Stability and Control of a Parametrically Excited Rotating System. Part I: Stability Analysis

This paper analyses the stability of a parametrically excited double pendulum rotating in the horizontal plane. The equations of motion for such a system contain time varying periodic coefficients. Floquet theory and the method of Hill's determinant are used to evaluate the stability of the linearized system. Stability charts are obtained for various sets of damping, parametric excitation, and rotation parameters. Several resonance conditions are found, and it is shown that the system stability can be significantly altered due to the rotation. Such systems can be used as preliminary models for studying the lag dynamics and control of helicopter blades and other gyroscopic systems.     

Multiple impacts of a planar kinematic chain with a granular matter

The theoretical model of a planar kinematic chain with multiple points impacting with a granular matter is studied. The force acting on the links penetrating the granular media is a linear superposition of a static (depth-dependent) resistance force and a dynamic (velocity-dependent) frictional force. A general algorithm for the m impacts for an n planar kinematic chain is presented. The complete solution of a two link chain with two impact points is simulated using different initial impact velocities and different impact geometries. We analyze how rapidly the ends of both links impacting a granular media slow upon collision. For most of the analyzed cases the tips of the kinematic chain under high impact force (higher initial velocity) come to rest faster in a granular matter than the same body under low impact force (lower initial velocity). There are also some exceptions to this rule.     

Electron Beam Technologies for Preparation of Polymeric Materials Used for Waste Water Treatment, Agriculture, and Medicine

Radiation research results in the field of polymeric materials, obtained in the last few years by electron beam irradiation of aqueous solutions containing appropriate monomer mixtures, such as acrylamide, acrylic acid and vinyl acetate, are presented. Two types of polymeric flocculants for waste water treatment and three kinds of hydrogels for agriculture and medicine are described. The effects of radiation absorbed dose, radiation absorbed dose rate, and chemical composition of the irradiated solutions upon the polymeric materials characteristics are discussed. The required absorbed dose levels to produce the polymeric flocculants are in the range of 0.3 to 9 kGy and 4 kGy to 12 kGy for hydrogels. Some experimental results obtained by testing polymeric flocculants with waste water from food industry are given. Polymeric material processing was developed on a pilot plant level with ALID-7 electron linear accelerator of 5.5 MeV and 0.7 kW, built in the Electron Accelerator Laboratory of the Institute of Atomic Physics, Bucharest. A new facility permitting the application of simultaneous electron beam and microwave irradiation is presently under investigation. Preliminary results demonstrated that some polymeric flocculant characteristics, such as linearity, were improved by simultaneous electron beam and microwave treatment. Also, the absorbed dose levels decreased and intrinsic viscosity increased, respectively, by about two times by this new material processing method.     

Analysis of a hand arm system

For this research a prototype for an anthropomorphic hand arm was developed and manufactured. We analyze the periodic motion of this artificial hand arm system for different angles and velocities. For the time series of the wrist joint of the artificial hand system we can conclude that the movement is periodic. For a better understanding of the robotic system next we study the motion of human hand arm. The kinematic data of the radio-carpal flexion–extension angles were analyzed for different initial conditions. The experimental data were acquired with a complex goniometer system. The human motion was characterized with the correlation dimension and the largest Lyapunov exponent (LLE) as nonlinear measures. The LLE obtained for each test of human hand were positive values and the mean value ranged from 0.020 to 0.032.     

Control of a Parametrically Excited Flexible Beam Undergoing Rotation and Impacts

The linear control of a parametrically excited impacting flexible link in rotational motion is considered. The equation of motion for such a system contains time-periodic coefficients. To suppress the vibrations resulting after impact with an external rigid body, a linear controller is designed via Lyapunov–Floquet transformation. In this approach, the equations of motion with time-periodic coefficients are transformed into a time-invariant form suitable for the application of standard time-invariant controller design techniques. The momentum balance method and an empirical coefficient of restitution is used to model the collision between the two bodies.     

Fuzzy Logic Control of Parametrically Excited Rotating Beam Using Inverse Model

In this article the control of an elastic link with parametrically excited base in rotational motion was considered. A decoupled controller and an inverse model was designed and employed to suppress the vibrations of the elastic beam. The inverse model has a transfer function like the reciprocal of the plant transfer function and becomes the actuator for the original model. The decoupling controller separates the global system in several independent components. A sliding mode strategy using fuzzy logic was developed to control the independent components. Simulations for damped and undamped system were provided.     

Elasto-plastic impact of a rotating link with a massive surface

This study presents the impact with friction of a rigid or a flexible body against a half-space, each with a small region of contact compliance where the compliance is obtained from the Jackson and Green theory. The model consists of a system of nonlinear differential equations which considers a nonlinear contact force as well as frictional effects at the contacting end, and allows one to predict the motion after the impact. The initial incidence angle, the initial impact velocity, and the contact radius of the link are found to influence the coefficient of restitution with friction. Analytical and experimental results were compared to establish the accuracy of the model.     

Stability and Control of a Parametrically Excited Rotating System. Part II: Controls

In Part-I of this paper, the stability of a parametrically excited rotating system was analyzed. In this part the design of a feedback controller and an observer for the same mechanical system is considered. First, the time periodic system equations are transformed to a time invariant form which is suitable for an application of the standard techniques of linear control theory. A full-state feedback controller is designed in the transformed domain using the pole placement technique. Next, a Luenberger observer is constructed for estimating the unmeasurable states. Robustness of the observer is tested under the assumption that white noise is present in the measured states. Simulations for several combination of excitation and rotation parameters are provided.     

Structural design of planar mechanisms with dyads

In this paper, the structural synthesis of planar mechanisms with one, two and three dyads is studied. First a new classification of dyads is introduced and then a new way of constructing mechanisms is explained. The scheme provides a consistent coding scheme for planar mechanisms. The advantage of the classification of a system lies in its simplicity. The solution of the whole system can then be obtained by composing partial solutions. This approach will eliminate the need of storing complete mechanism information in a large database.     

Combined Electron Beam and Microwave Treatment for Flue Gas Purification

The results of a research program concerning the application of the electron beam EB) irradiation, microwave MW) irradiation and simultaneous electron beam and microwave EB + MW) irradiation for removing nitrogen oxides NOX) and sulfur dioxide SO₂) in simulated Due gases are presented. Several microwave applicators and reaction chambers used for NO_X and SO₂ removal tests are also presented. The additional use of MW energy and EB energy or the use of MW energy only proved to be a promising method for removal of pollutants in view of the reduction of power consumption and flue gas treatment process cost. Experiments performed at lower temperature 65-70°C) of the gaseous mixture air, Argon up to 7%, H₂O up to 25%, CO₂ up to 10%, SO₂ up to 2000 ppm, NO_X up to 1000 ppm, NH₃ added in stoichiometric amounts) demonstrated a higher SO₂ removal efficiency with lower absorbed dose. Promising results are obtained especially for SO₂ removal efficiency: up to 80% for MW, 85% for EB irradiation and up to 90% for EB + MW irradiation. A considerable amount of SO₂ can be separated even without MW, EB or EB + MW irradiation due the spontaneous reaction with ammonia at gaseous mixture temperature below 70°C. The most important conclusion concerning MW irradiation is that efficiency of removal of pollutants strongly depends on microwave applicator structure type, residence time and MW power level.