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Context. Creating guaranteed competitive motion control systems for complex multidimensional moving objects, including un- stable ones, that operate under random controlled and uncontrolled disturbing factors, with minimal design costs, is one of the main requirements for achieving success in this class devices market. Additionally, to meet modern demands for the accuracy of motion control processes along a specified or programmed trajectory, it is essential to synthesize an optimal control system based on experimental data obtained under conditions closely approximating the real operating mode of the test object. Objective. The research presented in this article aims to synthesize an optimal tracking control system for the Stewart platform’s working surface motion, taking into account its multidimensional dynamic model. Method. The article employs a method of a multidimensional tracking control system structural transformation into an equivalent stabilization system for the motion of a multidimensional control object. It also utilizes an algorithm for synthesizing optimal stabilization systems for dynamic objects, whether stable or not, under stationary random external disturbances. The justified algorithm for synthesizing optimal stochastic stabilization systems is constructed using operations such as addition and multiplication of polynomial and fractional-rational matrices, Wiener factorization, Wiener separation of fractional-rational matrices, and the calculation of dispersion integrals. Results. As a result of the conducted research, the problem of defining the concept of analytical design for a Stewart platform’s optimal motion control system has been formalized. The results include the derived transformation equations from the tracking control system to the equivalent stabilization system of the Stewart platform’s working surface motion. Furthermore, the structure and parameters of the main controller transfer function matrix for of this control system have been determined. Conclusions. The justified use of the analytical design concept for the Stewart platform’s working surface optimal motion control system formalizes and significantly simplifies the solution to the problem of synthesizing complex dynamic systems, applying the developed technology presented in [1]. The obtained structure and parameters of the Stewart platform’s working surface motion control system main controller, which is divided into three components W1, W2, and W3, improve the tracking quality of the program signal vector, account for the cross-connections within the Stewart platform, and increase the accuracy of executing the specified trajectory by increasing the degrees of freedom in choosing the controller structure. [ABSTRACT FROM AUTHOR]

At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion. Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification. Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals. Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models. Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences. [ABSTRACT FROM AUTHOR]

Context. The article is devoted to overcoming the contradictions between the assumptions adopted in known methods of closedloop control system identification and the design and conditions of its operation. The article presents a new method of identifying the transfer functions matrix of a two-level closed-loop control system element, which functions under the conditions of multidimensional stationary centered random influences. Objective. The purpose of the study, the results of which are presented in this paper, is to extend the indirect identification method to the case of estimating one of the two-level closed-loop control system elements, dynamics model based on passive experiment data. Method. To solve the optimal identification problem, a variational method for minimizing the quality functional on the class of fractional-rational transfer function matrices was used. Results. As a result of the research, the identification problem formulation was formalized, the rules for obtaining experimental information about the input and output signals were determined, the rules for identifying the transfer functions matrix of a two-level closed-loop control system element, which minimizes the sum of the variances of identification errors in the frequency domain, and the verification of these rules was carried out. Conclusions. Justified rules allow to correctly determine transfer functions matrices of the closed-loop systems selected element when fulfilling the defined list of conditions. The closed-loop systems control paths signals analysis proves the possibility of the effect of changing these signals statistical means, even under conditions of only centered stationary input influences actions on the system. Based on this, the further development of research can be aimed at overcoming such effects. [ABSTRACT FROM AUTHOR]

Zeros of rational transfer function matrices R(λ) are the eigenvalues of associated polynomial system matrices P(λ) under minimality conditions. In this paper, we define a structured condition number for a simple eigenvalue λ0 of a (locally) minimal polynomial system matrix P(λ), which in turn is a simple zero λ0 of its transfer function matrix R(λ). Since any rational matrix can be written as the transfer function of a polynomial system matrix, our analysis yields a structured perturbation theory for simple zeros of rational matrices R(λ). To capture all the zeros of R(λ), regardless of whether they are poles, we consider the notion of root vectors. As corollaries of the main results, we pay particular attention to the special case of λ 0 being not a pole of R(λ) since in this case the results get simpler and can be useful in practice. We also compare our structured condition number with Tisseur's unstructured condition number for eigenvalues of matrix polynomials and show that the latter can be unboundedly larger. Finally, we corroborate our analysis by numerical experiments. [ABSTRACT FROM AUTHOR]

Heating, Ventilation and Air Conditioning (HVAC) is a multivariable process where any alteration with one system input affects most or all of the system's outputs simultaneously. Owing to its comprehensiveness, a readily derived multivariable HVAC mathematical model is selected for this work, mainly a hybrid distributed-lumped parameters model. As the transfer function matrix was not established in the selected HVAC model, it was exclusively developed in this study, using the time domain graphical responses of the chosen model. Based on the developed transfer function matrix, a conceptual two-step approach was followed to control HVAC model performance. The first was decoupling the interactions that affect all the system outputs, and the second was designing proper PID controllers for each decoupled loop similar to those used for single input single output (SISO) systems. A direct Nyquist Array (DNA) multivariable control strategy was used for this purpose and successfully decoupled the HVAC system into three separate (SISO) loops. Three PID controllers afterwards were applied for each decoupled loop. The results showed quite decoupled system outputs with a minor coupling percentage so that any change in a system input only affected the corresponding system output. The output responses are also underdamped with almost zero steady-state error confirming the effectiveness of the selected PID parameters. The values of steady-state responses are obtained in (10-15) s compared with (200-600) s of open-loop response time. However, various overshoot percentages in the responses are encountered but are relatively small, with a short settling time, so they don't affect the thermal comfort of the ventilated volume. System stability using the Nyquist criterion has also been examined and found to satisfy the criterion. The multivariable DNA control technique and the SISO closed-loop PID controllers have shown the capability to suppress external disturbances and restore the system to its original functional steady-state values. [ABSTRACT FROM AUTHOR]

Generalized independent coordinates are typically utilized within an analytical dynamics framework to model the motion of structural and mechanical engineering systems. Nevertheless, for complex systems, such as multi-body structures, an explicit formulation of the equations of motion by utilizing generalized, independent, coordinates can be a daunting task. In this regard, employing a set of redundant coordinates can facilitate the formulation of the governing dynamics equations. In this setting, however, standard response analysis techniques cannot be applied in a straightforward manner. For instance, defining and determining a transfer function within a frequency domain response analysis framework is challenging due to the presence of singular matrices, and thus, the machinery of generalized matrix inverses needs to be employed. An efficient frequency domain response analysis methodology for structural dynamical systems modeled via dependent coordinates is developed herein. This is done by resorting to the Moore–Penrose generalized matrix inverse in conjunction with a recently proposed extended modal analysis treatment. It is shown that not only the formulation is efficient in drastically reducing the computational cost when compared to a straightforward numerical evaluation of the involved generalized inverses, but also facilitates the derivation and implementation of the celebrated random vibration input–output frequency domain relationship between the excitation and the response power spectrum matrices. The validity of the methodology is demonstrated by considering a multi-degree-of-freedom shear type structure and a multi-body structural system as numerical examples. [ABSTRACT FROM AUTHOR]

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Lead-cooled Fast Reactor (LFR) with natural circulation in primary system is among the highlights in advance nuclear reactor research, due to its great superiority in reactor safety and reliability. In this work, a transfer function matrix describing coolant temperature dynamic process, obtained by Laplace transform of the one-dimensional system dynamic model is developed in order to investigate the temperature control characteristics of LFR. Based on the transfer function matrix, a close-loop coolant temperature control system without compensator is built. The frequency domain analysis indicates that the stability and steady-state of the temperature control system needs to be improved. Accordingly, a temperature compensator based on Proportion–Integration and feed-forward is designed. The dynamic simulation of the whole system with the temperature compensator for core power step change is performed with SIMULINK and RELAP5-HD. The result shows that the temperature compensator can provide superior coolant temperature control capabilities in LFR with natural circulation due to the efficiency of the frequency domain analysis method. [ABSTRACT FROM AUTHOR]

Super-resolution imaging (SRI) for mid-wave infrared (MWIR) has attracted increasing attention in recent years due to the expensive price for a large number of pixels MWIR cameras. Investigation of the compressed sensing method can partially improves the resolution. However, the quality of SRI is highly related to the transfer function matrix of the optical system, which is difficult to be accurately measured because of the noise existed in MWIR detection, especially in long-distance systems. In this work, we propose a transfer function matrix calculation method which overcomes the issues of low imaging contrast and signal-to-noise ratio compared with previous studies. And we further establish a long-distance focal plane array-based compressive imaging system with a resolution of two digital micro-mirror device pixels which just satisfies the system diffraction limit. In addition, we achieve the 4 × 4 times super-resolution high-quality reconstruction of long-distance digital and physical objects with only six measurements. • Establish a long-distance mid-wave infrared imaging system with high resolution. • Calculate the transfer function matrix for 256 × 256 pixels with 100 random masks. • Realize 4x4 times super-resolution reconstruction of digital or physical objects. • Enhance the peak signal-to-noise ratio of 50% with only 6 measurements. • Achieve the resolution of 2 pixels which fully utilizes the modulation resolution. [ABSTRACT FROM AUTHOR]

This paper presents an extended adjoint decoupling method to conduct the digital decoupling controller design for the continuous-time transfer function matrices with multiple (integer/fractional) time delays in both the denominator and the numerator matrix. First, based on the sampled unit-step response data of the afore-mentioned multiple time-delay system, the conventional balanced model-reduction method is utilised to construct an approximated discrete-time model of the original (known/unknown) multiple time-delay continuous-time transfer function matrix. Then, a digital decoupling controller is designed by utilising the extended adjoint decoupling method together with the conventional discrete-time root-locus method. An illustrative example is given to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM PUBLISHER]

This paper presents a thermoacoustic model in the frequency domain for multi-burner combustors composed of multiple plenum-nozzle-chamber modules with cross-talk at both plenums and chambers. The thermoacoustic model is given as a multi-input-multi-output transfer function matrix from heat fluctuation input vector to velocity fluctuation output vector. The discrete rotational symmetry of a multi-burner combustor is exploited to obtain a simple, diagonal transfer function matrix. The resonance equation, whose roots are resonances, is given as a set of scalar equations. The explicit form of the resonance equation reveals how combustor and operating parameters influence the resonances, and which parameters are significant for the longitudinal-azimuthal coupling and the plenum-chamber coupling. The diagonalization also allows us to show constructively that every mode shape is a Bloch wave and those mode shapes can characterize all resonances in terms of longitudinal and azimuthal mode numbers. At a low frequency, the resonance equation can be approximated as biquadratic and quadratic equations for a typical combustor geometry and operating conditions. A bunch of low-frequency resonances, peculiar to multi-burner combustors with cross-talk, are interpreted as azimuthal Helmholtz modes in which plenums/chambers and cross-talk ducts serve as the cavities and necks, respectively. Our combustor model is combined with a diagonal flame transfer function matrix for combustion instability analysis and we develop a set of scalar stability equations whose roots determine combustion instability. This stability equation reveals how combustion instability depends on the combustor geometry and operating parameters. Several numerical examples are presented to validate our thermoacoustic model and theoretical findings. • Acoustically, a multi-burner combustor is a collection of multiple single-burner combustors with cross-talks. • Thermoacoustics of a multi-burner combustor is a multi-input-multi-output transfer function matrix. • Cross-talk gives rise to resonance clusters whose spread is prominent at low frequency. • Low-frequency resonances are Helmholtz modes where cross-talk ducts and nozzle serve as necks. • A chunky cross-talk duct gives a strong cross-talk effect at low frequency. [ABSTRACT FROM AUTHOR]

• Simplified analytical model for the design of shape memory alloy dampers. • Optimal damper allocation algorithm for the seismic upgrade of inelastic structures. • Iterative approach for determining the transfer function matrix of nonlinear systems. The purpose of this paper is to present a simplified nonlinear equations-model that is intended to design shape memory alloy (SMA) dampers in three-dimensional structures of unsymmetrical-plan and in yielding shear-frames. The equations-model is based on a schematic idealization of the SMA damper's hysteretic behavior and the structure's transient tangent stiffness matrix, which corresponds to yielding shear-frames, and is commensurate with structural design methodologies. As of today, there are very few seismic design methodologies that use SMA dampers. In this paper, the analytical equations-model is implemented in a seismic retrofit search algorithm modified for SMA dampers. The algorithm sequentially places the SMA dampers at the story with the maximum interstory drift gain magnitude, calculated using the transfer function matrix between the ground acceleration components and the frames' interstory drifts. The transfer function matrix stems from a linear state-space formulation, but the tangent stiffness matrix is nonlinear. In order to cater to this issue, a new iterative approach suggests updating the tangent stiffness matrix in accordance with the transfer function matrix's peak interstory drift magnitudes – until the tangent stiffness matrix converges. A numerical example shows that the iterative process takes no more than two iterations. [ABSTRACT FROM AUTHOR]

• A double-layer shaking table (DLST) is proposed to reproduce wide band-frequency acceleration with a large displacement. • An offline iterative control method based on frequency-splitting is proposed to achieve acceleration control of DLST. • The proposed method can reproduce target signals for nonlinear structure very well in experimental verification. Large shaking tables with payload capacities exceeding 1000 t can be used to realistically evaluate the seismic performance of engineering structures. The working frequency of large shaking tables is typically limited to 0–30 Hz. This range is not sufficient for testing rigid engineering structures, such as dams and nuclear facilities, because these scaled structures usually have high fundamental frequencies. A new configuration has been proposed, in which a high-frequency shaking table is mounted atop a low-frequency shaking table. Referred to as a double-layer shaking table (DLST), the lower shaking table has a long stoke to reproduce large displacements and velocities in a low-frequency range, and the upper shaking table has a short stroke to reproduce high-frequency accelerations. With this configuration, the large payload capacity of the lower shaking table can be utilized while also achieving a high-frequency excitation. The control of such a complex system, however, is challenging because of strong interactions between the two tables. This paper proposes an offline iterative control method based on frequency-splitting to drive the two tables simultaneously. An input signal with a wide frequency spectrum is first split into two signals, i.e., one containing the low-frequency components and the other containing the high-frequency components. Successfully applying this control technique requires development of the transfer function matrix of the interacting tables by system identification. Numeric simulations and experiments demonstrate that this method can effectively drive a DLST to reproduce a target signal with a wide frequency range. [ABSTRACT FROM AUTHOR]

This paper presents a low-order thermoacoustic model for multi-burner combustors and proposes a control theoretic approach to linear combustion instability analysis in frequency domain, taking acoustic and flame interaction effects among burners into account under a non-zero mean flow condition. Our thermoacoustic model can deal with can-annular and annular combustors in a unified way and is given as a multi-input multi-output transfer function matrix from heat fluctuation input vector to velocity fluctuation output vector. We also propose a flame transfer function matrix description where off-diagonal components describe the effects of a local acoustic field of one burner location on the flame response at another burner location. The discrete rotational symmetry of burner arrangement in a combustor makes it possible to diagonalize both the aforementioned thermoacoustic and flame transfer function matrices analytically from a spatial discrete-time Fourier transformation. The decoupled thermoacoustic transfer function matrix provides a characterization of acoustic resonances, particularly the longitudinal-azimuthal coupled modes unique to multi-burner combustors. In addition, from the Bloch wave interpretation, we find general patterns in the mode shape of a multi-burner combustor and its relations to the mode shape of a single-burner combustor. Furthermore, from a diagonalized closed loop transfer function matrix, a simple combustion instability condition for a multi-burner combustor is developed. This stability condition shows how a single-burner combustor and a multi-burner combustor are different quantitatively, when it comes to combustion instability. Numerical examples are presented to validate our thermoacoustic model against three-dimensional FEM results, and to illustrate our developments and findings. [ABSTRACT FROM AUTHOR]

• Transfer function matrix from mechanical disturbances to mechanical powers is found to be, inherently, diagonally dominant. • Power spectral density of responses of non-source generators is predictable with generator terminal voltage. • Large mismatch between predicted and measured spectral density indicates the presence of oscillation source. • The method is able to locate oscillation sources to control devices. The location of the control devices that produce forced oscillation sources is crucial to the elimination of forced oscillations. This paper proposes two frequency domain approaches to reliably locate oscillation sources from mechanical parts and excitation systems of generators to their control devices. Firstly, the transfer function matrix from mechanical disturbances to mechanical powers is demonstrated to be inherently diagonally dominant. The property is used to monitor and preliminarily locate oscillation sources from mechanical parts. Moreover, this paper proposes a systematic method of power spectral density prediction to further locate oscillation source to control device by using the generator terminal voltage (or generator current) to predict the power spectral density of generator responses. It is shown that for non-source generators, the responses are determined by the generator terminal voltage. The generator with distinct mismatch between predicted and measured power spectral density is identified as the oscillation source. The mismatches between predicted and measured power spectral density of different responses are different, further enabling the method to identify the control device producing the oscillation source. The method of power spectral density prediction is used as a general method to provide further and detailed location results. Demonstrative examples of a 39-bus system and the 547-machine 8647-bus North China Power Grid show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

• A generic small-signal model for Hybrid-MTDC systems with flexible adaptability for different operation modes. • A time-frequency-domain quantitative analysis method for Hybrid-MTDC systems utilizing the transfer function matrix. • Investigate the feasible regions and dynamic performance of a 3-termial Hybrid HVDC system. To achieve better controller performance, the impact of control parameters on the stability and dynamic performance is essential to be clarified mathematically for hybrid multi-terminal HVDC (Hybrid-MTDC) systems considering different operation modes (OMs). In this paper, a generic small-signal model (SSM) is established, which can be modified flexibly for different OMs. Then the SSM can be converted into a transfer function matrix (TF-Matrix), which avoids deriving the transfer function separately for each controller of the system, and greatly improves the work efficiency. By inputting a step into the TF-Matrix, the time-domain mathematical model for the all system state variables can be obtained, and it is more efficient than iterative solutions of high-order differential equations. To this end, a quantitative control parameter analysis method based on a TF-Matrix is proposed. Utilizing the proposed method, a typical Hybrid-MTDC system is investigated, and the results demonstrate the practicality and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]