Dynamic analysis of belt-drives using the absolute nodal coordinate formulation

Belt-drive systems have been and still are the most commonly used power transmission form in various applications of different scale and use. The peculiar features of the dynamics of the belt-drives include highly nonlinear deformation,large rigid body motion, a dynamical contact through a dry friction interface between the belt and pulleys with sticking and slipping zones, cyclic tension of the belt during the operation and creeping of the belt against the pulleys. The life of the belt-drive is critically related on these features, and therefore, amodel which can be used to study the correlations between the initial values and the responses of the belt-drives is a valuable source of information for the development process of the belt-drives. Traditionally, the finite element models of the belt-drives consist of a large number of elements thatmay lead to computational inefficiency. In this research, the beneficial features of the absolute nodal coordinate formulation are utilized in the modeling of the belt-drives in order to fulfill the following requirements for the successful and efficient analysis of the belt-drive systems: the exact modeling of the rigid body inertia during an arbitrary rigid body motion, the consideration of theeffect of the shear deformation, the exact description of the highly nonlinear deformations and a simple and realistic description of the contact. The use of distributed contact forces and high order beam and plate elements based on the absolute nodal coordinate formulation are applied to the modeling of the belt-drives in two- and three-dimensional cases. According to the numerical results, a realistic behavior of the belt-drives can be obtained with a significantly smaller number of elements and degrees of freedom in comparison to the previously published finite element models of belt-drives. The results of theexamples demonstrate the functionality and suitability of the absolute nodal coordinate formulation for the computationally efficient and realistic modeling ofbelt-drives. This study also introduces an approach to avoid the problems related to the use of the continuum mechanics approach in the definition of elastic forces on the absolute nodal coordinate formulation. This approach is applied to a new computationally efficient two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation. The proposed beam element uses a linear displacement field neglecting higher-order terms and a reduced number of nodal coordinates, which leads to fewer degrees of freedom in a finite element.

Dynamic Analysis Model of Spherical Roller Bearings with Defects

Rolling element bearings are essential components of rotating machinery. The spherical roller bearing (SRB) is one variant seeing increasing use, because it is self-aligning and can support high loads. It is becoming increasingly important to understand how the SRB responds dynamically under a variety of conditions. This doctoral dissertation introduces a computationally efficient, three-degree-of-freedom, SRB model that was developed to predict the transient dynamic behaviors of a rotor-SRB system. In the model, bearing forces and deflections were calculated as a function of contact deformation and bearing geometry parameters according to nonlinear Hertzian contact theory. The results reveal how some of the more important parameters; such as diametral clearance, the number of rollers, and osculation number; influence ultimate bearing performance. Distributed defects, such as the waviness of the inner and outer ring, and localized defects, such as inner and outer ring defects, are taken into consideration in the proposed model. Simulation results were verified with results obtained by applying the formula for the spherical roller bearing radial deflection and the commercial bearing analysis software. Following model verification, a numerical simulation was carried out successfully for a full rotor-bearing system to demonstrate the application of this newly developed SRB model in a typical real world analysis. Accuracy of the model was verified by comparing measured to predicted behaviors for equivalent systems.

The Dynamic Analysis of a Human Skeleton Using the Flexile Multibody Simulation Approach

The human motion study, which relies on mathematical and computational models ingeneral, and multibody dynamic biomechanical models in particular, has become asubject of many recent researches. The human body model can be applied to different physical exercises and many important results such as muscle forces, which are difficult to be measured through practical experiments, can be obtained easily. In the work, human skeletal lower limb model consisting of three bodies in build using the flexible multibody dynamics simulation approach. The floating frame of reference formulation is used to account for the flexibility in the bones of the human lower limb model. The main reason of considering the flexibility inthe human bones is to measure the strains in the bone result from different physical exercises. It has been perceived the bone under strain will become stronger in order to cope with the exercise. On the other hand, the bone strength is considered and important factors in reducing the bone fractures. The simulation approach and model developed in this work are used to measure the bone strain results from applying raising the sole of the foot exercise. The simulation results are compared to the results available in literature. The comparison shows goof agreement. This study sheds the light on the importance of using the flexible multibody dynamic simulation approach to build human biomechanical models, which can be used in developing some exercises to achieve the optimalbone strength.

Flexible Multibody Simulation Approach in the Dynamic Analysis of Bone Strains Activity

The objective of this study is to show that bone strains due to dynamic mechanical loading during physical activity can be analysed using the flexible multibody simulation approach. Strains within the bone tissue play a major role in bone (re)modeling. Based on previous studies, it has been shown that dynamic loading seems to be more important for bone (re)modeling than static loading. The finite element method has been used previously to assess bone strains. However, the finite element method may be limited to static analysis of bone strains due to the expensive computation required for dynamic analysis, especially for a biomechanical system consisting of several bodies. Further, in vivo implementation of strain gauges on the surfaces of bone has been used previously in order to quantify the mechanical loading environment of the skeleton. However, in vivo strain measurement requires invasive methodology, which is challenging and limited to certain regions of superficial bones only, such as the anterior surface of the tibia. In this study, an alternative numerical approach to analyzing in vivo strains, based on the flexible multibody simulation approach, is proposed. In order to investigate the reliability of the proposed approach, three 3-dimensional musculoskeletal models where the right tibia is assumed to be flexible, are used as demonstration examples. The models are employed in a forward dynamics simulation in order to predict the tibial strains during walking on a level exercise. The flexible tibial model is developed using the actual geometry of the subject’s tibia, which is obtained from 3 dimensional reconstruction of Magnetic Resonance Images. Inverse dynamics simulation based on motion capture data obtained from walking at a constant velocity is used to calculate the desired contraction trajectory for each muscle. In the forward dynamics simulation, a proportional derivative servo controller is used to calculate each muscle force required to reproduce the motion, based on the desired muscle contraction trajectory obtained from the inverse dynamics simulation. Experimental measurements are used to verify the models and check the accuracy of the models in replicating the realistic mechanical loading environment measured from the walking test. The predicted strain results by the models show consistency with literature-based in vivo strain measurements. In conclusion, the non-invasive flexible multibody simulation approach may be used as a surrogate for experimental bone strain measurement, and thus be of use in detailed strain estimation of bones in different applications. Consequently, the information obtained from the present approach might be useful in clinical applications, including optimizing implant design and devising exercises to prevent bone fragility, accelerate fracture healing and reduce osteoporotic bone loss.

Dimensioning DC-voltage capacitor for a DC-distribution system and dynamic analysis

Technical analysis of Low Voltage Direct Current (LVDC) distribution systems shows that in LVDC transmission the customer voltage quality is higher. One of the problems in LVDC distribution networks that converters both ends of the DC line are required. Because of the converters produce not pure DC voltage, but some fluctuations as well, the huge electrolytic capacitors are required to reduce voltage distortions in the DC-side. This thesis master’s thesis is focused on calculating required DC-link capacitance for LVDC transmission and estimation of the influence of different parameters on the voltage quality. The goal is to investigate the methods of the DC-link capacitance estimation and location in the transmission line.

Simulation of structural stress history based on dynamic analysis

Modern machine structures are often fabricated by welding. From a fatigue point of view, the structural details and especially, the welded details are the most prone to fatigue damage and failure. Design against fatigue requires information on the fatigue resistance of a structure’s critical details and the stress loads that act on each detail. Even though, dynamic simulation of flexible bodies is already current method for analyzing structures, obtaining the stress history of a structural detail during dynamic simulation is a challenging task; especially when the detail has a complex geometry. In particular, analyzing the stress history of every structural detail within a single finite element model can be overwhelming since the amount of nodal degrees of freedom needed in the model may require an impractical amount of computational effort. The purpose of computer simulation is to reduce amount of prototypes and speed up the product development process. Also, to take operator influence into account, real time models, i.e. simplified and computationally efficient models are required. This in turn, requires stress computation to be efficient if it will be performed during dynamic simulation. The research looks back at the theoretical background of multibody dynamic simulation and finite element method to find suitable parts to form a new approach for efficient stress calculation. This study proposes that, the problem of stress calculation during dynamic simulation can be greatly simplified by using a combination of floating frame of reference formulation with modal superposition and a sub-modeling approach. In practice, the proposed approach can be used to efficiently generate the relevant fatigue assessment stress history for a structural detail during or after dynamic simulation. In this work numerical examples are presented to demonstrate the proposed approach in practice. The results show that approach is applicable and can be used as proposed.

Efficient Optimization Algorithms for Nonlinear Data Analysis

Identification of low-dimensional structures and main sources of variation from multivariate data are fundamental tasks in data analysis. Many methods aimed at these tasks involve solution of an optimization problem. Thus, the objective of this thesis is to develop computationally efficient and theoretically justified methods for solving such problems. Most of the thesis is based on a statistical model, where ridges of the density estimated from the data are considered as relevant features. Finding ridges, that are generalized maxima, necessitates development of advanced optimization methods. An efficient and convergent trust region Newton method for projecting a point onto a ridge of the underlying density is developed for this purpose. The method is utilized in a differential equation-based approach for tracing ridges and computing projection coordinates along them. The density estimation is done nonparametrically by using Gaussian kernels. This allows application of ridge-based methods with only mild assumptions on the underlying structure of the data. The statistical model and the ridge finding methods are adapted to two different applications. The first one is extraction of curvilinear structures from noisy data mixed with background clutter. The second one is a novel nonlinear generalization of principal component analysis (PCA) and its extension to time series data. The methods have a wide range of potential applications, where most of the earlier approaches are inadequate. Examples include identification of faults from seismic data and identification of filaments from cosmological data. Applicability of the nonlinear PCA to climate analysis and reconstruction of periodic patterns from noisy time series data are also demonstrated. Other contributions of the thesis include development of an efficient semidefinite optimization method for embedding graphs into the Euclidean space. The method produces structure-preserving embeddings that maximize interpoint distances. It is primarily developed for dimensionality reduction, but has also potential applications in graph theory and various areas of physics, chemistry and engineering. Asymptotic behaviour of ridges and maxima of Gaussian kernel densities is also investigated when the kernel bandwidth approaches infinity. The results are applied to the nonlinear PCA and to finding significant maxima of such densities, which is a typical problem in visual object tracking.

Dynamic Simulations of Rotors during Drop on Retainer Bearings

The active magnetic bearings have recently been intensively developed because of noncontact support having several advantages compared to conventional bearings. Due to improved materials, strategies of control, and electrical components, the performance and reliability of the active magnetic bearings are improving. However, additional bearings, retainer bearings, still have a vital role in the applications of the active magnetic bearings. The most crucial moment when the retainer bearings are needed is when the rotor drops from the active magnetic bearings on the retainer bearings due to component or power failure. Without appropriate knowledge of the retainer bearings, there is a chance that an active magnetic bearing supported rotor system will be fatal in a drop-down situation. This study introduces a detailed simulation model of a rotor system in order to describe a rotor drop-down situation on the retainer bearings. The introduced simulation model couples a finite element model with component mode synthesis and detailed bearing models. In this study, electrical components and electromechanical forces are not in the focus. The research looks at the theoretical background of the finite element method with component mode synthesis that can be used in the dynamic analysis of flexible rotors. The retainer bearings are described by using two ball bearing models, which include damping and stiffness properties, oil film, inertia of rolling elements and friction between races and rolling elements. Thefirst bearing model assumes that the cage of the bearing is ideal and that the cage holds the balls in their predefined positions precisely. The second bearing model is an extension of the first model and describes the behavior of the cageless bearing. In the bearing model, each ball is described by using two degrees of freedom. The models introduced in this study are verified with a corresponding actual structure. By using verified bearing models, the effects of the parameters of the rotor system onits dynamics during emergency stops are examined. As shown in this study, the misalignment of the retainer bearings has a significant influence on the behavior of the rotor system in a drop-down situation. In this study, a stability map of the rotor system as a function of rotational speed of the rotor and the misalignment of the retainer bearings is presented. In addition, the effects of parameters of the simulation procedure and the rotor system on the dynamics of system are studied.

Flexible multibody dynamics and intelligent control of a hydraulically driven hybrid redundant robot machine

The assembly and maintenance of the International Thermonuclear Experimental Reactor (ITER) vacuum vessel (VV) is highly challenging since the tasks performed by the robot involve welding, material handling, and machine cutting from inside the VV. The VV is made of stainless steel, which has poor machinability and tends to work harden very rapidly, and all the machining operations need to be carried out from inside of the ITER VV. A general industrial robot cannot be used due to its poor stiffness in the heavy duty machining process, and this will cause many problems, such as poor surface quality, tool damage, low accuracy. Therefore, one of the most suitable options should be a light weight mobile robot which is able to move around inside of the VV and perform different machining tasks by replacing different cutting tools. Reducing the mass of the robot manipulators offers many advantages: reduced material costs, reduced power consumption, the possibility of using smaller actuators, and a higher payload-to-robot weight ratio. Offsetting these advantages, the lighter weight robot is more flexible, which makes it more difficult to control. To achieve good machining surface quality, the tracking of the end effector must be accurate, and an accurate model for a more flexible robot must be constructed. This thesis studies the dynamics and control of a 10 degree-of-freedom (DOF) redundant hybrid robot (4-DOF serial mechanism and 6-DOF 6-UPS hexapod parallel mechanisms) hydraulically driven with flexible rods under the influence of machining forces. Firstly, the flexibility of the bodies is described using the floating frame of reference method (FFRF). A finite element model (FEM) provided the Craig-Bampton (CB) modes needed for the FFRF. A dynamic model of the system of six closed loop mechanisms was assembled using the constrained Lagrange equations and the Lagrange multiplier method. Subsequently, the reaction forces between the parallel and serial parts were used to study the dynamics of the serial robot. A PID control based on position predictions was implemented independently to control the hydraulic cylinders of the robot. Secondly, in machining, to achieve greater end effector trajectory tracking accuracy for surface quality, a robust control of the actuators for the flexible link has to be deduced. This thesis investigates the intelligent control of a hydraulically driven parallel robot part based on the dynamic model and two schemes of intelligent control for a hydraulically driven parallel mechanism based on the dynamic model: (1) a fuzzy-PID self-tuning controller composed of the conventional PID control and with fuzzy logic, and (2) adaptive neuro-fuzzy inference system-PID (ANFIS-PID) self-tuning of the gains of the PID controller, which are implemented independently to control each hydraulic cylinder of the parallel mechanism based on rod length predictions. The serial component of the hybrid robot can be analyzed using the equilibrium of reaction forces at the universal joint connections of the hexa-element. To achieve precise positional control of the end effector for maximum precision machining, the hydraulic cylinder should be controlled to hold the hexa-element. Thirdly, a finite element approach of multibody systems using the Special Euclidean group SE(3) framework is presented for a parallel mechanism with flexible piston rods under the influence of machining forces. The flexibility of the bodies is described using the nonlinear interpolation method with an exponential map. The equations of motion take the form of a differential algebraic equation on a Lie group, which is solved using a Lie group time integration scheme. The method relies on the local description of motions, so that it provides a singularity-free formulation, and no parameterization of the nodal variables needs to be introduced. The flexible slider constraint is formulated using a Lie group and used for modeling a flexible rod sliding inside a cylinder. The dynamic model of the system of six closed loop mechanisms was assembled using Hamilton’s principle and the Lagrange multiplier method. A linearized hydraulic control system based on rod length predictions was implemented independently to control the hydraulic cylinders. Consequently, the results of the simulations demonstrating the behavior of the robot machine are presented for each case study. In conclusion, this thesis studies the dynamic analysis of a special hybrid (serialparallel) robot for the above-mentioned special task involving the ITER and investigates different control algorithms that can significantly improve machining performance. These analyses and results provide valuable insight into the design and control of the parallel robot with flexible rods.

Studies of rotor dynamics using a multibody simulation approach

The non-idealities in a rotor-bearing system may cause undesirable subcritical superharmonic resonances that occur when the rotating speed of the rotor is a fraction of the natural frequency of the system. These resonances arise partly from the non-idealities of the bearings. This study introduces a novel simulation approach that can be used to study the superharmonic vibrations of rotor-bearing systems. The superharmonic vibrations of complex rotor-bearing systems can be studied in an accurate manner by combining a detailed rotor and bearing model in a multibody simulation approach. The research looks at the theoretical background of multibody formulations that can be used in the dynamic analysis of flexible rotors. The multibody formulations currently in use are suitable for linear deformation analysis only. However, nonlinear formulation may arise in high-speed rotor dynamics applications due to the cenrrifugal stiffening effect. For this reason, finite element formulations that can describe nonlinear deformation are also introduced in this work. The description of the elastic forces in the absolute nodal coordinate formulation is studied and improved. A ball bearing model that includes localized and distributed defects is developed in this study. This bearing model could be used in rotor dynamics or multibody code as an interface elements between the rotor and the supporting structure. The model includes descriptions of the nonlinear Hertzian contact deformation and the elastohydrodynamic fluid film. The simulation approaches and models developed here are applied in the analysis of two example rotor-bearing systems. The first example is an electric motor supported by two ball bearings and the second is a roller test rig that consists of the tube roll of a paper machine supported by a hard-bearing-type balanceing machine. The simulation results are compared to the results available in literature as well as to those obtained by measuring the existing structure. In both practical examples, the comparison shows that the simulation model is capable of predicting the realistic responses of a rotor system. The simulation approaches developed in this work can be used in the analysis of the superharmonic vibrations of general rotor-bearing systems.

Blender- ja Bullet-ohjelmiston soveltuvuus robotiikan simulointiin.

Työssä tutkittiin Blender- ja Bullet-ohjelmiston soveltuvuutta robotin dynamiikan analysointiin. Ohjelmistot ovat avoimia ohjelmistoja joten niiden käyttö oli maksutonta. Robotin osat mallinnettiin Blender-ohjelmistolla ja koottiin kokoonpanoksi asettamalla nivelet kappaleiden väleille. Kokoonpanon tiedot siirrettiin Bullet-ohjelmistoon COLLADA-tiedoston välityksellä. Bullet-ohjelmistossa robotin dynaaminen käyttäytyminen laskettiin matemaattisesti tietokoneen avulla.

Chassis frame design of a mobile platform equipped with robotic arms

The overall objective of the thesis is to design a robot chassis frame which is a bearing structure of a vehicle supporting all mechanical components and providing structure and stability. Various techniques and scientific principles were used to design a chassis frame.Design principles were applied throughout the process. By using Solid-Works software,virtual models was made for chassis frame. Chassis frame of overall dimension 1597* 800*950 mm3 was designed. Center of mass lieson 1/3 of the length from front wheel at height 338mm in the symmetry plane. Overall weight of the chassis frame is 80.12kg. Manufacturing drawing is also provided. Additionally,structural analysis was done in FEMAP which gives the busting result for chassis design by taking into consideration stress and deflection on different kind of loading resembling real life case. On the basis of simulated result, selected material was verified. Resulting design is expected to perform its intended function without failure. As a suggestion for further research, additional fatigue analysis and proper dynamic analysis can be conducted to make the study more robust.

Multibody models for examination of touchdown bearing systems

Increased rotational speed brings many advantages to an electric motor. One of the benefits is that when the desired power is generated at increased rotational speed, the torque demanded from the rotor decreases linearly, and as a consequence, a motor of smaller size can be used. Using a rotor with high rotational speed in a system with mechanical bearings can, however, create undesirable vibrations, and therefore active magnetic bearings (AMBs) are often considered a good option for the main bearings, as the rotor then has no mechanical contact with other parts of the system but levitates on the magnetic forces. On the other hand, such systems can experience overloading or a sudden shutdown of the electrical system, whereupon the magnetic field becomes extinct, and as a result of rotor delevitation, mechanical contact occurs. To manage such nonstandard operations, AMB-systems require mechanical touchdown bearings with an oversized bore diameter. The need for touchdown bearings seems to be one of the barriers preventing greater adoption of AMB technology, because in the event of an uncontrolled touchdown, failure may occur, for example, in the bearing’s cage or balls, or in the rotor. This dissertation consists of two parts: First, touchdown bearing misalignment in the contact event is studied. It is found that misalignment increases the likelihood of a potentially damaging whirling motion of the rotor. A model for analysis of the stresses occurring in the rotor is proposed. In the studies of misalignment and stresses, a flexible rotor using a finite element approach is applied. Simplified models of cageless and caged bearings are used for the description of touchdown bearings. The results indicate that an increase in misalignment can have a direct influence on the bending and shear stresses occurring in the rotor during the contact event. Thus, it was concluded that analysis of stresses arising in the contact event is essential to guarantee appropriate system dimensioning for possible contact events with misaligned touchdown bearings. One of the conclusions drawn from the first part of the study is that knowledge of the forces affecting the balls and cage of the touchdown bearings can enable a more reliable estimation of the service life of the bearing. Therefore, the second part of the dissertation investigates the forces occurring in the cage and balls of touchdown bearings and introduces two detailed models of touchdown bearings in which all bearing parts are modelled as independent bodies. Two multibody-based two-dimensional models of touchdown bearings are introduced for dynamic analysis of the contact event. All parts of the bearings are modelled with geometrical surfaces, and the bodies interact with each other through elastic contact forces. To assist in identification of the forces affecting the balls and cage in the contact event, the first model describes a touchdown bearing without a cage, and the second model describes a touchdown bearing with a cage. The introduced models are compared with the simplified models used in the first part of the dissertation through parametric study. Damages to the rotor, cage and balls are some of the main reasons for failures of AMB-systems. The stresses in the rotor in the contact event are defined in this work. Furthermore, the forces affecting key bodies of the bearings, cage and balls can be studied using the models of touchdown bearings introduced in this dissertation. Knowledge obtained from the introduced models is valuable since it can enable an optimum structure for a rotor and touchdown bearings to be designed.

Direct torque control of permanent magnet synchronous machines - analysis and implementation

Thedirect torque control (DTC) has become an accepted vector control method besidethe current vector control. The DTC was first applied to asynchronous machines,and has later been applied also to synchronous machines. This thesis analyses the application of the DTC to permanent magnet synchronous machines (PMSM). In order to take the full advantage of the DTC, the PMSM has to be properly dimensioned. Therefore the effect of the motor parameters is analysed taking the control principle into account. Based on the analysis, a parameter selection procedure is presented. The analysis and the selection procedure utilize nonlinear optimization methods. The key element of a direct torque controlled drive is the estimation of the stator flux linkage. Different estimation methods - a combination of current and voltage models and improved integration methods - are analysed. The effect of an incorrect measured rotor angle in the current model is analysed andan error detection and compensation method is presented. The dynamic performance of an earlier presented sensorless flux estimation method is made better by improving the dynamic performance of the low-pass filter used and by adapting the correction of the flux linkage to torque changes. A method for the estimation ofthe initial angle of the rotor is presented. The method is based on measuring the inductance of the machine in several directions and fitting the measurements into a model. The model is nonlinear with respect to the rotor angle and therefore a nonlinear least squares optimization method is needed in the procedure. A commonly used current vector control scheme is the minimum current control. In the DTC the stator flux linkage reference is usually kept constant. Achieving the minimum current requires the control of the reference. An on-line method to perform the minimization of the current by controlling the stator flux linkage reference is presented. Also, the control of the reference above the base speed is considered. A new estimation flux linkage is introduced for the estimation of the parameters of the machine model. In order to utilize the flux linkage estimates in off-line parameter estimation, the integration methods are improved. An adaptive correction is used in the same way as in the estimation of the controller stator flux linkage. The presented parameter estimation methods are then used in aself-commissioning scheme. The proposed methods are tested with a laboratory drive, which consists of a commercial inverter hardware with a modified software and several prototype PMSMs.

On the Analysis and Control of a Linear Synchronous Servomotor with a Flexible Load

Industry's growing need for higher productivity is placing new demands on mechanisms connected with electrical motors, because these can easily lead to vibration problems due to fast dynamics. Furthermore, the nonlinear effects caused by a motor frequently reduce servo stability, which diminishes the controller's ability to predict and maintain speed. Hence, the flexibility of a mechanism and its control has become an important area of research. The basic approach in control system engineering is to assume that the mechanism connected to a motor is rigid, so that vibrations in the tool mechanism, reel, gripper or any apparatus connected to the motor are not taken into account. This might reduce the ability of the machine system to carry out its assignment and shorten the lifetime of the equipment. Nonetheless, it is usually more important to know how the mechanism, or in other words the load on the motor, behaves. A nonlinear load control method for a permanent magnet linear synchronous motor is developed and implemented in the thesis. The purpose of the controller is to track a flexible load to the desired velocity reference as fast as possible and without awkward oscillations. The control method is based on an adaptive backstepping algorithm with its stability ensured by the Lyapunov stability theorem. As a reference controller for the backstepping method, a hybrid neural controller is introduced in which the linear motor itself is controlled by a conventional PI velocity controller and the vibration of the associated flexible mechanism is suppressed from an outer control loop using a compensation signal from a multilayer perceptron network. To avoid the local minimum problem entailed in neural networks, the initial weights are searched for offline by means of a differential evolution algorithm. The states of a mechanical system for controllers are estimated using the Kalman filter. The theoretical results obtained from the control design are validated with the lumped mass model for a mechanism. Generalization of the mechanism allows the methods derived here to be widely implemented in machine automation. The control algorithms are first designed in a specially introduced nonlinear simulation model and then implemented in the physical linear motor using a DSP (Digital Signal Processor) application. The measurements prove that both controllers are capable of suppressing vibration, but that the backstepping method is superior to others due to its accuracy of response and stability properties.