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.

Differential patterns of functional and structural plasticity within and between inferior frontal gyri support training-induced improvements in inhibitory control proficiency.

Ample evidence indicates that inhibitory control (IC), a key executive component referring to the ability to suppress cognitive or motor processes, relies on a right-lateralized fronto-basal brain network. However, whether and how IC can be improved with training and the underlying neuroplastic mechanisms remains largely unresolved. We used functional and structural magnetic resonance imaging to measure the effects of 2 weeks of training with a Go/NoGo task specifically designed to improve frontal top-down IC mechanisms. The training-induced behavioral improvements were accompanied by a decrease in neural activity to inhibition trials within the right pars opercularis and triangularis, and in the left pars orbitalis of the inferior frontal gyri. Analyses of changes in brain anatomy induced by the IC training revealed increases in grey matter volume in the right pars orbitalis and modulations of white matter microstructure in the right pars triangularis. The task-specificity of the effects of training was confirmed by an absence of change in neural activity to a control working memory task. Our combined anatomical and functional findings indicate that differential patterns of functional and structural plasticity between and within inferior frontal gyri enhanced the speed of top-down inhibition processes and in turn IC proficiency. The results suggest that training-based interventions might help overcoming the anatomic and functional deficits of inferior frontal gyri manifesting in inhibition-related clinical conditions. More generally, we demonstrate how multimodal neuroimaging investigations of training-induced neuroplasticity enable revealing novel anatomo-functional dissociations within frontal executive brain networks. Hum Brain Mapp 36:2527-2543, 2015. © 2015 Wiley Periodicals, Inc.

Microstructure of the superior longitudinal fasciculus predicts stimulation-induced interference with on-line motor control.

A cortical visuomotor network, comprising the medial intraparietal sulcus (mIPS) and the dorsal premotor area (PMd), encodes the sensorimotor transformations required for the on-line control of reaching movements. How information is transmitted between these two regions and which pathways are involved, are less clear. Here, we use a multimodal approach combining repetitive transcranial magnetic stimulation (rTMS) and diffusion tensor imaging (DTI) to investigate whether structural connectivity in the 'reaching' circuit is associated to variations in the ability to control and update a movement. We induced a transient disruption of the neural processes underlying on-line motor adjustments by applying 1Hz rTMS over the mIPS. After the stimulation protocol, participants globally showed a reduction of the number of corrective trajectories during a reaching task that included unexpected visual perturbations. A voxel-based analysis revealed that participants exhibiting higher fractional anisotropy (FA) in the second branch of the superior longitudinal fasciculus (SLF II) suffered less rTMS-induced behavioral impact. These results indicate that the microstructural features of the white matter bundles within the parieto-frontal 'reaching' circuit play a prominent role when action reprogramming is interfered. Moreover, our study suggests that the structural alignment and cohesion of the white matter tracts might be used as a predictor to characterize the extent of motor impairments.

ADHD candidate gene (DRD4 exon III) affects inhibitory control in a healthy sample.

Background Dopamine is believed to be a key neurotransmitter in the development of attention-deficit/ hyperactivity disorder (ADHD). Several recent studies point to an association of the dopamine D4 receptor (DRD4) gene and this condition. More specifically, the 7 repeat variant of a variable number of tandem repeats (VNTR) polymorphism in exon III of this gene is suggested to bear a higher risk for ADHD. In the present study, we investigated the role of this polymorphism in the modulation of neurophysiological correlates of response inhibition (Go/Nogo task) in a healthy, high-functioning sample. Results Homozygous 7 repeat carriers showed a tendency for more accurate behavior in the Go/Nogo task compared to homozygous 4 repeat carriers. Moreover, 7 repeat carriers presented an increased nogo-related theta band response together with a reduced go-related beta decrease. Conclusions These data point to improved cognitive functions and prefrontal control in the 7 repeat carriers, probably due to the D4 receptor's modulatory role in prefrontal areas. The results are discussed with respect to previous behavioral data on this polymorphism and animal studies on the impact of the D4 receptor on cognitive functions.

Neural synchrony indexes impaired motor slowing after errors and novelty following white matter damage.

In humans, action errors and perceptual novelty elicit activity in a shared frontostriatal brain network, allowing them to adapt their ongoing behavior to such unexpected action outcomes. Healthy and pathologic aging reduces the integrity of white matter pathways that connect individual hubs of such networks and can impair the associated cognitive functions. Here, we investigated whether structural disconnection within this network because of small-vessel disease impairs the neural processes that subserve motor slowing after errors and novelty (post-error slowing, PES; post-novel slowing, PNS). Participants with intact frontostriatal circuitry showed increased right-lateralized beta-band (12-24 Hz) synchrony between frontocentral and frontolateral electrode sites in the electroencephalogram after errors and novelty, indexing increased neural communication. Importantly, this synchrony correlated with PES and PNS across participants. Furthermore, such synchrony was reduced in participants with frontostriatal white matter damage, in line with reduced PES and PNS. The results demonstrate that behavioral change after errors and novelty result from coordinated neural activity across a frontostriatal brain network and that such cognitive control is impaired by reduced white matter integrity.

The role of executive functions in the control of aggressive behavior

An extensive literature suggests a link between executive functions and aggressive behavior in humans, pointing mostly to an inverse relationship, i.e., increased tendencies toward aggression in individuals scoring low on executive function tests. This literature is limited, though, in terms of the groups studied and the measures of executive functions. In this paper, we present data from two studies addressing these issues. In a first behavioral study, we asked whether high trait aggressiveness is related to reduced executive functions. A sample of over 600 students performed in an extensive behavioral test battery including paradigms addressing executive functions such as the Eriksen Flanker task, Stroop task, n-back task, and Tower of London (TOL). High trait aggressive participants were found to have a significantly reduced latency score in the TOL, indicating more impulsive behavior compared to low trait aggressive participants. No other differences were detected. In an EEG-study, we assessed neural and behavioral correlates of error monitoring and response inhibition in participants who were characterized based on their laboratory-induced aggressive behavior in a competitive reaction time task. Participants who retaliated more in the aggression paradigm and had reduced frontal activity when being provoked did not, however, show any reduction in behavioral or neural correlates of executive control compared to the less aggressive participants. Our results question a strong relationship between aggression and executive functions at least for healthy, high-functioning people.

In vivo co-ordinated interactions between inhibitory systems to control glutamate mediated hippocampal excitability.

We present an overview of the long-term adaptation of hippocampal neurotransmission to cholinergic and GABAergic deafferentation caused by excitotoxic lesion of the medial septum. Two months after septal microinjection of 2.7 nmol a -amino-3-hydroxy-5-methylisoxazole-4-propionate (AMPA), a 220% increase of GABA A receptor labelling in the hippo- campal CA3 and the hilus was shown, and also changes in hippocampal neurotransmission characterised by in vivo microdialysis and HPLC. Basal amino acid and purine extra- cellular levels were studied in control and lesioned rats. In vivo effects of 100 m M KCl perfusion and adenosine A 1 receptor blockade with 1,3-dipropyl- 8-cyclopentylxanthine (DPCPX) on their release were also investigated. In lesioned animals GABA, glutamate and glutamine basal levels were decreased and taurine, adenosine and uric acid levels increased. A similar response to KCl infusion occurred in both groups except for GABA and glutamate, which release decreased in lesioned rats. Only in lesioned rats, DPCPX increased GABA basal level and KCl-induced glutamate release, and decreased glutamate turnover. Our results evidence that an excitotoxic septal lesion leads to increased hippocampal GABA A receptors and decreased glutamate neurotransmis- sion. In this situation, a co-ordinated response of hippocampal retaliatory systems takes place to control neuron excitability.

Neural mechanisms underlying adaptive actions after slips

An increase in cognitive control has been systematically observed in responses produced immediately after the commission of an error. Such responses show a delay in reaction time (post-error slowing) and an increase in accuracy. To characterize the neurophysiological mechanism involved in the adaptation of cognitive control, we examined oscillatory electrical brain activity by electroencephalogram and its corresponding neural network by event-related functional magnetic resonance imaging in three experiments. We identified a new oscillatory thetabeta component related to the degree of post-error slowing in the correct responses following an erroneous trial. Additionally, we found that the activity of the right dorsolateral prefrontal cortex, the right inferior frontal cortex, and the right superior frontal cortex was correlated with the degree of caution shown in the trial following the commission of an error. Given the overlap between this brain network and the regions activated by the need to inhibit motor responses in a stop-signal manipulation, we conclude that the increase in cognitive control observed after the commission of an error is implemented through the participation of an inhibitory mechanism.

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.

Control of the phosphorylation of the astrocyte marker glial fibrillary acidic protein (GFAP) in the immature rat hippocampus by glutamate and calcium ions: possible key factor in astrocytic plasticity

The present review describes recent research on the regulation by glutamate and Ca2+ of the phosphorylation state of the intermediate filament protein of the astrocytic cytoskeleton, glial fibrillary acidic protein (GFAP), in immature hippocampal slices. The results of this research are discussed against a background of modern knowledge of the functional importance of astrocytes in the brain and of the structure and dynamic properties of intermediate filament proteins. Astrocytes are now recognized as partners with neurons in many aspects of brain function with important roles in neural plasticity. Site-specific phosphorylation of intermediate filament proteins, including GFAP, has been shown to regulate the dynamic equilibrium between the polymerized and depolymerized state of the filaments and to play a fundamental role in mitosis. Glutamate was found to increase the phosphorylation state of GFAP in hippocampal slices from rats in the post-natal age range of 12-16 days in a reaction that was dependent on external Ca2+. The lack of external Ca2+ in the absence of glutamate also increased GFAP phosphorylation to the same extent. These effects of glutamate and Ca2+ were absent in adult hippocampal slices, where the phosphorylation of GFAP was completely Ca2+-dependent. Studies using specific agonists of glutamate receptors showed that the glutamate response was mediated by a G protein-linked group II metabotropic glutamate receptor (mGluR). Since group II mGluRs do not act by liberating Ca2+ from internal stores, it is proposed that activation of the receptor by glutamate inhibits Ca2+ entry into the astrocytes and consequently down-regulates a Ca2+-dependent dephosphorylation cascade regulating the phosphorylation state of GFAP. The functional significance of these results may be related to the narrow developmental window when the glutamate response is present. In the rat brain this window corresponds to the period of massive synaptogenesis during which astrocytes are known to proliferate. Possibly, glutamate liberated from developing synapses during this period may signal an increase in the phosphorylation

Neural reflex regulation of arterial pressure in pathophysiological conditions: interplay among the baroreflex, the cardiopulmonary reflexes and the chemoreflex

The maintenance of arterial pressure at levels adequate to perfuse the tissues is a basic requirement for the constancy of the internal environment and survival. The objective of the present review was to provide information about the basic reflex mechanisms that are responsible for the moment-to-moment regulation of the cardiovascular system. We demonstrate that this control is largely provided by the action of arterial and non-arterial reflexes that detect and correct changes in arterial pressure (baroreflex), blood volume or chemical composition (mechano- and chemosensitive cardiopulmonary reflexes), and changes in blood-gas composition (chemoreceptor reflex). The importance of the integration of these cardiovascular reflexes is well understood and it is clear that processing mainly occurs in the nucleus tractus solitarii, although the mechanism is poorly understood. There are several indications that the interactions of baroreflex, chemoreflex and Bezold-Jarisch reflex inputs, and the central nervous system control the activity of autonomic preganglionic neurons through parallel afferent and efferent pathways to achieve cardiovascular homeostasis. It is surprising that so little appears in the literature about the integration of these neural reflexes in cardiovascular function. Thus, our purpose was to review the interplay between peripheral neural reflex mechanisms of arterial blood pressure and blood volume regulation in physiological and pathophysiological states. Special emphasis is placed on the experimental model of arterial hypertension induced by N-nitro-L-arginine methyl ester (L-NAME) in which the interplay of these three reflexes is demonstrable

Gastroduodenal resistance and neural mechanisms involved in saline flow decrease elicited by acute blood volume expansion in anesthetized rats

We have previously demonstrated that blood volume (BV) expansion decreases saline flow through the gastroduodenal (GD) segment in anesthetized rats (Xavier-Neto J, dos Santos AA & Rola FH (1990) Gut, 31: 1006-1010). The present study attempts to identify the site(s) of resistance and neural mechanisms involved in this phenomenon. Male Wistar rats (N = 97, 200-300 g) were surgically manipulated to create four gut circuits: GD, gastric, pyloric and duodenal. These circuits were perfused under barostatically controlled pressure (4 cmH2O). Steady-state changes in flow were taken to reflect modifications in circuit resistances during three periods of time: normovolemic control (20 min), expansion (10-15 min), and expanded (30 min). Perfusion flow rates did not change in normovolemic control animals over a period of 60 min. BV expansion (Ringer bicarbonate, 1 ml/min up to 5% body weight) significantly (P<0.05) reduced perfusion flow in the GD (10.3 ± 0.5 to 7.6 ± 0.6 ml/min), pyloric (9.0 ± 0.6 to 5.6 ± 1.2 ml/min) and duodenal (10.8 ± 0.4 to 9.0 ± 0.6 ml/min) circuits, but not in the gastric circuit (11.9 ± 0.4 to 10.4 ± 0.6 ml/min). Prazosin (1 mg/kg) and yohimbine (3 mg/kg) prevented the expansion effect on the duodenal but not on the pyloric circuit. Bilateral cervical vagotomy prevented the expansion effect on the pylorus during the expansion but not during the expanded period and had no effect on the duodenum. Atropine (0.5 mg/kg), hexamethonium (10 mg/kg) and propranolol (2 mg/kg) were ineffective on both circuits. These results indicate that 1) BV expansion increases the GD resistance to liquid flow, 2) pylorus and duodenum are important sites of resistance, and 3) yohimbine and prazosin prevented the increase in duodenal resistance and vagotomy prevented it partially in the pylorus

Chemoreceptors and cardiovascular control in acute and chronic systemic hypoxia

This review describes the ways in which the primary bradycardia and peripheral vasoconstriction evoked by selective stimulation of peripheral chemoreceptors can be modified by the secondary effects of a chemoreceptor-induced increase in ventilation. The evidence that strong stimulation of peripheral chemoreceptors can evoke the behavioural and cardiovascular components of the alerting or defence response which is characteristically evoked by novel or noxious stimuli is considered. The functional significance of all these influences in systemic hypoxia is then discussed with emphasis on the fact that these reflex changes can be overcome by the local effects of hypoxia: central neural hypoxia depresses ventilation, hypoxia acting on the heart causes bradycardia and local hypoxia of skeletal muscle and brain induces vasodilatation. Further, it is proposed that these local influences can become interdependent, so generating a positive feedback loop that may explain sudden infant death syndrome (SIDS). It is also argued that a major contributor to these local influences is adenosine. The role of adenosine in determining the distribution of O2 in skeletal muscle microcirculation in hypoxia is discussed, together with its possible cellular mechanisms of action. Finally, evidence is presented that in chronic systemic hypoxia, the reflex vasoconstrictor influences of the sympathetic nervous system are reduced and/or the local dilator influences of hypoxia are enhanced. In vitro and in vivo findings suggest this is partly explained by upregulation of nitric oxide (NO) synthesis by the vascular endothelium which facilitates vasodilatation induced by adenosine and other NO-dependent dilators and attenuates noradrenaline-evoked vasoconstriction.

Endogenous vasopressin and the central control of heart rate during dynamic exercise

The present article contains a brief review on the role of vasopressinergic projections to the nucleus tractus solitarii in the genesis of reflex bradycardia and in the modulation of heart rate control during exercise. The effects of vasopressin on exercise tachycardia are discussed on the basis of both the endogenous peptide content changes and the heart rate response changes observed during running in sedentary and trained rats. Dynamic exercise caused a specific vasopressin content increase in dorsal and ventral brainstem areas. In accordance, rats pretreated with the peptide or the V1 blocker into the nucleus tractus solitarii showed a significant potentiation or a marked blunting of the exercise tachycardia, respectively, without any change in the pressure response to exercise. It is proposed that the long-descending vasopressinergic pathway to the nucleus tractus solitarii serves as one link between the two main neural controllers of circulation, i.e., the central command and feedback control mechanisms driven by the peripheral receptors. Therefore, vasopressinergic input could contribute to the adjustment of heart rate response (and cardiac output) to the circulatory demand during exercise.

Stiffness based trajectory planning and feedforward based vibration suppression control of parallel robot machines

The dissertation proposes two control strategies, which include the trajectory planning and vibration suppression, for a kinematic redundant serial-parallel robot machine, with the aim of attaining the satisfactory machining performance. For a given prescribed trajectory of the robot's end-effector in the Cartesian space, a set of trajectories in the robot's joint space are generated based on the best stiffness performance of the robot along the prescribed trajectory. To construct the required system-wide analytical stiffness model for the serial-parallel robot machine, a variant of the virtual joint method (VJM) is proposed in the dissertation. The modified method is an evolution of Gosselin's lumped model that can account for the deformations of a flexible link in more directions. The effectiveness of this VJM variant is validated by comparing the computed stiffness results of a flexible link with the those of a matrix structural analysis (MSA) method. The comparison shows that the numerical results from both methods on an individual flexible beam are almost identical, which, in some sense, provides mutual validation. The most prominent advantage of the presented VJM variant compared with the MSA method is that it can be applied in a flexible structure system with complicated kinematics formed in terms of flexible serial links and joints. Moreover, by combining the VJM variant and the virtual work principle, a systemwide analytical stiffness model can be easily obtained for mechanisms with both serial kinematics and parallel kinematics. In the dissertation, a system-wide stiffness model of a kinematic redundant serial-parallel robot machine is constructed based on integration of the VJM variant and the virtual work principle. Numerical results of its stiffness performance are reported. For a kinematic redundant robot, to generate a set of feasible joints' trajectories for a prescribed trajectory of its end-effector, its system-wide stiffness performance is taken as the constraint in the joints trajectory planning in the dissertation. For a prescribed location of the end-effector, the robot permits an infinite number of inverse solutions, which consequently yields infinite kinds of stiffness performance. Therefore, a differential evolution (DE) algorithm in which the positions of redundant joints in the kinematics are taken as input variables was employed to search for the best stiffness performance of the robot. Numerical results of the generated joint trajectories are given for a kinematic redundant serial-parallel robot machine, IWR (Intersector Welding/Cutting Robot), when a particular trajectory of its end-effector has been prescribed. The numerical results show that the joint trajectories generated based on the stiffness optimization are feasible for realization in the control system since they are acceptably smooth. The results imply that the stiffness performance of the robot machine deviates smoothly with respect to the kinematic configuration in the adjacent domain of its best stiffness performance. To suppress the vibration of the robot machine due to varying cutting force during the machining process, this dissertation proposed a feedforward control strategy, which is constructed based on the derived inverse dynamics model of target system. The effectiveness of applying such a feedforward control in the vibration suppression has been validated in a parallel manipulator in the software environment. The experimental study of such a feedforward control has also been included in the dissertation. The difficulties of modelling the actual system due to the unknown components in its dynamics is noticed. As a solution, a back propagation (BP) neural network is proposed for identification of the unknown components of the dynamics model of the target system. To train such a BP neural network, a modified Levenberg-Marquardt algorithm that can utilize an experimental input-output data set of the entire dynamic system is introduced in the dissertation. Validation of the BP neural network and the modified Levenberg- Marquardt algorithm is done, respectively, by a sinusoidal output approximation, a second order system parameters estimation, and a friction model estimation of a parallel manipulator, which represent three different application aspects of this method.