Degree Of System Stability Research Articles

Synthesis of the Control Algorithm for Third-Order Object Models with Additional Zero and Time Delay

In this paper, the tuning procedure for the standardized PID controller for third-order object models with additional zero and time delay using the maximum stability degree method with iteration is analyzed. Analytical calculation expressions for the tuning parameters of the controller were obtained as nonlinear functions of the argument - the degree of system stability, and linear functions of the known parameters of the object model. By varying the degree of stability, these functions are graphically constructed, after which, for the same argument value, sets of controller tuning parameter values are chosen, and the performances of the automatic control system for the control object are verified. The proposed method was compared with other known methods and tested for tuning the PID controller for the temperature control in the extruder of a 3D printer. The advantages of the elaborated procedure were highlighted.

Optimization of the Processes of Attenuation of Transverse Movements of a Trailer Following a Tractor

The article considers the issues of optimizing the processes of attenuation of the transverse movements of the trailer, which is attached to a tractor moving at a constant speed with the help of a hinge and taking into account the compliant clutch. As an optimization criterion characterizing the efficiency of this attenuation, the maximization of the degree of system stability is taken. In this case, the distance from the center of mass of the trailer to the point of its adhesion to the tractor acts as an optimized parameter. A detailed analytical solution of the problem is carried out, during which the optimal curve on the plane of dimensionless parameters is determined, which consists of several sections and is located in the region of motion stability. Visual graphic illustrations are given, explaining the meaning of the found solution and its main features. In addition, the obtained results are compared with the variant of the location of the center of mass of the trailer exactly in the middle between the point of its coupling with the tractor and the axle of the wheelset, and an assessment is made of the effectiveness of the obtained optimal solution. The conclusions made in the work are not only of theoretical interest, but can also find some practical application.

Qualitative and Quantitative Transient Stability Assessment of Stand-Alone Hybrid Microgrids in a Cluster Environment

Neighboring stand-alone hybrid microgrids with diesel generators (DGs) as well as grid-feeding photovoltaics (PV) and grid-forming battery storage systems (BSS) can be coupled to reduce fuel costs and emissions as well as to enhance the security of supply. In contrast to the research in control and small-signal rotor angle stability of microgrids, there is a significant lack of knowledge regarding the transient stability of off-grid hybrid microgrids in a cluster environment. Therefore, the large-signal rotor angle stability of pooled microgrids was assessed qualitatively and also quantitatively in this research work. Quantitative transient stability assessment (TSA) was carried out with the help of the—recently developed and validated—micro-hybrid method by combining time-domain simulations and transient energy function analyses. For this purpose, three realistic dynamic microgrids were modelled regarding three operating modes (island, interconnection, and cluster) as well as the conventional scenario “classical” and four hybrid scenarios (“storage”, “sun”, “sun & storage”, and “night”) regarding different instants of time on a tropical partly sunny day. It can be inferred that, coupling hybrid microgrids is feasible from the voltage, frequency, and also transient stability point of view. However, the risk of large-signal rotor angle instability in pooled microgrids is relatively higher than in islanded microgrids. Along with critical clearing times, new stability-related indicators such as system stability degree and corrected critical clearing times should be taken into account in the planning phase and in the operation of microgrids. In principle, a general conclusion concerning the best operating mode and scenario of the investigated microgrids cannot be drawn. TSA of pooled hybrid microgrids should be performed—on a regular basis especially in the grid operation—for different loading conditions, tie-line power flows, topologies, operating modes, and scenarios.

The micro-hybrid method to assess transient stability quantitatively in pooled off-grid microgrids

In interconnected off-grid microgrids an in-depth knowledge of dynamic limits can be obtained by performing quantitative transient stability assessment. Quantitative stability results using the new hybrid method can be used for optimal generation dispatching, adjusting protection system settings, optimal clustering of microgrids etc. However, a discrepancy in the profiles of kinetic and potential energy has been noticed. Therefore, in this research work an improved new hybrid method, the so-called micro-hybrid method, was developed by adjusting the transient energy function, which is valid for transmission systems. Further, the new approach was validated and applied in a stand-alone multi-machine microgrid comprising detailed dynamic models of diesel generators with fast-reacting controllers. Finally, the transient stability of three clustered microgrids was assessed quantitatively. From the results it can be concluded that the profiles of the energies obtained by using the micro-hybrid method are exact mirror images. The critical fault clearing times can be corrected based on the profiles of the system stability degree and stability reserve degree of individual generators for different clearing times. Lastly, pooling of the investigated microgrids has a negative impact on the critical clearing times as well as on the profiles of system stability degree with respect to various clearing times.

Stability of a flat arch subjected to deterministic and stochastic loads taking into account nonlocal damping

In the example of a flat arch, a problem of vibrational stability of systems subjected to deterministic and stochastic loads is considered taking into account the geometric nonlinearity and nonlocal damping of a material, which is characteristic of certain types of composites and nanomaterials. To study the stability of arch motion within the deterministic statement of the problem (stability in the sense of Lyapunov) and the stability in the almost certain stochastic statement, a method is used which is based on the calculation of the maximal Lyapunov’s exponent. The influence of damping and loading parameters on the degree of system stability is analyzed.

Chaotic Characteristic Analysis of Concrete Fracture System Based on Lyapunov Exponent Stability Criterion

According to the research on whole curves of strain-stress of concrete materials, the paper illustrates in evidence features of stages and shows that the discrete feature of curve often occurs in strain-softening stage. After chaotic dynamic analysis of testing datas, it presents that system of whole process of strain-stress evolves from ordered steady state to low chaotic state and then to high chaotic state along with increase of compressive strength. The linear relationship of strain-stress grows evident and the system evolves from strong ordered steady state to low chaos state. The strain-stress system before compressive strength peak is basically in weak chaotic state. Theis proposed to be the stability criterion of concrete features in different stress stages, and the is regarded as the representative value of the system stability degree. The calculation of example shows that the stability criterion definited by the proposed method is consistent with the actural situation.

Lyapunov-based Small Signal Analysis for Power Systems of Russia

A new mathematical general approach has been suggested to carry out small signals analysis of power systems by computing gramians spectral expansion in time and frequency domains. The gramians expansions are bilinear and quadratic forms for sequences of Faddeev matrices, generated by resolvents of the original matrices in the Lyapunov equation. A new tool for assessment of power system stability degree in small signals has been suggested. It is shown, that Frobenius norm of the system gramian may be considered as an index of the power system vicinity to stability boundary in small signals.

Research on Lyapunov Exponent of Chaos Feature in Different Stress Stage of Concrete Joint System

: According to the research on whole curves of strain-stress of concrete materials, the paper illustrates in evidence features of stages and shows that the discrete feature of curve often occurs in strain-softening stage. After chaotic dynamic analysis of testing datas, it presents that system of whole process of strain-stress evolves from ordered steady state to low chaotic state and then to high chaotic state along with increase of compressive strength. The linear relationship of strain- stress grows evident and the system evolves from strong ordered steady state to low chaos state. The strain-stress system before compressive strength peak is basically in weak chaotic state. The is proposed to be the stability criterion of concrete features in different stress stages, and the is regarded as the representative value of the system stability degree. The calculation of example shows that the stability criterion definited by the proposed method is consistent with the actural situation.

Analysis and Design of Machine Tool Chatter Control Systems Using the Regeneration Spectrum

This paper introduces a new concept in the analysis and design of machine tool chatter control systems, the regeneration spectrum. This development follows from a recognition of the fact that the stability analysis of time delayed systems such as machining systems is considerably simplified for large values of the time delay. The regeneration spectrum is a function of frequency whose definition is based on the system characteristic equation. Features of the distribution of the system characteristic roots in the s-plane are related quantitatively to the regeneration spectrum. Moreover, a quantitative measure of the degree of system stability is provided by the closeness of the regeneration spectrum peak to unity. Minimization of the regeneration spectrum peak is therefore the basis for determining controller parameters. The application of the regeneration spectrum to prior chatter control systems is illustrated. The use of the regeneration spectrum enables the formulation of the controller design problem as a multi-parameter optimization problem. Experimental work was performed to demonstrate the efficacy of this design methodology.