Adams and Matlab/Simulink is constructed. On this platform, the mechanical structure model of LCT can be integrated with its control system model such that a collaborative simulation of the mechanical structure and the control system of LCT can be conducted. The mechanical structure model of LCT, which contains both rigid body models (i.e., the mount) and flexible body models (i.e., the primary reflector), is developed by using Adams. The servo system model and the wind disturbance model are constructed by using Matlab/Simulink. By conducting collaborative simulation, the performances of the servo controller based on the rigid body model and the rigid-flexible coupling model of LCT are compared. The comparison shows that the controller designed based on the rigid body model does not perform well when it is employed to control the rigid-flexible coupling model of LCT. However, by readjusting parameters of the servo controller, its performance can be further improved when applied to the rigid-flexible coupling model. Therefore, an LCT model of integrated mechanical structure and control systems is very helpful for analyzing its performance more accurately and designing a better servo controller.

Within the affine connection framework of Lagrangian control systems, based on the results of Sussmann on small-time locally controllability of single-input affine nonlinear control systems, the controllability results for mechanical control systems with single-input are extended to the case of the systems with isotropic damping, where the Lagrangian is the kinetic energy associated with a Riemannian metric. A sufficient condition of negative small-time locally controllability for the system is obtained. Then,it is demonstrated that such systems are smalt-time locally configuration controllable if and only if the dimension of the configuration manifold is one. Finally, two examples are given to illustrate the results. Lie bracketting of vector fields and the symmetric product show the advantages in the discussion.

A major goal in the control of complex mechanical systems such as advanced aircraft, spacecraft, and power plants is to achieve high performance with increased reliability, availability, component durability, and maintainability. The current state-of-the-art of control systems synthesis focuses on improving performance and diagnostic capabilities under constraints that often do not adequately represent the dynamic properties of the materials. The reason is that the traditional design is based upon the assumption of conventional materials with invariant characteristics. In view of high performance requirements and availability of improved materials, the lack of appropriate knowledge about the properties of these materials will lead to either less than achievable performance due to overly conservative design, or over-straining of the structure leading to unexpected failures and drastic reduction of the service life. The key idea of the research reported in this paper is that a significant improvement in service life can be achieved by a small reduction in the system dynamic performance. This requires augmentation of the current system-theoretic techniques for synthesis of decision and control laws with governing equations and inequality constraints that would model the properties of the materials for the purpose of damage representation and failure prognosis. The major challenge in this research is to characterize the damage generation process in a continuous-time setting, and then utilize this information for synthesizing algorithms of robust control, diagnostics, and risk assessment in complex mechanical systems. Damage mitigation for control of mechanical systems is reported in the two-part paper. The concept of damage mitigation is introduced and a continuous-time model of fatigue damage dynamics is formulated in this paper which is the first part. The second part which is a companion paper presents the synthesis of the open-loop control policy and the results of simulation experiments for transient operations of a reusable rocket engine.

Traditionally, robot control has been done typically by “highly precise control algorithms”: their joint angle trajectories are accurately determined at any time with vast amount of computation. This, however, causes serious problems, particularly in terms of adaptability and energy efficiency. On the other hand, an extreme approach has been gaining a lot of attention recently. A good instantiation is the passive dynamic walker, driven only by exploiting the intrinsic dynamics of its mechanical system. However, mechanical system is not everything as well as control system is not everything: “well-balanced” coupling between control and mechanical systems should be considered. In addition, the “meeting point” between the two systems should be varied according to the environment encountered. In light of these facts, this study particularly focuses on the stiffness of robots’ joints, since this strongly contributes to tuning the dominance relationship between control and mechanical systems. More specifically, the aim of this study is to develop a “Real-time tunable spring” that can smoothly change its elasticity without changing its natural length, allowing robot’s joints to change their position and stiffness independently.

Traditionally, robot control has been done typically by "highly precise control algorithms": the position of each movable body part is accurately determined at any time with vast amount of computation. This, however, causes serious problems, particularly in terms of adaptability and energy efficiency. On the other hand, an extreme approach has been gaining a lot of attention recently. A good instantiation is the passive dynamic walker, driven only by exploiting the intrinsic dynamics of its mechanical system. However, the mechanical system is not everything, just as the control system is not everything; "well-balanced" coupling between control and mechanical systems should be considered. In addition, the "meeting point" between the two systems should be flexibly varied according to the environment encountered. In light of these facts, this study intensively focuses on the stiffness of robots' joints, since this effectively influences the dominance relationship between control and mechanical systems. More specifically, the aim of this study is to develop a "real-time tunable spring" that can smoothly change its elasticity without changing its natural length, allowing robot's joints to change their position and stiffness independently

The performance of a damping-controllable dynamic damper was investigated with an adaptive neural net control system. The damping controllability of the dynamic damper was accomplished by introducing the Electro-Rheological (ER) fluid, which is known as one of the highly functional materials and whose apparent viscosity can be varied in accordance with applied electric field strength in a wide range as well as in a short time. As a control system for the present dynamic damper, an adaptive neural net control system was developed ; it was composed of a forward model network and a controller network. With the proposed neural net control system, the damping-controllable dynamic damper can be tuned by itself even if response of a structure shows nonlinearity to input disturbances or varies its own dynamic characteristic. Moreover, the vibration amplitude corresponding to several natural frequencies can be reduced with only a single dynamic damper. Numerical and experimental investigations were performed, and the results shows the superiority of the present adaptive vibration control system.

The control and mechanical systems of an embodied agent should be tightly coupled so as to emerge useful functionalities such as adaptivity. This indicates that the mechanical system as well as the control system should be responsible for a certain amount of computation for generating the behavior. However, there still leaves much to be understood about how such “computational offloading” from the control system to the mechanical system can be achieved. In order to intensively investigate this, here we particularly focus on the “softness” of the body, and show how the computational offloading derived from this property is exploited to simplify the control system and to increase the degree of adaptivity. To this end, we employ a two-dimensional amoeboid robot as a practical example, consisting of incompressive fluid (i.e. protoplasm) covered with an outer skin composed of a network of real-time tunable springs. Preliminary simulation results show that the exploitation of the “long-distant interaction” stemming from “the law of conservation of protoplasmic mass” allows us to simplify the control mechanism; and that adaptive amoeboid locomotion can be realized without the need of a central controller. The results obtained are expected to shed light on how control and mechanical systems should be coupled, and what the “brain-body-interaction” carefully designed brings to the resulting behavior.