SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL
The System Theory, Control and Computing Journal – issued from merging of journals traditionally (along some half-century) edited by Control and Computing Engineering departments and faculties (schools) – is promoting theoretical and applied results in a large field of System Theory, Control and Computing (with particular reference to Applied Informatics and Applications in Systems and Control). ISSN: 2810–4099 ISSN–L: 2668–2966
Around the dynamics and control of a model arising from vibroimpact mechanics
It is considered a simple model arising from vibroimpact machinery modeling. This model is deduced using the variational principle of Hamilton applied to a structure with distributed parameters. Its novelty includes introduction of the elastic strain induced by the external force at the boundary. The non-penetrating contact is modeled by the Hertz-Signorini-Moreau complementarity condition - again in the simplest case. Next, there is studied asymptotic stability of the autonomous system, based on the energy Lyapunov functional and the Barbashin-Krasovskii-LaSalle invariance principle.
vibroimpact mechanics,complementarity condition,stability,energy Lyapunov functional, Barbashin-Krasovskii-LaSalle invariance principle.
Copyright (c) 2024 SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL
Classification of Microorganism Using Convolutional Neural Network and H2O AutoML
The study advances microorganism image classification through a hybrid approach that integrates a Convolutional Neural Network (CNN), modified from the VGG19 architecture, with an ensemble model powered by H2O AutoML. Employing data augmentation and feature extraction, the approach enhances performance on a dataset encapsulating a broad spectrum of microorganism classes. The CNN model shows significant accuracy enhancements in complex bacteria classes, as depicted by the confusion matrix. Concurrently, the AutoML ensemble delivers comparable accuracy, notably in some classes where CNNs struggles. This research highlights the complementary strengths of deep learning and AutoML, demonstrating their impact in achieving high-precision microorganism recognition. Such advancements promise to significantly benefit bioinformatics and diagnostic applications, addressing the complexity of multi-class image classification tasks. The results indicate a successful combination of CNN and AutoML methodologies, setting a benchmark in automated microorganism classification, and also showcase the unique contributions and nuances of each method.
Analyzing deep learning algorithms with statistical methods
A number of farmers use human inspection to classify the quality of their fruits visually; this process could be done automatically with a Learning algorithm. This paper investigates the classification of apples, peaches, and oranges and verifies the quality of classification with the density of the edges detected in each image by the Sobel filter. The novelty of the study consists of comparing the classification accuracy of a convolutional neural network (CNN) and the statistical analysis of edge histograms. The edges are the main elements of what the CNN learns; this was the reason for verifying the deep learning algorithms with skewness, kurtosis, and standard deviation metrics extracted from the histogram of edge density detected by the Sobel filter. In the empirical process, four algorithms were proposed: a CNN with one convolutional layer, a DNN without convolutional layers, and two pre-trained networks, AlexNet and GoogLeNet. From clustering of the row data and analyzing the accuracy, the best classification is obtained by simple CNN for 20 epochs when the apples vs. oranges were classified.
convolutional neural network, pretrained networks, skewness, kurtosis and standard deviation
Digital Signal Processing Simulation Based on Matrix-Vector description
Even a small error in the design and implementation of a DSP algorithm can cause complete inoperability, finding and fixing these errors is laborious and time-consuming. Of course, the validation of the correct operation of a DSP algorithm must be confirmed by measurement. In case of a deviation, it is important to find the root of the problem, the simulation of the DSP algorithm is a reliable and efficient task which can be performed by a desktop computer running some mathematical program. The simulation – as an operation check – could be performed in the time domain, or in the frequency domain or in both. The system of equations describing the DSP algorithm can also be written in matrix-vector form, therefore these algorithms can be effectively simulated in the Matlab® environment.
Improvement Performances of the SMO Observer for PMSM Sensorless Control Based on DTC Strategy Using Simulated Annealing and Reinforcement Learning TD3 Agent
From the elements that contribute to increasing the reliability of the control system of a Permanent Magnet Synchronous Motor (PMSM), could be enumerated the replacement of the speed transducers with software-implemented speed observers. On this basis, this paper focuses on the sensorless regulation of a PMSM using a Direct Torque Control (DTC) type strategy, in which a speed observer is used in combination with a Reinforcement Learning-Twin Delayed Deep Deterministic Policy Gradient (RL-TD3) type agent to increase the accuracy of the PMSM rotor speed estimate. Simulated Annealing (SA) is also used to achieve superior performance of the velocity observer for optimal tuning of the PI-type velocity controller parameters. The latter can, after the training phase, provide correction signals to the speed observer so that the estimated speed is as close as possible to the estimated speed. The control structures, control algorithms, and operating equations of the PMSM, the control strategy of the DTC type, and the speed observer are presented in this paper. Numerical simulations carried out in the Matlab/Simulink programming environment validate the superiority of the PMSM rotor speed estimation performance in the case of the use of an RL-TD3-type agent in combination with a speed observer, compared to the case of the use of the speed observer alone.
PMSM, DTC, Simulated Annealing, SMO, Reinforcement Learning
Copyright (c) 2023 SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL
Post-Quantum Security Overview of the Public Key Infrastructure
Recently, there has been an increasing focus on the investigation of quantum-safe solutions for a variety of applications. One of the pressing issues that needs to be made quantum secure is the TLS (Transport Layer Security) protocol. Proposals for its implementation have been discussed in several articles. The TLS protocol is based on PKI (Public Key Infrastructure). In addition, there are many other PKI applications that are used every day in both private and enterprise environments, so securing their use is essential. The methods currently developed to ensure adequate security will become obsolete with the advent of quantum computers. According to the Cloud Security Alliance, by around 2030, the performance of quantum computers will increase to the point where the risk of vulnerability of traditionally encrypted data will be very high. It is therefore important to make the right preparations in time to ensure that we can transform our solutions into quantum secure solutions by the time quantum computing becomes a real threat. In this paper, we present an analysis to this end, presenting quantum-safe solutions already in use and, in comparison, proposing new, well-performing solutions for a quantum-resistant PKI.
Low latency 3D image streaming in medicine
3D visualization has been present in medicine for several decades, just think of the CT (Computer Tomography) imaging modality, which is capable of creating 3D images of the examined object by determining the radiation attenuation coefficient. In addition to CT equipment, there are many solutions capable of collecting and displaying various 3D data (MRI [Magnetic Resonance Imaging], PET [Positron Emission Tomography], OCT [Optical Computer Tomography]). In digital pathology, 3D visualization is not nearly as widespread as the previously mentioned solutions. One of the main reasons for this is the size of the digitized pathological samples and the hardware resources required for their 3D visualization. In the paper, we present a client-server architecture that can provide a solution to the existing hardware limitations during the 3D visualization of digitized pathological samples. In the paper, we present the basic structure of our solution, several main functionalities, and the testing of the server software we developed.
Algorithm for Analyzing the Microenvironment Surrounding Melanoma
Peritumoral areas or microenvironments surrounding melanoma are unexplored and partially understood, so that, in the following paper, an algorithm that predicts the trend of the melanoma progression is proposed. Additionally, in case of melanoma the peritumoral area is significantly correlated with the texture that belongs inside the skin lesion. The proposed algorithm analyses the region of interest (ROI) with Normalized 2-D cross-correlation (NCC) method and predicts the pattern in the peritumoral area which is most similar with the texture of the melanoma. An important step is the detection of the peritumoral area, in which case, the mathematical morphology techniques were proposed. The verifying of similarity between the samples cropped from inside the melanoma and peritumoral area with Structural Similarity Index (SSIM) was performed. The main advantage of the proposed algorithm is that it can be applied on different medical image types and tumors. The algorithm was tested on two datasets 7-Point and PH2, and two computes.
peritumoral area, Normalized 2-D cross-correlation, Structural Similarity Index
Object Detection for Reinforcement Learning Agents
In traditional reinforcement learning applications with images as input, the observation for the agent to learn from, is an image. In these models, a Convolutional Neural Network (CNN) is typically used to extract the features before for the learning process, in order to maximize the cumulative reward. In this paper, a different approach for pre-processing the input for reinforcement learning agents is considered. The proposed approach uses object detectors instead instead of CNNs, and converts each input image into bounding boxes and object locations for the agent to learn from.
The monitoring of burning buildings with convolutional neural network
Artificial intelligence is constantly expanding. This is used in many domains, from agriculture to the medical field. Lately, the focus has been on image-based learning (deep learning) because it has greater applicability in reality. An example is the identification of buildings that burn in real-time, the purpose being the saving as many lives as possible by the firefighters. This paper aims to identify the optimal color space for the identification of fire in images. To achieve this the images were selected from two databases taken from the Kaggle platform, and the images were processed with six color spaces: RGB, YCbCr, HSV, HLS, L*a*b, and L*u*v. In this form the images fed convolutional neural networks (CNNs). After that, the models were trained on six datasets, a dataset for each color space, and after compiling of CNNs, a testing set for the prediction model was proposed. The results of the model were analyzed and interpreted according to accuracy and loss function and the space YCbCr identified the fire from the images with an accuracy of 100% and loss function of 4.02*10-05.
color space, convolutional neural network
Homogeneous Parametric Modeling of Airloads
This work proposes two parametric modeling strategies for steady aerodynamic forces. We point out that airloads are homogeneous and introduce a parametrization based on spherical harmonics and a neural network. The parametrization using spherical harmonics enables an analogue of frequency-based truncation and a variation on the Singular Value Decomposition (SVD), constituting an orthogonal decomposition of the modeled airloads. Since neural networks are universal function approximators, the model based on this allows for more flexible parametrizations, including actuations and model inversions. Both parametrization strategies are showcased for model identification and reduction purposes, highlighting their strengths and weaknesses.
The Over-Damped String Stability Condition for a Platooning System
The over-damped string stability criterion is a very strong stability condition that not only addresses the stability in a stricter sense but also adequately captures the safety performance of a platoon. However, the mathematical representation of this criterion is incomplete in the literature. Here, this representation is completely described. Moreover, this article presents the mathematical test method to evaluate this stability condition for linear or linearized systems from the transfer function. The classical sting stability condition does not address the transient undesired convergent dynamics of a platoon, such as over-shooting, under-shooting or damped oscillating dynamics. This paper demonstrates that the over-damped string stability characteristic significantly attenuates these undesired convergent dynamics in the upstream direction. Thus, the advantage of this condition over the classical criterion for linear system is clarified theoretically and by simulation. Later, the numerical method to analyze the over-damped string stability criterion for nonlinear systems is discussed. Additionally, numerical simulations of an over-damped string stable adaptive cruise control (ACC) vehicle model are compared with that of some experimental test results on platoons of commercially implemented ACC equipped vehicles.
Transfer function approaches for SEEG brain electrode interface applied to tissue classification
This paper is about transfer function approaches for brain-electrode interface modelling in the context of StereoElectroEncephaloGraphy, and their possible use in tissue classification (between grey and white matter). Monopolar and bipolar configurations are first reviewed, giving rise to possible nonparametric and parametric identification methods, as well as related possible classification results (for identical tissues and distinct tissues at measurement points, respectively). A method combining both approaches is then proposed, so as to end up with a classification at each measurement point in any case. The proposed methodology is implemented with clinical data collected from a set of epileptic patients, confirming its interest by providing more than 70% of accuracy in the obtained results.
Distributed Buck Converter Realization Based on a Transmission Line
The buck converter is a widely used switched converter to adapt a higher DC voltage to a lower DC voltage. In the conventional design, the converter has two reactive elements, an inductor and a capacitor. Replacing these dynamical elements by a transmission line results in a distributed buck converter. Modeling the transmission line by the telegrapher's equations yields a model with completely new properties. We investigate the behavior of this system and present a practical circuit realization.
Analysis of Industrial Sensor Data Using Statistical and Regression Methods
Today's industrial landscape is primarily driven by rapid and effective data processing and evaluation. Consequently, industries should devote considerable attention and resources towards real-time examination of the large data sets acquired, enabling timely extraction of vital information for outlier detection, fake data identification, and predictive analysis to mitigate unforeseen expenses. This rigorous process of data analysis necessitates the employment of a diverse set of algorithms that align with the specific objectives, spanning a wide spectrum of potential solutions. In this manuscript, we demonstrate how Apache Spark's unified engine can be harnessed for conducting statistical analysis of time series data, thereby expediting industrial data analysis processes. Furthermore, we examine and implement both linear and random forest regression models within the context of the demonstrated use case.
Sewer Network Multi-objective Optimization using Genetic Algorithms
This paper focuses on the multi-objective optimization of a sewer network that serves a medium-sized Romanian city, with a population of 250,000 residents. The sewer network is modeled using BSMSewer software package. The obtained results are based on numerical simulations with the optimization algorithm considering two performance criteria: the volume of overflow and the quality of the overflowed wastewater. For optimization, two approaches that use a controlled elitist genetic algorithm were employed: a multi-objective optimization and a two-steps multi-objective optimization. Results analysis involved comparing them with a scenario where each performance criterion was separately minimized. Additionally, a comparison was made to the situation where the sewer network operated without a control system, meaning the valves were fully open and the pumps were running at maximum capacity.
Harnessing performance counters to detect malware using deep learning models
Computing systems are challenged by security exploits and malware. The following methods are used for detecting anomalies and discovering vulnerabilities in computing systems: malware aware processors, static program analysis, and dynamic program analysis. Online hardware to detect malware is not always a practical and scalable solution because of the costs. Automated static analysis tools have limited performance and detection capabilities that may not meet the criticality requirements of the project regarding static analysis methods. In the latest trends, dynamic analysis has overcome static analysis. Several approaches have been used to analyze performance counters in this sense. Performance counters are collected from both operating systems/software and processors/hardware and stored as time series: 1) in the presence and 2) in the absence of malware. For software performance counters (SPCs), fourteen deep learning models were used for time series classification, while for hardware perfornamce counters (HPCs), ten deep learning models were used. For SPCs two models were able to detect accurately malware in infected operating systems, while the rest tend to overfit the data. For HPCs three models were able to detect malware.
Copyright (c) 2022 SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL
Application of Heavy and Underestimated Dynamic Models in Adaptive Receding Horizon Control Without Constraints
In the heuristic “Adaptive Receding Horizon Controller” (ARHC) the available dynamic model of the controlled system usually is placed in the role of a constraint under which various cost functions can be minimized over a horizon. A possible secure design can be making calculations for a “heavy dynamic model” that may produce high dynamical burden that is efficiently penalized by the cost functions and instead of the original nominal trajectory results a “deformed” one that can be realized by the controlled system of “less heavy dynamics”. In the lack of accurate system model a fixed point iterationbased adaptive approach is suggested for the precise realization of this deformed trajectory. To reduce the computational burden of the control the usual approach in which the dynamic model is considered as constraint and Lagrange-multipliers are introduced as co-state variables is evaded. The heavy dynamic model is directly built in the cost and the computationally greedy Reduced Gradient Algorithm is replaced by a transition between the simple and fast Newton-Raphson and the slower Gradient Descent algorithms (GDA). In the paper simulation examples are presented for two dynamically coupled van der Pol oscillators as a strongly nonlinear system. The comparative use of simple nondifferentiable and differentiable cost functions is considered, too.
Fixed Point Iteration-based Adaptive Control
On Certain Noise Filtering Techniques in Fixed Point Iteration-based Adaptive Control
In control applications the use of noise-burdened sensor signals cannot be evaded. Also, certain signals can be lost. This problem traditionally is tackled by the use of Kalman filters that provide some “optimal solution” to these problems based on reasonable assumptions that are not always well underpinned in the practice. These are assumptions are made with regard to the system model and the statistical distribution of the noise signals. The Fixed Point Iteration-based adaptive controller is applicable for various strongly nonlinear models. Because feeding back the order of time-derivative of the system’s variable that immediately can be varied by the control signal, its noise sensitivity can be considerable. In this paper the operation of an unscented Kalman filter-based technique is compared with that of a simple moving window with affine signal approximation, and the use of a third order low pass filter in the control of a modified van der Pol oscillator. In this model a quadratic drag term is added to the original model to describe the motion of the system in turbulent fluid environment. According to the numerical simulations it can be stated that the simpler methods can replace the more complicated Kalman filter.
fixed point iteration- based adaptive control
Application Development with Finite Element Method to Calculate Photogeneration Rate and Open-Circuit Voltage of Dye Sensitized Solar Cell
Amongst the several alternative resources, renewable energy source (RES) can provide continuous and clean energy. Furthermore, RESs have received a worldwide attention and an outstanding role is attributed to them. The sun energy can be exploited using light energy conversion applications such as photovoltaics. Dye Sensitized Solar Cell (DSSC) is third-generation photovoltaic device and a forwardlooking, easily producible solar cell. Nevertheless, buying a commercially available DSSC, datasheet and material information are unavailable. Thus, the purchased DSSC is a black box. The main motivation is that to develop a MatLab application which is able to determine the material information and parameters of the Dye Sensitized Solar Cell from some incoming parameters. The goal of the study is to describe the peration of the developed MatLab application which calculated the photogeneration rate in function of the thickness of the cell, the open-circuit voltage, and to illustrate its operation via an example. The photogeneration rate is solved using the numerical finite element method as a numerical procedure. In our model the Beer-Lambert law is implemented. The model takes into consideration the measured parameters of the light such as photoncount-wavelength spectrum, transmissionwavelength spectrum and irradiation intensity-wavelength spectrum. Furthermore, the open-circuit voltage is an elementary electric parameter of a solar cell.
Approach to the Design of a Microservice Architecture Based on Praxeme
Frequent updates of business needs are one of the factors of the evolution of a company. These permanent changes require a large flexibility of the Information System (IS). SOA (Service Oriented Architecture) is an architecture that offers more scalability to an application by subdividing the monolithic block into independent services. Nevertheless, it is not sufficiently suitable in terms of accessibility of services and data. It is thus necessary to orient the design of the IS towards a new architecture called Microservice Architecture (MSA). The objective of this paper is to recommend a methodology to design MSA. Indeed, our approach is based on Praxeme which is an enterprise methodology appropriate to SOA. The result obtained from the approach proposed in this paper is a model allowing to automate the MSA design.
software architecture design methodology
Limiting State Estimation of Switched Interval Systems with Metzler-Takagi-Sugeno Models
The paper deals with interval observer design for fuzzy switched positive systems. The systems are represented by the Takagi-Sugeno fuzzy models, with premise variables depending on a measurable part of the state vector. Stability conditions for the proposed interval observer structure are formulated via linear matrix inequalities to ensure nonnegative system state estimation. The proposed method allows to compute the lower and upper bounds of the system state under the assumption that the system disturbance are bounded. The properties of proposed approach are illustrated in numerical example.
Takagi-Sugeno models, switched systems, Metzler systems, parametric constraints, interval observer design.
Sparse Filtering Under Norm-Bounded Exogenous Disturbances Using Observers
The paper considers the sparse filtering problem under arbitrary norm-bounded exogenous disturbances. We propose a simple and universal observer-based approach to its solution, based on the LMI technique and the method of invariant ellipsoids; it allows the use of a reduced number of system outputs. From a technical point of view of application, we reduce the original problem to semi-definite programming, which is easily solved numerically. The proposed simple approach is easy to implement and can be equally extended to systems in continuous and discrete time.
Global Position Feedback Tracking Control of a Serial Robot Manipulator with Revolute Joints
In this paper, we present the controller which globally stabilizes a non-stationary motion of a serial robot manipulator with revolute joints without velocity measurements. A family of desired manipulator motions is considered such that the first vertical link of the manipulator performs a given rotation, and the remaining links retain the given relative angular positions. It is proved that such motions of the manipulator can be made globally asymptotically stable using dynamic position feedback. The problem is solved taking into account the periodicity of the dynamics equations along the angular coordinates of the links. As an example, a numerical simulation of the three-link manipulator motion under the constructed controller is presented.
Full and Partial Eigenvalue Placement for Minimum Norm Static Output Feedback Control
The controller design for linear time-invariant state space systems seems to be straightforward and well established. This is not true for static output feedback control, which is still a challenging task. This paper deals with controller design based on eigenvalue assignment. We consider the placement of distinct as well as multiple real eigenvalues or complex conjugate pairs. The desired eigenvalue configurations are characterised in terms of algebraic divisibility of the characteristic polynomial of the closed-loop system. We also consider the problem of partial eigenvalue placement, where not all eigenvalues are fixed by feedback. Degrees of freedom in the controller design are used for the minimization of various matrix norms of the feedback gain matrix.
On functional differential equations connected to Huygens synchronization under propagation
The structure represented by one or several oscillators couple to a one-dimensional transmission environment (e.g. a vibrating string in the mechanical case or a lossless transmission line in the electrical case) turned to be attractive for the research in the field of complex structures and/or complex behavior. This is due to the fact that such a structure represents some generalization of various interconnection modes with lumped parameters for the oscillators. On the other hand the lossless and distortionless propagation along transmission lines has generated several research in electrical, thermal, hydro and control engineering leading to the association of some functional differential equations to the basic initial boundary value problems. The present research is performed at the crossroad of the aforementioned directions. We shall associate to the starting models some functional differential equations - in most cases of neutral type - and make use of the general theorems for existence and stability of forced oscillations for functional differential equations. The challenges introduced by the analyzed problems for the general theory are emphasized, together with the implication of the results for various applications.
Flat input based canonical form observers for non-integrable nonlinear systems
In this contribution, the design of canonical form observers for nonlinear non-integrable systems is investigated. These systems cannot be transformed into observer canonical form, therefore an exact observer error linearization cannot be achieved. However, using flat inputs and dynamic compensators, the original dynamics can be rendered into an integrable flat system. For this modified flat input system a canonical form observer can be designed. By utilizing a state transformation, it is then possible to obtain an estimate of the original state, where the observer error is approximately linearized. This procedure is exemplified by the Rössler system. Furthermore, we illustrate the relationship of this approach with high-gain observers.
Conservation Laws -- a Source for Distortionless Propagation and Time Delays
Since the very first paper of J. Bernoulli in 1728, a connection exists between initial boundary value problems for hyperbolic Partial Differential Equations (PDE) in the plane (with a single space coordinate accounting for wave propagation) and some associated Functional Equations (FE). From the point of view of dynamics and control (to be specific, of dynamics for control) both type of equations generate dynamical and controlled dynamical systems. The functional equations may be difference equations (in continuous time), delay-differential (mostly of neutral type) or even integral/integro-differential. It is possible to discuss dynamics and control either for PDE or FE since both may be viewed as self contained mathematical objects. A more recent topic is control of systems displaying conservation laws. Conservation laws are described by nonlinear hyperbolic PDE belonging to the class ``lossless'' (conservative); their dynamics and control theory is well served by the associated energy integral. It is however not without interest to discuss association of some FE. Lossless implies usually distortionless propagation hence one would expect here also lumped time delays. The paper contains some illustrating applications from various fields: nuclear reactors with circulating fuel, canal flows control, overhead crane, drilling devices, without forgetting the standard classical example of the nonhomogeneous transmission lines for distortionless and lossless propagation. Specific features of the control models are discussed in connection with the control approach wherever it applies.
conservation laws, distortionless propagation, time delays
Copyright (c) 2021 SYSTEM THEORY, CONTROL AND COMPUTING JOURNAL
Systems Actuated by Shape Memory Alloys: Identification and Modeling
This paper presents the identification of thermal and mechanical parameters of shape memory alloys by using the heat transfer equation and a constitutive model. The identified parameters are then used to describe the mathematical model of a fiber-elastomer composite embedded with shape memory alloys. To verify the validity of the obtained equations, numerical simulations of the SMA temperature and composite bending are carried out and compared with the experimental results.
Accelerated Reduced Gradient Algorithm with Constraint Relaxation in Differential Inverse Kinematics
The Moore-Penrose pseudoinverse-based solution of the differential inverse kinematic task of redundant robots corresponds to the result of a particular optimization underconstraints in which the implementation of Lagrange’s ReducedGradient Algorithm can be evaded simply by considering the zero partial derivatives of the ”Auxiliary Function” associated with this problem. This possibility arises because of the fact that the cost term is built up of quadratic functions of the variable of optimization while the constraint term is linear function of the same variables. Any modification in the cost and/or constraint structure makes it necessary the use of the numerical algorithm. Anyway, the penalty effect of the cost terms is always overridden by the hard constraints that makes practical problems in the vicinity of kinematic singularities where the possible solution still exists but needs huge joint coordinate time-derivatives. While in the special case the pseudoinverse simply can be deformed, in the more general one more sophisticated constraint relaxation can be applied. In this paper a formerly proposed accelerated treatment of the constraint terms is further developed by the introduction of a simple constraint relaxation. Furthermore, the numerical results of the algorithm are smoothed by a third order tracking strategy to obtain dynamically implementable solution. The improved method’s operation is exemplified by computation results for a 7 degree of freedom open kinematic chain